id	sid	tid	token	lemma	pos
bracis-19038	1	1	a	a	DET
bracis-19038	1	2	systematic	systematic	ADJ
bracis-19038	1	3	approach	approach	NOUN
bracis-19038	1	4	to	to	PART
bracis-19038	1	5	define	define	VERB
bracis-19038	1	6	semantics	semantic	NOUN
bracis-19038	1	7	for	for	ADP
bracis-19038	1	8	prioritised	prioritise	VERB
bracis-19038	1	9	logic	logic	NOUN
bracis-19038	1	10	programs	program	NOUN
bracis-19038	1	11	|	|	ADV
bracis-19038	1	12	springer	springer	NOUN
bracis-19038	1	13	nature	nature	PROPN
bracis-19038	1	14	link	link	PROPN
bracis-19038	1	15	(	(	PUNCT
bracis-19038	1	16	formerly	formerly	ADV
bracis-19038	1	17	springerlink	springerlink	NOUN
bracis-19038	1	18	)	)	PUNCT
bracis-19038	1	19	skip	skip	VERB
bracis-19038	1	20	to	to	ADP
bracis-19038	1	21	main	main	ADJ
bracis-19038	1	22	content	content	NOUN
bracis-19038	1	23	advertisement	advertisement	NOUN
bracis-19038	1	24	log	log	NOUN
bracis-19038	1	25	in	in	ADP
bracis-19038	1	26	menu	menu	NOUN
bracis-19038	1	27	find	find	VERB
bracis-19038	1	28	a	a	DET
bracis-19038	1	29	journal	journal	NOUN
bracis-19038	1	30	publish	publish	VERB
bracis-19038	1	31	with	with	ADP
bracis-19038	1	32	us	we	PRON
bracis-19038	1	33	track	track	VERB
bracis-19038	1	34	your	your	PRON
bracis-19038	1	35	research	research	NOUN
bracis-19038	1	36	search	search	NOUN
bracis-19038	1	37	cart	cart	NOUN
bracis-19038	1	38	home	home	NOUN
bracis-19038	1	39	intelligent	intelligent	ADJ
bracis-19038	1	40	systems	system	NOUN
bracis-19038	1	41	conference	conference	NOUN
bracis-19038	1	42	paper	paper	NOUN
bracis-19038	1	43	a	a	DET
bracis-19038	1	44	systematic	systematic	ADJ
bracis-19038	1	45	approach	approach	NOUN
bracis-19038	1	46	to	to	PART
bracis-19038	1	47	define	define	VERB
bracis-19038	1	48	semantics	semantic	NOUN
bracis-19038	1	49	for	for	ADP
bracis-19038	1	50	prioritised	prioritised	ADJ
bracis-19038	1	51	logic	logic	NOUN
bracis-19038	1	52	programs	program	NOUN
bracis-19038	1	53	conference	conference	NOUN
bracis-19038	1	54	paper	paper	NOUN
bracis-19038	1	55	first	first	ADV
bracis-19038	1	56	online	online	ADV
bracis-19038	1	57	:	:	PUNCT
bracis-19038	1	58	28	28	NUM
bracis-19038	1	59	november	november	NOUN
bracis-19038	1	60	2021	2021	NUM
bracis-19038	1	61	pp	pp	ADP
bracis-19038	1	62	297–312	297–312	NUM
bracis-19038	1	63	cite	cite	VERB
bracis-19038	1	64	this	this	DET
bracis-19038	1	65	conference	conference	NOUN
bracis-19038	1	66	paper	paper	NOUN
bracis-19038	1	67	access	access	NOUN
bracis-19038	1	68	provided	provide	VERB
bracis-19038	1	69	by	by	ADP
bracis-19038	1	70	university	university	PROPN
bracis-19038	1	71	of	of	ADP
bracis-19038	1	72	notre	notre	PROPN
bracis-19038	1	73	dame	dame	PROPN
bracis-19038	1	74	hesburgh	hesburgh	PROPN
bracis-19038	1	75	library	library	PROPN
bracis-19038	1	76	download	download	PROPN
bracis-19038	1	77	book	book	NOUN
bracis-19038	1	78	pdf	pdf	PROPN
bracis-19038	1	79	download	download	NOUN
bracis-19038	1	80	book	book	NOUN
bracis-19038	1	81	epub	epub	PROPN
bracis-19038	1	82	intelligent	intelligent	ADJ
bracis-19038	1	83	systems	system	NOUN
bracis-19038	1	84	(	(	PUNCT
bracis-19038	1	85	bracis	bracis	NOUN
bracis-19038	1	86	2021	2021	NUM
bracis-19038	1	87	)	)	PUNCT
bracis-19038	1	88	a	a	DET
bracis-19038	1	89	systematic	systematic	ADJ
bracis-19038	1	90	approach	approach	NOUN
bracis-19038	1	91	to	to	PART
bracis-19038	1	92	define	define	VERB
bracis-19038	1	93	semantics	semantic	NOUN
bracis-19038	1	94	for	for	ADP
bracis-19038	1	95	prioritised	prioritised	ADJ
bracis-19038	1	96	logic	logic	NOUN
bracis-19038	1	97	programs	program	NOUN
bracis-19038	1	98	download	download	VERB
bracis-19038	1	99	book	book	NOUN
bracis-19038	1	100	pdf	pdf	PROPN
bracis-19038	1	101	download	download	NOUN
bracis-19038	1	102	book	book	PROPN
bracis-19038	1	103	epub	epub	PROPN
bracis-19038	1	104	renan	renan	PROPN
bracis-19038	1	105	cordeiro10	cordeiro10	PROPN
bracis-19038	1	106	,	,	PUNCT
bracis-19038	1	107	guilherme	guilherme	PROPN
bracis-19038	1	108	fernandes10	fernandes10	PROPN
bracis-19038	1	109	,	,	PUNCT
bracis-19038	1	110	joão	joão	PROPN
bracis-19038	1	111	alcântara10	alcântara10	PROPN
bracis-19038	1	112	&	&	CCONJ
bracis-19038	1	113	…	…	PUNCT
bracis-19038	1	114	henrique	henrique	PROPN
bracis-19038	1	115	viana11	viana11	PROPN
bracis-19038	1	116	  	  	SPACE
bracis-19038	1	117	show	show	VERB
bracis-19038	1	118	authors	author	NOUN
bracis-19038	1	119	part	part	NOUN
bracis-19038	1	120	of	of	ADP
bracis-19038	1	121	the	the	DET
bracis-19038	1	122	book	book	NOUN
bracis-19038	1	123	series	series	NOUN
bracis-19038	1	124	:	:	PUNCT
bracis-19038	1	125	lecture	lecture	NOUN
bracis-19038	1	126	notes	note	NOUN
bracis-19038	1	127	in	in	ADP
bracis-19038	1	128	computer	computer	NOUN
bracis-19038	1	129	science	science	NOUN
bracis-19038	1	130	(	(	PUNCT
bracis-19038	1	131	(	(	PUNCT
bracis-19038	1	132	lnai	lnai	ADJ
bracis-19038	1	133	,	,	PUNCT
bracis-19038	1	134	volume	volume	NOUN
bracis-19038	1	135	13073	13073	NUM
bracis-19038	1	136	)	)	PUNCT
bracis-19038	1	137	)	)	PUNCT
bracis-19038	1	138	included	include	VERB
bracis-19038	1	139	in	in	ADP
bracis-19038	1	140	the	the	DET
bracis-19038	1	141	following	follow	VERB
bracis-19038	1	142	conference	conference	NOUN
bracis-19038	1	143	series	series	NOUN
bracis-19038	1	144	:	:	PUNCT
bracis-19038	1	145	brazilian	brazilian	ADJ
bracis-19038	1	146	conference	conference	NOUN
bracis-19038	1	147	on	on	ADP
bracis-19038	1	148	intelligent	intelligent	ADJ
bracis-19038	1	149	systems	system	NOUN
bracis-19038	1	150	737	737	NUM
bracis-19038	1	151	accesses	access	NOUN
bracis-19038	1	152	abstract	abstract	ADV
bracis-19038	1	153	we	we	PRON
bracis-19038	1	154	propose	propose	VERB
bracis-19038	1	155	in	in	ADP
bracis-19038	1	156	this	this	DET
bracis-19038	1	157	paper	paper	NOUN
bracis-19038	1	158	a	a	DET
bracis-19038	1	159	framework	framework	NOUN
bracis-19038	1	160	of	of	ADP
bracis-19038	1	161	prioritised	prioritise	VERB
bracis-19038	1	162	logic	logic	NOUN
bracis-19038	1	163	programs	program	NOUN
bracis-19038	1	164	(	(	PUNCT
bracis-19038	1	165	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	1	166	)	)	PUNCT
bracis-19038	1	167	)	)	PUNCT
bracis-19038	1	168	to	to	PART
bracis-19038	1	169	represent	represent	VERB
bracis-19038	1	170	priority	priority	NOUN
bracis-19038	1	171	information	information	NOUN
bracis-19038	1	172	explicitly	explicitly	ADV
bracis-19038	1	173	in	in	ADP
bracis-19038	1	174	a	a	DET
bracis-19038	1	175	program	program	NOUN
bracis-19038	1	176	.	.	PUNCT
bracis-19038	2	1	differently	differently	ADV
bracis-19038	2	2	of	of	ADP
bracis-19038	2	3	others	other	NOUN
bracis-19038	2	4	approaches	approach	NOUN
bracis-19038	2	5	,	,	PUNCT
bracis-19038	2	6	we	we	PRON
bracis-19038	2	7	do	do	AUX
bracis-19038	2	8	not	not	PART
bracis-19038	2	9	restrain	restrain	VERB
bracis-19038	2	10	the	the	DET
bracis-19038	2	11	preference	preference	NOUN
bracis-19038	2	12	relation	relation	NOUN
bracis-19038	2	13	only	only	ADV
bracis-19038	2	14	to	to	ADP
bracis-19038	2	15	literals	literal	NOUN
bracis-19038	2	16	,	,	PUNCT
bracis-19038	2	17	but	but	CCONJ
bracis-19038	2	18	to	to	ADP
bracis-19038	2	19	sets	set	NOUN
bracis-19038	2	20	of	of	ADP
bracis-19038	2	21	literals	literal	NOUN
bracis-19038	2	22	.	.	PUNCT
bracis-19038	3	1	as	as	ADP
bracis-19038	3	2	consequence	consequence	NOUN
bracis-19038	3	3	,	,	PUNCT
bracis-19038	3	4	we	we	PRON
bracis-19038	3	5	can	can	AUX
bracis-19038	3	6	express	express	VERB
bracis-19038	3	7	in	in	ADP
bracis-19038	3	8	\(\textit{plp}\)s	\(\textit{plp}\)s	ADJ
bracis-19038	3	9	sophisticated	sophisticated	ADJ
bracis-19038	3	10	forms	form	NOUN
bracis-19038	3	11	of	of	ADP
bracis-19038	3	12	preferences	preference	NOUN
bracis-19038	3	13	without	without	ADP
bracis-19038	3	14	changing	change	VERB
bracis-19038	3	15	the	the	DET
bracis-19038	3	16	programs	program	NOUN
bracis-19038	3	17	or	or	CCONJ
bracis-19038	3	18	introducing	introduce	VERB
bracis-19038	3	19	new	new	ADJ
bracis-19038	3	20	atoms	atom	NOUN
bracis-19038	3	21	to	to	PART
bracis-19038	3	22	obtain	obtain	VERB
bracis-19038	3	23	artificially	artificially	ADV
bracis-19038	3	24	the	the	DET
bracis-19038	3	25	intended	intend	VERB
bracis-19038	3	26	preferences	preference	NOUN
bracis-19038	3	27	.	.	PUNCT
bracis-19038	4	1	besides	besides	ADV
bracis-19038	4	2	,	,	PUNCT
bracis-19038	4	3	inspired	inspire	VERB
bracis-19038	4	4	on	on	ADP
bracis-19038	4	5	various	various	ADJ
bracis-19038	4	6	developments	development	NOUN
bracis-19038	4	7	in	in	ADP
bracis-19038	4	8	the	the	DET
bracis-19038	4	9	literature	literature	NOUN
bracis-19038	4	10	on	on	ADP
bracis-19038	4	11	preference	preference	NOUN
bracis-19038	4	12	,	,	PUNCT
bracis-19038	4	13	we	we	PRON
bracis-19038	4	14	present	present	VERB
bracis-19038	4	15	a	a	DET
bracis-19038	4	16	comprehensive	comprehensive	ADJ
bracis-19038	4	17	and	and	CCONJ
bracis-19038	4	18	systematic	systematic	ADJ
bracis-19038	4	19	treatment	treatment	NOUN
bracis-19038	4	20	to	to	PART
bracis-19038	4	21	deal	deal	VERB
bracis-19038	4	22	with	with	ADP
bracis-19038	4	23	preferences	preference	NOUN
bracis-19038	4	24	in	in	ADP
bracis-19038	4	25	logic	logic	NOUN
bracis-19038	4	26	programming	programming	NOUN
bracis-19038	4	27	.	.	PUNCT
bracis-19038	5	1	in	in	ADP
bracis-19038	5	2	fact	fact	NOUN
bracis-19038	5	3	,	,	PUNCT
bracis-19038	5	4	we	we	PRON
bracis-19038	5	5	introduced	introduce	VERB
bracis-19038	5	6	32	32	NUM
bracis-19038	5	7	different	different	ADJ
bracis-19038	5	8	criteria	criterion	NOUN
bracis-19038	5	9	(	(	PUNCT
bracis-19038	5	10	semantics	semantic	NOUN
bracis-19038	5	11	)	)	PUNCT
bracis-19038	5	12	to	to	PART
bracis-19038	5	13	establish	establish	VERB
bracis-19038	5	14	preference	preference	NOUN
bracis-19038	5	15	between	between	ADP
bracis-19038	5	16	partial	partial	ADJ
bracis-19038	5	17	stable	stable	ADJ
bracis-19038	5	18	models	model	NOUN
bracis-19038	5	19	as	as	ADV
bracis-19038	5	20	well	well	ADV
bracis-19038	5	21	as	as	ADP
bracis-19038	5	22	those	those	DET
bracis-19038	5	23	semantics	semantic	NOUN
bracis-19038	5	24	whose	whose	DET
bracis-19038	5	25	definition	definition	NOUN
bracis-19038	5	26	depends	depend	VERB
bracis-19038	5	27	on	on	ADP
bracis-19038	5	28	partial	partial	ADJ
bracis-19038	5	29	stable	stable	ADJ
bracis-19038	5	30	models	model	NOUN
bracis-19038	5	31	.	.	PUNCT
bracis-19038	6	1	we	we	PRON
bracis-19038	6	2	show	show	VERB
bracis-19038	6	3	some	some	DET
bracis-19038	6	4	properties	property	NOUN
bracis-19038	6	5	of	of	ADP
bracis-19038	6	6	our	our	PRON
bracis-19038	6	7	framework	framework	NOUN
bracis-19038	6	8	;	;	PUNCT
bracis-19038	6	9	in	in	ADP
bracis-19038	6	10	particular	particular	ADJ
bracis-19038	6	11	,	,	PUNCT
bracis-19038	6	12	we	we	PRON
bracis-19038	6	13	guarantee	guarantee	VERB
bracis-19038	6	14	these	these	DET
bracis-19038	6	15	semantics	semantic	NOUN
bracis-19038	6	16	for	for	ADP
bracis-19038	6	17	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	6	18	)	)	PUNCT
bracis-19038	6	19	generalise	generalise	VERB
bracis-19038	6	20	their	their	PRON
bracis-19038	6	21	counterparts	counterpart	NOUN
bracis-19038	6	22	for	for	ADP
bracis-19038	6	23	logic	logic	NOUN
bracis-19038	6	24	programs	program	NOUN
bracis-19038	6	25	without	without	ADP
bracis-19038	6	26	preferences	preference	NOUN
bracis-19038	6	27	.	.	PUNCT
bracis-19038	7	1	access	access	NOUN
bracis-19038	7	2	provided	provide	VERB
bracis-19038	7	3	by	by	ADP
bracis-19038	7	4	university	university	PROPN
bracis-19038	7	5	of	of	ADP
bracis-19038	7	6	notre	notre	PROPN
bracis-19038	7	7	dame	dame	PROPN
bracis-19038	7	8	hesburgh	hesburgh	PROPN
bracis-19038	7	9	library	library	PROPN
bracis-19038	7	10	.	.	PUNCT
bracis-19038	8	1	download	download	PROPN
bracis-19038	8	2	conference	conference	NOUN
bracis-19038	8	3	paper	paper	NOUN
bracis-19038	8	4	pdf	pdf	NOUN
bracis-19038	8	5	similar	similar	ADJ
bracis-19038	8	6	content	content	NOUN
bracis-19038	8	7	being	be	AUX
bracis-19038	8	8	viewed	view	VERB
bracis-19038	8	9	by	by	ADP
bracis-19038	8	10	others	other	NOUN
bracis-19038	8	11	representing	represent	VERB
bracis-19038	8	12	morality	morality	NOUN
bracis-19038	8	13	in	in	ADP
bracis-19038	8	14	logic	logic	NOUN
bracis-19038	8	15	programming	programming	NOUN
bracis-19038	8	16	chapter	chapter	NOUN
bracis-19038	8	17	©	©	PROPN
bracis-19038	8	18	2016	2016	NUM
bracis-19038	8	19	a	a	DET
bracis-19038	8	20	language	language	NOUN
bracis-19038	8	21	-	-	PUNCT
bracis-19038	8	22	independent	independent	ADJ
bracis-19038	8	23	framework	framework	NOUN
bracis-19038	8	24	for	for	ADP
bracis-19038	8	25	reasoning	reason	VERB
bracis-19038	8	26	about	about	ADP
bracis-19038	8	27	preferences	preference	NOUN
bracis-19038	8	28	for	for	ADP
bracis-19038	8	29	declarative	declarative	ADJ
bracis-19038	8	30	problem	problem	NOUN
bracis-19038	8	31	solving	solve	VERB
bracis-19038	8	32	chapter	chapter	NOUN
bracis-19038	8	33	©	©	PROPN
bracis-19038	8	34	2019	2019	NUM
bracis-19038	8	35	probabilistic	probabilistic	ADJ
bracis-19038	8	36	hyperproperties	hyperpropertie	NOUN
bracis-19038	8	37	of	of	ADP
bracis-19038	8	38	markov	markov	NOUN
bracis-19038	8	39	decision	decision	NOUN
bracis-19038	8	40	processes	process	NOUN
bracis-19038	8	41	chapter	chapter	NOUN
bracis-19038	8	42	©	©	PROPN
bracis-19038	8	43	2020	2020	NUM
bracis-19038	8	44	explore	explore	VERB
bracis-19038	8	45	related	relate	VERB
bracis-19038	8	46	subjects	subject	NOUN
bracis-19038	8	47	discover	discover	VERB
bracis-19038	8	48	the	the	DET
bracis-19038	8	49	latest	late	ADJ
bracis-19038	8	50	articles	article	NOUN
bracis-19038	8	51	,	,	PUNCT
bracis-19038	8	52	books	book	NOUN
bracis-19038	8	53	and	and	CCONJ
bracis-19038	8	54	news	news	NOUN
bracis-19038	8	55	in	in	ADP
bracis-19038	8	56	related	related	ADJ
bracis-19038	8	57	subjects	subject	NOUN
bracis-19038	8	58	,	,	PUNCT
bracis-19038	8	59	suggested	suggest	VERB
bracis-19038	8	60	using	use	VERB
bracis-19038	8	61	machine	machine	NOUN
bracis-19038	8	62	learning	learning	NOUN
bracis-19038	8	63	.	.	PUNCT
bracis-19038	9	1	formal	formal	ADJ
bracis-19038	9	2	logic	logic	NOUN
bracis-19038	9	3	linear	linear	PROPN
bracis-19038	9	4	logic	logic	NOUN
bracis-19038	9	5	logic	logic	NOUN
bracis-19038	9	6	logic	logic	NOUN
bracis-19038	9	7	design	design	NOUN
bracis-19038	9	8	utilitarianism	utilitarianism	NOUN
bracis-19038	9	9	computer	computer	NOUN
bracis-19038	9	10	science	science	NOUN
bracis-19038	9	11	logic	logic	NOUN
bracis-19038	9	12	and	and	CCONJ
bracis-19038	9	13	foundations	foundation	NOUN
bracis-19038	9	14	of	of	ADP
bracis-19038	9	15	programming	programming	NOUN
bracis-19038	9	16	1	1	NUM
bracis-19038	9	17	introduction	introduction	NOUN
bracis-19038	9	18	in	in	ADP
bracis-19038	9	19	many	many	ADJ
bracis-19038	9	20	applications	application	NOUN
bracis-19038	9	21	of	of	ADP
bracis-19038	9	22	artificial	artificial	ADJ
bracis-19038	9	23	intelligence	intelligence	NOUN
bracis-19038	9	24	and	and	CCONJ
bracis-19038	9	25	commonsense	commonsense	ADJ
bracis-19038	9	26	reasoning	reasoning	NOUN
bracis-19038	9	27	,	,	PUNCT
bracis-19038	9	28	we	we	PRON
bracis-19038	9	29	have	have	VERB
bracis-19038	9	30	to	to	PART
bracis-19038	9	31	deal	deal	VERB
bracis-19038	9	32	with	with	ADP
bracis-19038	9	33	uncertain	uncertain	ADJ
bracis-19038	9	34	,	,	PUNCT
bracis-19038	9	35	vague	vague	ADJ
bracis-19038	9	36	,	,	PUNCT
bracis-19038	9	37	inaccurate	inaccurate	ADJ
bracis-19038	9	38	,	,	PUNCT
bracis-19038	9	39	doubtful	doubtful	ADJ
bracis-19038	9	40	and	and	CCONJ
bracis-19038	9	41	even	even	ADV
bracis-19038	9	42	contradictory	contradictory	ADJ
bracis-19038	9	43	information	information	NOUN
bracis-19038	9	44	as	as	ADV
bracis-19038	9	45	well	well	ADV
bracis-19038	9	46	as	as	ADP
bracis-19038	9	47	with	with	ADP
bracis-19038	9	48	certain	certain	ADJ
bracis-19038	9	49	,	,	PUNCT
bracis-19038	9	50	precise	precise	ADJ
bracis-19038	9	51	and	and	CCONJ
bracis-19038	9	52	reliable	reliable	ADJ
bracis-19038	9	53	information	information	NOUN
bracis-19038	9	54	.	.	PUNCT
bracis-19038	10	1	in	in	ADP
bracis-19038	10	2	this	this	DET
bracis-19038	10	3	scenario	scenario	NOUN
bracis-19038	10	4	,	,	PUNCT
bracis-19038	10	5	conflicts	conflict	NOUN
bracis-19038	10	6	can	can	AUX
bracis-19038	10	7	naturally	naturally	ADV
bracis-19038	10	8	arise	arise	VERB
bracis-19038	10	9	and	and	CCONJ
bracis-19038	10	10	,	,	PUNCT
bracis-19038	10	11	it	it	PRON
bracis-19038	10	12	urges	urge	VERB
bracis-19038	10	13	to	to	PART
bracis-19038	10	14	develop	develop	VERB
bracis-19038	10	15	mechanisms	mechanism	NOUN
bracis-19038	10	16	to	to	PART
bracis-19038	10	17	resolve	resolve	VERB
bracis-19038	10	18	them	they	PRON
bracis-19038	10	19	.	.	PUNCT
bracis-19038	11	1	adopting	adopt	VERB
bracis-19038	11	2	some	some	DET
bracis-19038	11	3	criteria	criterion	NOUN
bracis-19038	11	4	to	to	PART
bracis-19038	11	5	establish	establish	VERB
bracis-19038	11	6	preferences	preference	NOUN
bracis-19038	11	7	between	between	ADP
bracis-19038	11	8	these	these	DET
bracis-19038	11	9	conflicting	conflict	VERB
bracis-19038	11	10	information	information	NOUN
bracis-19038	11	11	is	be	AUX
bracis-19038	11	12	an	an	DET
bracis-19038	11	13	effective	effective	ADJ
bracis-19038	11	14	way	way	NOUN
bracis-19038	11	15	of	of	ADP
bracis-19038	11	16	reasoning	reasoning	NOUN
bracis-19038	11	17	with	with	ADP
bracis-19038	11	18	them	they	PRON
bracis-19038	11	19	.	.	PUNCT
bracis-19038	12	1	somehow	somehow	ADV
bracis-19038	12	2	we	we	PRON
bracis-19038	12	3	have	have	VERB
bracis-19038	12	4	to	to	PART
bracis-19038	12	5	prioritise	prioritise	VERB
bracis-19038	12	6	the	the	DET
bracis-19038	12	7	information	information	NOUN
bracis-19038	12	8	to	to	PART
bracis-19038	12	9	separate	separate	VERB
bracis-19038	12	10	the	the	DET
bracis-19038	12	11	wheat	wheat	NOUN
bracis-19038	12	12	from	from	ADP
bracis-19038	12	13	the	the	DET
bracis-19038	12	14	chaff	chaff	NOUN
bracis-19038	12	15	.	.	PUNCT
bracis-19038	13	1	for	for	ADP
bracis-19038	13	2	representing	represent	VERB
bracis-19038	13	3	and	and	CCONJ
bracis-19038	13	4	reasoning	reason	VERB
bracis-19038	13	5	with	with	ADP
bracis-19038	13	6	preferences	preference	NOUN
bracis-19038	13	7	,	,	PUNCT
bracis-19038	13	8	several	several	ADJ
bracis-19038	13	9	prioritised	prioritise	VERB
bracis-19038	13	10	systems	system	NOUN
bracis-19038	13	11	have	have	AUX
bracis-19038	13	12	been	be	AUX
bracis-19038	13	13	proposed	propose	VERB
bracis-19038	13	14	(	(	PUNCT
bracis-19038	13	15	see	see	VERB
bracis-19038	13	16	[	[	X
bracis-19038	13	17	1	1	X
bracis-19038	13	18	]	]	PUNCT
bracis-19038	13	19	for	for	ADP
bracis-19038	13	20	a	a	DET
bracis-19038	13	21	survey	survey	NOUN
bracis-19038	13	22	)	)	PUNCT
bracis-19038	13	23	.	.	PUNCT
bracis-19038	14	1	when	when	SCONJ
bracis-19038	14	2	moving	move	VERB
bracis-19038	14	3	our	our	PRON
bracis-19038	14	4	eyes	eye	NOUN
bracis-19038	14	5	to	to	ADP
bracis-19038	14	6	preferences	preference	NOUN
bracis-19038	14	7	in	in	ADP
bracis-19038	14	8	logic	logic	NOUN
bracis-19038	14	9	programming	programming	NOUN
bracis-19038	14	10	,	,	PUNCT
bracis-19038	14	11	we	we	PRON
bracis-19038	14	12	see	see	VERB
bracis-19038	14	13	a	a	DET
bracis-19038	14	14	plethora	plethora	NOUN
bracis-19038	14	15	of	of	ADP
bracis-19038	14	16	proposals	proposal	NOUN
bracis-19038	14	17	(	(	PUNCT
bracis-19038	14	18	see	see	VERB
bracis-19038	14	19	[	[	X
bracis-19038	14	20	2,3,4,5,6,7,8,9,10,11,12	2,3,4,5,6,7,8,9,10,11,12	NUM
bracis-19038	14	21	]	]	X
bracis-19038	14	22	for	for	ADP
bracis-19038	14	23	a	a	DET
bracis-19038	14	24	non	non	X
bracis-19038	14	25	exhaustive	exhaustive	ADJ
bracis-19038	14	26	list	list	NOUN
bracis-19038	14	27	)	)	PUNCT
bracis-19038	14	28	.	.	PUNCT
bracis-19038	15	1	as	as	SCONJ
bracis-19038	15	2	witnessed	witness	VERB
bracis-19038	15	3	by	by	ADP
bracis-19038	15	4	the	the	DET
bracis-19038	15	5	multitude	multitude	NOUN
bracis-19038	15	6	of	of	ADP
bracis-19038	15	7	formalisms	formalism	NOUN
bracis-19038	15	8	with	with	ADP
bracis-19038	15	9	preferences	preference	NOUN
bracis-19038	15	10	,	,	PUNCT
bracis-19038	15	11	a	a	DET
bracis-19038	15	12	key	key	ADJ
bracis-19038	15	13	issue	issue	NOUN
bracis-19038	15	14	here	here	ADV
bracis-19038	15	15	is	be	AUX
bracis-19038	15	16	the	the	DET
bracis-19038	15	17	lack	lack	NOUN
bracis-19038	15	18	of	of	ADP
bracis-19038	15	19	consensus	consensus	NOUN
bracis-19038	15	20	on	on	ADP
bracis-19038	15	21	the	the	DET
bracis-19038	15	22	role	role	NOUN
bracis-19038	15	23	played	play	VERB
bracis-19038	15	24	by	by	ADP
bracis-19038	15	25	preferences	preference	NOUN
bracis-19038	15	26	.	.	PUNCT
bracis-19038	16	1	roughly	roughly	ADV
bracis-19038	16	2	speaking	speak	VERB
bracis-19038	16	3	,	,	PUNCT
bracis-19038	16	4	we	we	PRON
bracis-19038	16	5	find	find	VERB
bracis-19038	16	6	in	in	ADP
bracis-19038	16	7	the	the	DET
bracis-19038	16	8	literature	literature	NOUN
bracis-19038	16	9	various	various	ADJ
bracis-19038	16	10	works	work	NOUN
bracis-19038	16	11	with	with	ADP
bracis-19038	16	12	diverging	diverging	ADJ
bracis-19038	16	13	intuitions	intuition	NOUN
bracis-19038	16	14	,	,	PUNCT
bracis-19038	16	15	and	and	CCONJ
bracis-19038	16	16	as	as	ADP
bracis-19038	16	17	a	a	DET
bracis-19038	16	18	consequence	consequence	NOUN
bracis-19038	16	19	,	,	PUNCT
bracis-19038	16	20	conceptually	conceptually	ADV
bracis-19038	16	21	different	different	ADJ
bracis-19038	16	22	formal	formal	ADJ
bracis-19038	16	23	techniques	technique	NOUN
bracis-19038	16	24	to	to	PART
bracis-19038	16	25	deal	deal	VERB
bracis-19038	16	26	with	with	ADP
bracis-19038	16	27	preference	preference	NOUN
bracis-19038	16	28	.	.	PUNCT
bracis-19038	17	1	while	while	SCONJ
bracis-19038	17	2	there	there	PRON
bracis-19038	17	3	are	be	VERB
bracis-19038	17	4	many	many	ADJ
bracis-19038	17	5	proposals	proposal	NOUN
bracis-19038	17	6	on	on	ADP
bracis-19038	17	7	preferences	preference	NOUN
bracis-19038	17	8	in	in	ADP
bracis-19038	17	9	the	the	DET
bracis-19038	17	10	reasoning	reasoning	NOUN
bracis-19038	17	11	process	process	NOUN
bracis-19038	17	12	and	and	CCONJ
bracis-19038	17	13	knowledge	knowledge	NOUN
bracis-19038	17	14	representation	representation	NOUN
bracis-19038	17	15	,	,	PUNCT
bracis-19038	17	16	there	there	PRON
bracis-19038	17	17	is	be	VERB
bracis-19038	17	18	still	still	ADV
bracis-19038	17	19	much	much	ADJ
bracis-19038	17	20	space	space	NOUN
bracis-19038	17	21	for	for	ADP
bracis-19038	17	22	improvement	improvement	NOUN
bracis-19038	17	23	.	.	PUNCT
bracis-19038	18	1	indeed	indeed	ADV
bracis-19038	18	2	,	,	PUNCT
bracis-19038	18	3	as	as	SCONJ
bracis-19038	18	4	noticed	notice	VERB
bracis-19038	18	5	in	in	ADP
bracis-19038	18	6	[	[	PUNCT
bracis-19038	18	7	13	13	NUM
bracis-19038	18	8	]	]	PUNCT
bracis-19038	18	9	,	,	PUNCT
bracis-19038	18	10	one	one	NUM
bracis-19038	18	11	of	of	ADP
bracis-19038	18	12	the	the	DET
bracis-19038	18	13	main	main	ADJ
bracis-19038	18	14	problems	problem	NOUN
bracis-19038	18	15	a	a	DET
bracis-19038	18	16	user	user	NOUN
bracis-19038	18	17	faces	face	VERB
bracis-19038	18	18	when	when	SCONJ
bracis-19038	18	19	expressing	express	VERB
bracis-19038	18	20	preferences	preference	NOUN
bracis-19038	18	21	is	be	AUX
bracis-19038	18	22	any	any	DET
bracis-19038	18	23	preference	preference	NOUN
bracis-19038	18	24	representation	representation	NOUN
bracis-19038	18	25	language	language	NOUN
bracis-19038	18	26	based	base	VERB
bracis-19038	18	27	on	on	ADP
bracis-19038	18	28	the	the	DET
bracis-19038	18	29	direct	direct	ADJ
bracis-19038	18	30	assessment	assessment	NOUN
bracis-19038	18	31	of	of	ADP
bracis-19038	18	32	user	user	NOUN
bracis-19038	18	33	preferences	preference	NOUN
bracis-19038	18	34	over	over	ADP
bracis-19038	18	35	the	the	DET
bracis-19038	18	36	complete	complete	ADJ
bracis-19038	18	37	set	set	NOUN
bracis-19038	18	38	of	of	ADP
bracis-19038	18	39	options	option	NOUN
bracis-19038	18	40	is	be	AUX
bracis-19038	18	41	simply	simply	ADV
bracis-19038	18	42	infeasible	infeasible	ADJ
bracis-19038	18	43	.	.	PUNCT
bracis-19038	19	1	we	we	PRON
bracis-19038	19	2	have	have	VERB
bracis-19038	19	3	to	to	PART
bracis-19038	19	4	resort	resort	VERB
bracis-19038	19	5	to	to	ADP
bracis-19038	19	6	compact	compact	ADJ
bracis-19038	19	7	preference	preference	NOUN
bracis-19038	19	8	representation	representation	NOUN
bracis-19038	19	9	languages	language	NOUN
bracis-19038	19	10	which	which	PRON
bracis-19038	19	11	represent	represent	VERB
bracis-19038	19	12	partial	partial	ADJ
bracis-19038	19	13	descriptions	description	NOUN
bracis-19038	19	14	of	of	ADP
bracis-19038	19	15	preferences	preference	NOUN
bracis-19038	19	16	and	and	CCONJ
bracis-19038	19	17	rank	rank	NOUN
bracis-19038	19	18	-	-	PUNCT
bracis-19038	19	19	order	order	NOUN
bracis-19038	19	20	the	the	DET
bracis-19038	19	21	possible	possible	ADJ
bracis-19038	19	22	options	option	NOUN
bracis-19038	19	23	.	.	PUNCT
bracis-19038	20	1	with	with	ADP
bracis-19038	20	2	such	such	DET
bracis-19038	20	3	a	a	DET
bracis-19038	20	4	motivation	motivation	NOUN
bracis-19038	20	5	in	in	ADP
bracis-19038	20	6	view	view	NOUN
bracis-19038	20	7	,	,	PUNCT
bracis-19038	20	8	in	in	ADP
bracis-19038	20	9	this	this	DET
bracis-19038	20	10	paper	paper	NOUN
bracis-19038	20	11	,	,	PUNCT
bracis-19038	20	12	we	we	PRON
bracis-19038	20	13	generalise	generalise	VERB
bracis-19038	20	14	the	the	DET
bracis-19038	20	15	notion	notion	NOUN
bracis-19038	20	16	of	of	ADP
bracis-19038	20	17	prioritised	prioritised	ADJ
bracis-19038	20	18	logic	logic	NOUN
bracis-19038	20	19	programs	program	NOUN
bracis-19038	20	20	(	(	PUNCT
bracis-19038	20	21	\(\textit{plp}\)s	\(\textit{plp}\)s	ADJ
bracis-19038	20	22	)	)	PUNCT
bracis-19038	20	23	proposed	propose	VERB
bracis-19038	20	24	in	in	ADP
bracis-19038	20	25	[	[	X
bracis-19038	20	26	4	4	NUM
bracis-19038	20	27	]	]	PUNCT
bracis-19038	20	28	to	to	PART
bracis-19038	20	29	encompass	encompass	VERB
bracis-19038	20	30	not	not	PART
bracis-19038	20	31	only	only	ADV
bracis-19038	20	32	the	the	DET
bracis-19038	20	33	relation	relation	NOUN
bracis-19038	20	34	of	of	ADP
bracis-19038	20	35	priority	priority	NOUN
bracis-19038	20	36	between	between	ADP
bracis-19038	20	37	literals	literal	NOUN
bracis-19038	20	38	(	(	PUNCT
bracis-19038	20	39	atoms	atom	NOUN
bracis-19038	20	40	or	or	CCONJ
bracis-19038	20	41	its	its	PRON
bracis-19038	20	42	negation	negation	NOUN
bracis-19038	20	43	)	)	PUNCT
bracis-19038	20	44	,	,	PUNCT
bracis-19038	20	45	but	but	CCONJ
bracis-19038	20	46	also	also	ADV
bracis-19038	20	47	sets	set	VERB
bracis-19038	20	48	of	of	ADP
bracis-19038	20	49	literals	literal	NOUN
bracis-19038	20	50	.	.	PUNCT
bracis-19038	21	1	the	the	DET
bracis-19038	21	2	resulting	result	VERB
bracis-19038	21	3	framework	framework	NOUN
bracis-19038	21	4	offers	offer	VERB
bracis-19038	21	5	a	a	DET
bracis-19038	21	6	preference	preference	NOUN
bracis-19038	21	7	representation	representation	NOUN
bracis-19038	21	8	language	language	NOUN
bracis-19038	21	9	expressive	expressive	ADJ
bracis-19038	21	10	enough	enough	ADV
bracis-19038	21	11	to	to	PART
bracis-19038	21	12	represent	represent	VERB
bracis-19038	21	13	complex	complex	ADJ
bracis-19038	21	14	forms	form	NOUN
bracis-19038	21	15	of	of	ADP
bracis-19038	21	16	preference	preference	NOUN
bracis-19038	21	17	in	in	ADP
bracis-19038	21	18	a	a	DET
bracis-19038	21	19	compact	compact	ADJ
bracis-19038	21	20	manner	manner	NOUN
bracis-19038	21	21	.	.	PUNCT
bracis-19038	22	1	while	while	SCONJ
bracis-19038	22	2	in	in	ADP
bracis-19038	22	3	[	[	PUNCT
bracis-19038	22	4	4	4	NUM
bracis-19038	22	5	]	]	PUNCT
bracis-19038	22	6	,	,	PUNCT
bracis-19038	22	7	in	in	ADP
bracis-19038	22	8	order	order	NOUN
bracis-19038	22	9	to	to	PART
bracis-19038	22	10	represent	represent	VERB
bracis-19038	22	11	a	a	DET
bracis-19038	22	12	conjunction	conjunction	NOUN
bracis-19038	22	13	of	of	ADP
bracis-19038	22	14	preferences	preference	NOUN
bracis-19038	22	15	,	,	PUNCT
bracis-19038	22	16	they	they	PRON
bracis-19038	22	17	have	have	VERB
bracis-19038	22	18	to	to	PART
bracis-19038	22	19	include	include	VERB
bracis-19038	22	20	new	new	ADJ
bracis-19038	22	21	rules	rule	NOUN
bracis-19038	22	22	in	in	ADP
bracis-19038	22	23	the	the	DET
bracis-19038	22	24	program	program	NOUN
bracis-19038	22	25	and	and	CCONJ
bracis-19038	22	26	preferences	preference	NOUN
bracis-19038	22	27	between	between	ADP
bracis-19038	22	28	new	new	ADJ
bracis-19038	22	29	atoms	atom	NOUN
bracis-19038	22	30	,	,	PUNCT
bracis-19038	22	31	we	we	PRON
bracis-19038	22	32	will	will	AUX
bracis-19038	22	33	surmount	surmount	VERB
bracis-19038	22	34	this	this	DET
bracis-19038	22	35	problem	problem	NOUN
bracis-19038	22	36	by	by	ADP
bracis-19038	22	37	representing	represent	VERB
bracis-19038	22	38	conjunctions	conjunction	NOUN
bracis-19038	22	39	of	of	ADP
bracis-19038	22	40	preferences	preference	NOUN
bracis-19038	22	41	directly	directly	ADV
bracis-19038	22	42	.	.	PUNCT
bracis-19038	23	1	a	a	DET
bracis-19038	23	2	second	second	ADJ
bracis-19038	23	3	fundamental	fundamental	ADJ
bracis-19038	23	4	challenge	challenge	NOUN
bracis-19038	23	5	is	be	AUX
bracis-19038	23	6	to	to	PART
bracis-19038	23	7	select	select	VERB
bracis-19038	23	8	the	the	DET
bracis-19038	23	9	most	most	ADV
bracis-19038	23	10	preferable	preferable	ADJ
bracis-19038	23	11	models	model	NOUN
bracis-19038	23	12	given	give	VERB
bracis-19038	23	13	the	the	DET
bracis-19038	23	14	priorities	priority	NOUN
bracis-19038	23	15	between	between	ADP
bracis-19038	23	16	the	the	DET
bracis-19038	23	17	sets	set	NOUN
bracis-19038	23	18	of	of	ADP
bracis-19038	23	19	literals	literal	NOUN
bracis-19038	23	20	.	.	PUNCT
bracis-19038	24	1	which	which	DET
bracis-19038	24	2	criteria	criterion	NOUN
bracis-19038	24	3	should	should	AUX
bracis-19038	24	4	be	be	AUX
bracis-19038	24	5	regarded	regard	VERB
bracis-19038	24	6	?	?	PUNCT
bracis-19038	25	1	in	in	ADP
bracis-19038	25	2	order	order	NOUN
bracis-19038	25	3	to	to	PART
bracis-19038	25	4	decide	decide	VERB
bracis-19038	25	5	a	a	DET
bracis-19038	25	6	model	model	NOUN
bracis-19038	25	7	\(i_1\	\(i_1\	NOUN
bracis-19038	25	8	)	)	PUNCT
bracis-19038	25	9	is	be	AUX
bracis-19038	25	10	more	more	ADV
bracis-19038	25	11	preferable	preferable	ADJ
bracis-19038	25	12	than	than	ADP
bracis-19038	25	13	a	a	DET
bracis-19038	25	14	model	model	NOUN
bracis-19038	25	15	\(i_2\	\(i_2\	PROPN
bracis-19038	25	16	)	)	PUNCT
bracis-19038	25	17	,	,	PUNCT
bracis-19038	25	18	someone	someone	PRON
bracis-19038	25	19	would	would	AUX
bracis-19038	25	20	require	require	VERB
bracis-19038	25	21	any	any	DET
bracis-19038	25	22	set	set	NOUN
bracis-19038	25	23	of	of	ADP
bracis-19038	25	24	literals	literal	NOUN
bracis-19038	25	25	associated	associate	VERB
bracis-19038	25	26	with	with	ADP
bracis-19038	25	27	\(i_1\	\(i_1\	NOUN
bracis-19038	25	28	)	)	PUNCT
bracis-19038	25	29	should	should	AUX
bracis-19038	25	30	have	have	VERB
bracis-19038	25	31	higher	high	ADJ
bracis-19038	25	32	priority	priority	NOUN
bracis-19038	25	33	than	than	ADP
bracis-19038	25	34	any	any	DET
bracis-19038	25	35	set	set	NOUN
bracis-19038	25	36	of	of	ADP
bracis-19038	25	37	literals	literal	NOUN
bracis-19038	25	38	associated	associate	VERB
bracis-19038	25	39	with	with	ADP
bracis-19038	25	40	\(i_2\	\(i_2\	PROPN
bracis-19038	25	41	)	)	PUNCT
bracis-19038	25	42	.	.	PUNCT
bracis-19038	26	1	for	for	ADP
bracis-19038	26	2	others	other	NOUN
bracis-19038	26	3	,	,	PUNCT
bracis-19038	26	4	it	it	PRON
bracis-19038	26	5	suffices	suffice	VERB
bracis-19038	26	6	to	to	PART
bracis-19038	26	7	guarantee	guarantee	VERB
bracis-19038	26	8	the	the	DET
bracis-19038	26	9	worst	worst	ADV
bracis-19038	26	10	-	-	PUNCT
bracis-19038	26	11	ranked	rank	VERB
bracis-19038	26	12	sets	set	NOUN
bracis-19038	26	13	of	of	ADP
bracis-19038	26	14	literals	literal	NOUN
bracis-19038	26	15	associated	associate	VERB
bracis-19038	26	16	with	with	ADP
bracis-19038	26	17	\(i_1\	\(i_1\	NOUN
bracis-19038	26	18	)	)	PUNCT
bracis-19038	26	19	should	should	AUX
bracis-19038	26	20	have	have	VERB
bracis-19038	26	21	higher	high	ADJ
bracis-19038	26	22	priority	priority	NOUN
bracis-19038	26	23	than	than	ADP
bracis-19038	26	24	those	those	DET
bracis-19038	26	25	worst	worst	ADV
bracis-19038	26	26	-	-	PUNCT
bracis-19038	26	27	ranked	rank	VERB
bracis-19038	26	28	sets	set	NOUN
bracis-19038	26	29	of	of	ADP
bracis-19038	26	30	literals	literal	NOUN
bracis-19038	26	31	associated	associate	VERB
bracis-19038	26	32	with	with	ADP
bracis-19038	26	33	\(i_2\	\(i_2\	PROPN
bracis-19038	26	34	)	)	PUNCT
bracis-19038	26	35	.	.	PUNCT
bracis-19038	27	1	depending	depend	VERB
bracis-19038	27	2	on	on	ADP
bracis-19038	27	3	the	the	DET
bracis-19038	27	4	criteria	criterion	NOUN
bracis-19038	27	5	employed	employ	VERB
bracis-19038	27	6	to	to	PART
bracis-19038	27	7	select	select	VERB
bracis-19038	27	8	the	the	DET
bracis-19038	27	9	most	most	ADV
bracis-19038	27	10	preferable	preferable	ADJ
bracis-19038	27	11	models	model	NOUN
bracis-19038	27	12	,	,	PUNCT
bracis-19038	27	13	we	we	PRON
bracis-19038	27	14	would	would	AUX
bracis-19038	27	15	obtain	obtain	VERB
bracis-19038	27	16	different	different	ADJ
bracis-19038	27	17	semantics	semantic	NOUN
bracis-19038	27	18	for	for	ADP
bracis-19038	27	19	\(\textit{plp}\)s	\(\textit{plp}\)s	PROPN
bracis-19038	27	20	.	.	PUNCT
bracis-19038	28	1	overall	overall	ADV
bracis-19038	28	2	,	,	PUNCT
bracis-19038	28	3	there	there	PRON
bracis-19038	28	4	is	be	VERB
bracis-19038	28	5	no	no	DET
bracis-19038	28	6	consensual	consensual	ADJ
bracis-19038	28	7	way	way	NOUN
bracis-19038	28	8	to	to	PART
bracis-19038	28	9	define	define	VERB
bracis-19038	28	10	these	these	DET
bracis-19038	28	11	semantics	semantic	NOUN
bracis-19038	28	12	and	and	CCONJ
bracis-19038	28	13	,	,	PUNCT
bracis-19038	28	14	we	we	PRON
bracis-19038	28	15	will	will	AUX
bracis-19038	28	16	find	find	VERB
bracis-19038	28	17	many	many	ADJ
bracis-19038	28	18	disconnected	disconnected	ADJ
bracis-19038	28	19	approaches	approach	NOUN
bracis-19038	28	20	.	.	PUNCT
bracis-19038	29	1	in	in	ADP
bracis-19038	29	2	this	this	DET
bracis-19038	29	3	work	work	NOUN
bracis-19038	29	4	,	,	PUNCT
bracis-19038	29	5	we	we	PRON
bracis-19038	29	6	will	will	AUX
bracis-19038	29	7	not	not	PART
bracis-19038	29	8	cling	cling	VERB
bracis-19038	29	9	to	to	ADP
bracis-19038	29	10	a	a	DET
bracis-19038	29	11	unique	unique	ADJ
bracis-19038	29	12	path	path	NOUN
bracis-19038	29	13	,	,	PUNCT
bracis-19038	29	14	but	but	CCONJ
bracis-19038	29	15	present	present	ADJ
bracis-19038	29	16	comprehensive	comprehensive	ADJ
bracis-19038	29	17	and	and	CCONJ
bracis-19038	29	18	systematic	systematic	ADJ
bracis-19038	29	19	criteria	criterion	NOUN
bracis-19038	29	20	to	to	PART
bracis-19038	29	21	define	define	VERB
bracis-19038	29	22	semantics	semantic	NOUN
bracis-19038	29	23	for	for	ADP
bracis-19038	29	24	them	they	PRON
bracis-19038	29	25	.	.	PUNCT
bracis-19038	30	1	as	as	ADP
bracis-19038	30	2	result	result	NOUN
bracis-19038	30	3	,	,	PUNCT
bracis-19038	30	4	we	we	PRON
bracis-19038	30	5	will	will	AUX
bracis-19038	30	6	have	have	VERB
bracis-19038	30	7	a	a	DET
bracis-19038	30	8	clearer	clear	ADJ
bracis-19038	30	9	notion	notion	NOUN
bracis-19038	30	10	of	of	ADP
bracis-19038	30	11	what	what	PRON
bracis-19038	30	12	we	we	PRON
bracis-19038	30	13	mean	mean	VERB
bracis-19038	30	14	when	when	SCONJ
bracis-19038	30	15	selecting	select	VERB
bracis-19038	30	16	the	the	DET
bracis-19038	30	17	most	most	ADV
bracis-19038	30	18	preferable	preferable	ADJ
bracis-19038	30	19	models	model	NOUN
bracis-19038	30	20	.	.	PUNCT
bracis-19038	31	1	the	the	DET
bracis-19038	31	2	rest	rest	NOUN
bracis-19038	31	3	of	of	ADP
bracis-19038	31	4	the	the	DET
bracis-19038	31	5	paper	paper	NOUN
bracis-19038	31	6	develops	develop	VERB
bracis-19038	31	7	as	as	SCONJ
bracis-19038	31	8	follows	follow	VERB
bracis-19038	31	9	.	.	PUNCT
bracis-19038	32	1	in	in	ADP
bracis-19038	32	2	sect	sect	NOUN
bracis-19038	32	3	.	.	PUNCT
bracis-19038	32	4	 	 	SPACE
bracis-19038	32	5	2	2	NUM
bracis-19038	32	6	,	,	PUNCT
bracis-19038	32	7	we	we	PRON
bracis-19038	32	8	will	will	AUX
bracis-19038	32	9	introduce	introduce	VERB
bracis-19038	32	10	the	the	DET
bracis-19038	32	11	basic	basic	ADJ
bracis-19038	32	12	concepts	concept	NOUN
bracis-19038	32	13	related	relate	VERB
bracis-19038	32	14	to	to	ADP
bracis-19038	32	15	normal	normal	ADJ
bracis-19038	32	16	logic	logic	NOUN
bracis-19038	32	17	programs	program	NOUN
bracis-19038	32	18	\((\textit{nlp})\	\((\textit{nlp})\	PROPN
bracis-19038	32	19	)	)	PUNCT
bracis-19038	32	20	and	and	CCONJ
bracis-19038	32	21	their	their	PRON
bracis-19038	32	22	semantics	semantic	NOUN
bracis-19038	32	23	.	.	PUNCT
bracis-19038	33	1	the	the	DET
bracis-19038	33	2	main	main	ADJ
bracis-19038	33	3	contributions	contribution	NOUN
bracis-19038	33	4	of	of	ADP
bracis-19038	33	5	the	the	DET
bracis-19038	33	6	paper	paper	NOUN
bracis-19038	33	7	can	can	AUX
bracis-19038	33	8	be	be	AUX
bracis-19038	33	9	found	find	VERB
bracis-19038	33	10	in	in	ADP
bracis-19038	33	11	sect	sect	NOUN
bracis-19038	33	12	.	.	PUNCT
bracis-19038	33	13	 	 	SPACE
bracis-19038	34	1	3	3	NUM
bracis-19038	34	2	,	,	PUNCT
bracis-19038	34	3	where	where	SCONJ
bracis-19038	34	4	we	we	PRON
bracis-19038	34	5	will	will	AUX
bracis-19038	34	6	present	present	VERB
bracis-19038	34	7	the	the	DET
bracis-19038	34	8	prioritised	prioritise	VERB
bracis-19038	34	9	logic	logic	NOUN
bracis-19038	34	10	programs	program	NOUN
bracis-19038	34	11	(	(	PUNCT
bracis-19038	34	12	\(\textit{plp}\)s	\(\textit{plp}\)s	ADJ
bracis-19038	34	13	)	)	PUNCT
bracis-19038	34	14	and	and	CCONJ
bracis-19038	34	15	comprehensive	comprehensive	ADJ
bracis-19038	34	16	and	and	CCONJ
bracis-19038	34	17	systematic	systematic	ADJ
bracis-19038	34	18	criteria	criterion	NOUN
bracis-19038	34	19	to	to	PART
bracis-19038	34	20	define	define	VERB
bracis-19038	34	21	semantics	semantic	NOUN
bracis-19038	34	22	for	for	ADP
bracis-19038	34	23	them	they	PRON
bracis-19038	34	24	.	.	PUNCT
bracis-19038	35	1	next	next	ADV
bracis-19038	35	2	,	,	PUNCT
bracis-19038	35	3	we	we	PRON
bracis-19038	35	4	show	show	VERB
bracis-19038	35	5	how	how	SCONJ
bracis-19038	35	6	complex	complex	ADJ
bracis-19038	35	7	forms	form	NOUN
bracis-19038	35	8	of	of	ADP
bracis-19038	35	9	priorities	priority	NOUN
bracis-19038	35	10	can	can	AUX
bracis-19038	35	11	be	be	AUX
bracis-19038	35	12	expressed	express	VERB
bracis-19038	35	13	straightforwardly	straightforwardly	ADV
bracis-19038	35	14	in	in	ADP
bracis-19038	35	15	\(\textit{plp}\)s	\(\textit{plp}\)s	NOUN
bracis-19038	35	16	.	.	PUNCT
bracis-19038	36	1	in	in	ADP
bracis-19038	36	2	sect	sect	NOUN
bracis-19038	36	3	.	.	PUNCT
bracis-19038	36	4	 	 	SPACE
bracis-19038	36	5	5	5	NUM
bracis-19038	36	6	,	,	PUNCT
bracis-19038	36	7	we	we	PRON
bracis-19038	36	8	prove	prove	VERB
bracis-19038	36	9	some	some	DET
bracis-19038	36	10	properties	property	NOUN
bracis-19038	36	11	of	of	ADP
bracis-19038	36	12	our	our	PRON
bracis-19038	36	13	proposal	proposal	NOUN
bracis-19038	36	14	;	;	PUNCT
bracis-19038	36	15	in	in	ADP
bracis-19038	36	16	particular	particular	ADJ
bracis-19038	36	17	,	,	PUNCT
bracis-19038	36	18	we	we	PRON
bracis-19038	36	19	guarantee	guarantee	VERB
bracis-19038	36	20	these	these	DET
bracis-19038	36	21	semantics	semantic	NOUN
bracis-19038	36	22	for	for	ADP
bracis-19038	36	23	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	36	24	)	)	PUNCT
bracis-19038	36	25	generalise	generalise	VERB
bracis-19038	36	26	their	their	PRON
bracis-19038	36	27	counterparts	counterpart	NOUN
bracis-19038	36	28	for	for	ADP
bracis-19038	36	29	logic	logic	NOUN
bracis-19038	36	30	programs	program	NOUN
bracis-19038	36	31	without	without	ADP
bracis-19038	36	32	preferences	preference	NOUN
bracis-19038	36	33	.	.	PUNCT
bracis-19038	37	1	section	section	NOUN
bracis-19038	37	2	 	 	SPACE
bracis-19038	37	3	6	6	NUM
bracis-19038	37	4	provides	provide	VERB
bracis-19038	37	5	an	an	DET
bracis-19038	37	6	overview	overview	NOUN
bracis-19038	37	7	of	of	ADP
bracis-19038	37	8	related	related	ADJ
bracis-19038	37	9	works	work	NOUN
bracis-19038	37	10	.	.	PUNCT
bracis-19038	38	1	finally	finally	ADV
bracis-19038	38	2	,	,	PUNCT
bracis-19038	38	3	sect	sect	NOUN
bracis-19038	38	4	.	.	PUNCT
bracis-19038	38	5	 	 	SPACE
bracis-19038	39	1	7	7	NUM
bracis-19038	39	2	summarises	summarise	NOUN
bracis-19038	39	3	our	our	PRON
bracis-19038	39	4	contributions	contribution	NOUN
bracis-19038	39	5	and	and	CCONJ
bracis-19038	39	6	pointed	point	VERB
bracis-19038	39	7	out	out	ADP
bracis-19038	39	8	future	future	ADJ
bracis-19038	39	9	works	work	NOUN
bracis-19038	39	10	.	.	PUNCT
bracis-19038	40	1	2	2	NUM
bracis-19038	40	2	preliminaries	preliminary	NOUN
bracis-19038	40	3	in	in	ADP
bracis-19038	40	4	the	the	DET
bracis-19038	40	5	sequel	sequel	NOUN
bracis-19038	40	6	,	,	PUNCT
bracis-19038	40	7	we	we	PRON
bracis-19038	40	8	will	will	AUX
bracis-19038	40	9	consider	consider	VERB
bracis-19038	40	10	propositional	propositional	ADJ
bracis-19038	40	11	normal	normal	ADJ
bracis-19038	40	12	logic	logic	NOUN
bracis-19038	40	13	programs	program	NOUN
bracis-19038	40	14	,	,	PUNCT
bracis-19038	40	15	which	which	PRON
bracis-19038	40	16	we	we	PRON
bracis-19038	40	17	will	will	AUX
bracis-19038	40	18	call	call	VERB
bracis-19038	40	19	logic	logic	NOUN
bracis-19038	40	20	programs	program	NOUN
bracis-19038	40	21	or	or	CCONJ
bracis-19038	40	22	simply	simply	ADV
bracis-19038	40	23	programs	program	NOUN
bracis-19038	40	24	from	from	ADP
bracis-19038	40	25	now	now	ADV
bracis-19038	40	26	on	on	ADV
bracis-19038	40	27	.	.	PUNCT
bracis-19038	41	1	definition	definition	NOUN
bracis-19038	41	2	1	1	NUM
bracis-19038	41	3	a	a	DET
bracis-19038	41	4	normal	normal	ADJ
bracis-19038	41	5	logic	logic	NOUN
bracis-19038	41	6	program	program	NOUN
bracis-19038	41	7	(	(	PUNCT
bracis-19038	41	8	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	41	9	)	)	PUNCT
bracis-19038	41	10	)	)	PUNCT
bracis-19038	41	11	,	,	PUNCT
bracis-19038	41	12	p	p	X
bracis-19038	41	13	,	,	PUNCT
bracis-19038	41	14	is	be	AUX
bracis-19038	41	15	a	a	DET
bracis-19038	41	16	set	set	NOUN
bracis-19038	41	17	of	of	ADP
bracis-19038	41	18	rules	rule	NOUN
bracis-19038	41	19	of	of	ADP
bracis-19038	41	20	the	the	DET
bracis-19038	41	21	form	form	NOUN
bracis-19038	41	22	\(a	\(a	NOUN
bracis-19038	41	23	\leftarrow	\leftarrow	PROPN
bracis-19038	41	24	a_1	a_1	NOUN
bracis-19038	41	25	,	,	PUNCT
bracis-19038	41	26	\ldots	\ldots	PROPN
bracis-19038	41	27	,	,	PUNCT
bracis-19038	41	28	a_m,\mathtt	a_m,\mathtt	PROPN
bracis-19038	41	29	{	{	PUNCT
bracis-19038	41	30	not\	not\	PROPN
bracis-19038	41	31	}	}	PUNCT
bracis-19038	41	32	b_1,\	b_1,\	NOUN
bracis-19038	41	33	)	)	PUNCT
bracis-19038	41	34	\(\ldots	\(\ldot	NOUN
bracis-19038	41	35	,	,	PUNCT
bracis-19038	41	36	\mathtt	\mathtt	PROPN
bracis-19038	41	37	{	{	PUNCT
bracis-19038	41	38	not\	not\	PROPN
bracis-19038	41	39	}	}	PUNCT
bracis-19038	41	40	b_n\	b_n\	PROPN
bracis-19038	41	41	)	)	PUNCT
bracis-19038	41	42	(	(	PUNCT
bracis-19038	41	43	\(m	\(m	PROPN
bracis-19038	41	44	,	,	PUNCT
bracis-19038	41	45	n	n	PRON
bracis-19038	41	46	\in	\in	PROPN
bracis-19038	41	47	\mathbb	\mathbb	PROPN
bracis-19038	41	48	{	{	PUNCT
bracis-19038	41	49	n}\	n}\	NUM
bracis-19038	41	50	)	)	PUNCT
bracis-19038	41	51	)	)	PUNCT
bracis-19038	41	52	,	,	PUNCT
bracis-19038	41	53	where	where	SCONJ
bracis-19038	41	54	a	a	DET
bracis-19038	41	55	,	,	PUNCT
bracis-19038	41	56	\(a_i\	\(a_i\	NOUN
bracis-19038	41	57	)	)	PUNCT
bracis-19038	41	58	(	(	PUNCT
bracis-19038	41	59	\(1	\(1	PROPN
bracis-19038	41	60	\le	\le	PROPN
bracis-19038	41	61	i	i	PRON
bracis-19038	41	62	\le	\le	NOUN
bracis-19038	41	63	m\	m\	NOUN
bracis-19038	41	64	)	)	PUNCT
bracis-19038	41	65	)	)	PUNCT
bracis-19038	41	66	and	and	CCONJ
bracis-19038	41	67	\(b_j\	\(b_j\	X
bracis-19038	41	68	)	)	PUNCT
bracis-19038	41	69	(	(	PUNCT
bracis-19038	41	70	\(1	\(1	PROPN
bracis-19038	41	71	\le	\le	PROPN
bracis-19038	41	72	j	j	PROPN
bracis-19038	41	73	\le	\le	PROPN
bracis-19038	41	74	n\	n\	PROPN
bracis-19038	41	75	)	)	PUNCT
bracis-19038	41	76	)	)	PUNCT
bracis-19038	41	77	are	be	AUX
bracis-19038	41	78	atoms	atom	NOUN
bracis-19038	41	79	;	;	PUNCT
bracis-19038	41	80	\(\mathtt	\(\mathtt	NOUN
bracis-19038	41	81	{	{	PUNCT
bracis-19038	41	82	not}\	not}\	NOUN
bracis-19038	41	83	)	)	PUNCT
bracis-19038	41	84	represents	represent	VERB
bracis-19038	41	85	default	default	NOUN
bracis-19038	41	86	negation	negation	NOUN
bracis-19038	41	87	,	,	PUNCT
bracis-19038	41	88	and	and	CCONJ
bracis-19038	41	89	\(\mathtt	\(\mathtt	NOUN
bracis-19038	41	90	{	{	PUNCT
bracis-19038	41	91	not\	not\	PROPN
bracis-19038	41	92	}	}	PUNCT
bracis-19038	41	93	b_j\	b_j\	PROPN
bracis-19038	41	94	)	)	PUNCT
bracis-19038	41	95	is	be	AUX
bracis-19038	41	96	a	a	DET
bracis-19038	41	97	default	default	NOUN
bracis-19038	41	98	literal	literal	NOUN
bracis-19038	41	99	.	.	PUNCT
bracis-19038	42	1	a	a	DET
bracis-19038	42	2	literal	literal	NOUN
bracis-19038	42	3	is	be	AUX
bracis-19038	42	4	an	an	DET
bracis-19038	42	5	atom	atom	NOUN
bracis-19038	42	6	or	or	CCONJ
bracis-19038	42	7	a	a	DET
bracis-19038	42	8	default	default	NOUN
bracis-19038	42	9	literal	literal	NOUN
bracis-19038	42	10	.	.	PUNCT
bracis-19038	43	1	we	we	PRON
bracis-19038	43	2	say	say	VERB
bracis-19038	43	3	a	a	PRON
bracis-19038	43	4	is	be	AUX
bracis-19038	43	5	the	the	DET
bracis-19038	43	6	head	head	NOUN
bracis-19038	43	7	of	of	ADP
bracis-19038	43	8	the	the	DET
bracis-19038	43	9	rule	rule	NOUN
bracis-19038	43	10	,	,	PUNCT
bracis-19038	43	11	and	and	CCONJ
bracis-19038	43	12	\(a_1	\(a_1	NUM
bracis-19038	43	13	,	,	PUNCT
bracis-19038	43	14	\ldots	\ldots	PROPN
bracis-19038	43	15	,	,	PUNCT
bracis-19038	43	16	a_m	a_m	ADV
bracis-19038	43	17	,	,	PUNCT
bracis-19038	43	18	\mathtt	\mathtt	PROPN
bracis-19038	43	19	{	{	PUNCT
bracis-19038	43	20	not\	not\	PROPN
bracis-19038	43	21	}	}	PUNCT
bracis-19038	43	22	b_1	b_1	PROPN
bracis-19038	43	23	,	,	PUNCT
bracis-19038	43	24	\ldots	\ldots	PROPN
bracis-19038	43	25	,	,	PUNCT
bracis-19038	43	26	\mathtt	\mathtt	PROPN
bracis-19038	43	27	{	{	PUNCT
bracis-19038	43	28	not\	not\	PROPN
bracis-19038	43	29	}	}	PUNCT
bracis-19038	43	30	b_n\	b_n\	PROPN
bracis-19038	43	31	)	)	PUNCT
bracis-19038	43	32	is	be	AUX
bracis-19038	43	33	its	its	PRON
bracis-19038	43	34	body	body	NOUN
bracis-19038	43	35	.	.	PUNCT
bracis-19038	44	1	if	if	SCONJ
bracis-19038	44	2	p	p	NOUN
bracis-19038	44	3	has	have	VERB
bracis-19038	44	4	no	no	DET
bracis-19038	44	5	occurrence	occurrence	NOUN
bracis-19038	44	6	of	of	ADP
bracis-19038	44	7	default	default	NOUN
bracis-19038	44	8	literals	literal	NOUN
bracis-19038	44	9	,	,	PUNCT
bracis-19038	44	10	it	it	PRON
bracis-19038	44	11	is	be	AUX
bracis-19038	44	12	called	call	VERB
bracis-19038	44	13	a	a	DET
bracis-19038	44	14	definite	definite	ADJ
bracis-19038	44	15	logic	logic	NOUN
bracis-19038	44	16	program	program	NOUN
bracis-19038	44	17	.	.	PUNCT
bracis-19038	45	1	the	the	DET
bracis-19038	45	2	herbrand	herbrand	PROPN
bracis-19038	45	3	base	base	NOUN
bracis-19038	45	4	of	of	ADP
bracis-19038	45	5	p	p	NOUN
bracis-19038	45	6	is	be	AUX
bracis-19038	45	7	the	the	DET
bracis-19038	45	8	set	set	NOUN
bracis-19038	45	9	\	\	PROPN
bracis-19038	45	10	(	(	PUNCT
bracis-19038	45	11	hb	hb	X
bracis-19038	45	12	_	_	PUNCT
bracis-19038	45	13	p\	p\	NOUN
bracis-19038	45	14	)	)	PUNCT
bracis-19038	45	15	of	of	ADP
bracis-19038	45	16	all	all	DET
bracis-19038	45	17	atoms	atom	NOUN
bracis-19038	45	18	occurring	occur	VERB
bracis-19038	45	19	in	in	ADP
bracis-19038	45	20	p.	p.	PROPN
bracis-19038	45	21	the	the	DET
bracis-19038	45	22	set	set	NOUN
bracis-19038	45	23	of	of	ADP
bracis-19038	45	24	literals	literal	NOUN
bracis-19038	45	25	of	of	ADP
bracis-19038	45	26	p	p	NOUN
bracis-19038	45	27	is	be	AUX
bracis-19038	45	28	\	\	PROPN
bracis-19038	45	29	(	(	PUNCT
bracis-19038	45	30	lit	light	VERB
bracis-19038	45	31	_	_	PUNCT
bracis-19038	45	32	p=	p=	NOUN
bracis-19038	45	33	hb	hb	X
bracis-19038	46	1	_	_	PUNCT
bracis-19038	46	2	p\cup	p\cup	PROPN
bracis-19038	46	3	\left\	\left\	PROPN
bracis-19038	46	4	{	{	PUNCT
bracis-19038	46	5	\mathtt	\mathtt	PROPN
bracis-19038	46	6	{	{	PUNCT
bracis-19038	46	7	not\	not\	PROPN
bracis-19038	46	8	}	}	PUNCT
bracis-19038	46	9	a	a	DET
bracis-19038	46	10	\mid	\mid	NOUN
bracis-19038	46	11	a	a	DET
bracis-19038	46	12	\in	\in	PROPN
bracis-19038	46	13	hb	hb	X
bracis-19038	46	14	_	_	NOUN
bracis-19038	46	15	p\right\	p\right\	ADJ
bracis-19038	46	16	}	}	PUNCT
bracis-19038	46	17	\	\	NOUN
bracis-19038	46	18	)	)	PUNCT
bracis-19038	46	19	.	.	PUNCT
bracis-19038	47	1	a	a	DET
bracis-19038	47	2	wide	wide	ADJ
bracis-19038	47	3	range	range	NOUN
bracis-19038	47	4	of	of	ADP
bracis-19038	47	5	logic	logic	NOUN
bracis-19038	47	6	programming	programming	NOUN
bracis-19038	47	7	semantics	semantic	NOUN
bracis-19038	47	8	can	can	AUX
bracis-19038	47	9	be	be	AUX
bracis-19038	47	10	defined	define	VERB
bracis-19038	47	11	based	base	VERB
bracis-19038	47	12	on	on	ADP
bracis-19038	47	13	the	the	DET
bracis-19038	47	14	3	3	NUM
bracis-19038	47	15	-	-	PUNCT
bracis-19038	47	16	valued	value	VERB
bracis-19038	47	17	interpretations	interpretation	NOUN
bracis-19038	47	18	(	(	PUNCT
bracis-19038	47	19	for	for	ADP
bracis-19038	47	20	short	short	ADJ
bracis-19038	47	21	,	,	PUNCT
bracis-19038	47	22	interpretations	interpretation	NOUN
bracis-19038	47	23	)	)	PUNCT
bracis-19038	47	24	of	of	ADP
bracis-19038	47	25	programs	program	NOUN
bracis-19038	47	26	:	:	PUNCT
bracis-19038	47	27	definition	definition	NOUN
bracis-19038	47	28	2	2	NUM
bracis-19038	47	29	[	[	X
bracis-19038	47	30	14	14	NUM
bracis-19038	47	31	]	]	PUNCT
bracis-19038	47	32	a	a	DET
bracis-19038	47	33	set	set	NOUN
bracis-19038	47	34	\(i	\(i	NOUN
bracis-19038	47	35	\subseteq	\subseteq	AUX
bracis-19038	47	36	lit	light	VERB
bracis-19038	47	37	_	_	PUNCT
bracis-19038	47	38	p\	p\	X
bracis-19038	47	39	)	)	PUNCT
bracis-19038	47	40	is	be	AUX
bracis-19038	47	41	a	a	DET
bracis-19038	47	42	3	3	NUM
bracis-19038	47	43	-	-	PUNCT
bracis-19038	47	44	valued	value	VERB
bracis-19038	47	45	interpretation	interpretation	NOUN
bracis-19038	47	46	of	of	ADP
bracis-19038	47	47	an	an	DET
bracis-19038	47	48	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	47	49	)	)	PUNCT
bracis-19038	48	1	p	p	NOUN
bracis-19038	48	2	if	if	SCONJ
bracis-19038	48	3	\(\not	\(\not	PRON
bracis-19038	48	4	\exists	\exist	VERB
bracis-19038	48	5	a	a	DET
bracis-19038	48	6	\in	\in	PROPN
bracis-19038	48	7	hb	hb	NOUN
bracis-19038	48	8	_	_	PUNCT
bracis-19038	48	9	p\	p\	NOUN
bracis-19038	48	10	)	)	PUNCT
bracis-19038	48	11	with	with	ADP
bracis-19038	48	12	\(\left\	\(\left\	PROPN
bracis-19038	48	13	{	{	PUNCT
bracis-19038	48	14	a	a	NOUN
bracis-19038	48	15	,	,	PUNCT
bracis-19038	48	16	\mathtt	\mathtt	PROPN
bracis-19038	48	17	{	{	PUNCT
bracis-19038	48	18	not\	not\	PROPN
bracis-19038	48	19	}	}	PUNCT
bracis-19038	48	20	a\right\	a\right\	VERB
bracis-19038	48	21	}	}	PUNCT
bracis-19038	48	22	\subseteq	\subseteq	PROPN
bracis-19038	48	23	i\	i\	PROPN
bracis-19038	48	24	)	)	PUNCT
bracis-19038	48	25	.	.	PUNCT
bracis-19038	49	1	we	we	PRON
bracis-19038	49	2	say	say	VERB
bracis-19038	49	3	i	i	PRON
bracis-19038	49	4	is	be	AUX
bracis-19038	49	5	a	a	DET
bracis-19038	49	6	model	model	NOUN
bracis-19038	49	7	of	of	ADP
bracis-19038	49	8	p	p	PROPN
bracis-19038	49	9	iff	iff	PROPN
bracis-19038	49	10	for	for	ADP
bracis-19038	49	11	each	each	DET
bracis-19038	49	12	rule	rule	NOUN
bracis-19038	49	13	\(a	\(a	NOUN
bracis-19038	49	14	\leftarrow	\leftarrow	PROPN
bracis-19038	49	15	a_1	a_1	NOUN
bracis-19038	49	16	,	,	PUNCT
bracis-19038	49	17	\ldots	\ldots	INTJ
bracis-19038	49	18	,	,	PUNCT
bracis-19038	49	19	a_m,\	a_m,\	ADJ
bracis-19038	49	20	)	)	PUNCT
bracis-19038	49	21	\(\mathtt	\(\mathtt	VERB
bracis-19038	49	22	{	{	PUNCT
bracis-19038	49	23	not\	not\	PROPN
bracis-19038	49	24	}	}	PUNCT
bracis-19038	49	25	b_1	b_1	PROPN
bracis-19038	49	26	,	,	PUNCT
bracis-19038	49	27	\ldots	\ldots	PROPN
bracis-19038	49	28	,	,	PUNCT
bracis-19038	49	29	\	\	ADJ
bracis-19038	49	30	)	)	PUNCT
bracis-19038	49	31	\(\mathtt	\(\mathtt	VERB
bracis-19038	49	32	{	{	PUNCT
bracis-19038	49	33	not\	not\	PROPN
bracis-19038	49	34	}	}	PUNCT
bracis-19038	49	35	b_n	b_n	SYM
bracis-19038	49	36	\in	\in	PROPN
bracis-19038	49	37	p\	p\	NOUN
bracis-19038	49	38	)	)	PUNCT
bracis-19038	49	39	,	,	PUNCT
bracis-19038	49	40	if	if	SCONJ
bracis-19038	49	41	\(\left\	\(\left\	PROPN
bracis-19038	49	42	{	{	PUNCT
bracis-19038	49	43	a_1	a_1	NOUN
bracis-19038	49	44	,	,	PUNCT
bracis-19038	49	45	\ldots	\ldots	PROPN
bracis-19038	49	46	,	,	PUNCT
bracis-19038	49	47	a_m	a_m	ADV
bracis-19038	49	48	,	,	PUNCT
bracis-19038	49	49	\mathtt	\mathtt	PROPN
bracis-19038	49	50	{	{	PUNCT
bracis-19038	49	51	not\	not\	PROPN
bracis-19038	49	52	}	}	PUNCT
bracis-19038	49	53	b_1	b_1	PROPN
bracis-19038	49	54	,	,	PUNCT
bracis-19038	49	55	\ldots	\ldots	PROPN
bracis-19038	49	56	,	,	PUNCT
bracis-19038	49	57	\mathtt	\mathtt	PROPN
bracis-19038	49	58	{	{	PUNCT
bracis-19038	49	59	not\	not\	PROPN
bracis-19038	49	60	}	}	PUNCT
bracis-19038	49	61	b_n\right\	b_n\right\	PROPN
bracis-19038	49	62	}	}	PUNCT
bracis-19038	49	63	\subseteq	\subseteq	PROPN
bracis-19038	49	64	i\	i\	PROPN
bracis-19038	49	65	)	)	PUNCT
bracis-19038	49	66	,	,	PUNCT
bracis-19038	49	67	then	then	ADV
bracis-19038	49	68	\(a	\(a	PROPN
bracis-19038	49	69	\in	\in	PROPN
bracis-19038	49	70	i\	i\	PROPN
bracis-19038	49	71	)	)	PUNCT
bracis-19038	49	72	.	.	PUNCT
bracis-19038	50	1	we	we	PRON
bracis-19038	50	2	refer	refer	VERB
bracis-19038	50	3	to	to	AUX
bracis-19038	50	4	\(t_i	\(t_i	VERB
bracis-19038	50	5	=	=	SYM
bracis-19038	50	6	\left\	\left\	PROPN
bracis-19038	50	7	{	{	PUNCT
bracis-19038	50	8	a	a	DET
bracis-19038	50	9	\in	\in	PROPN
bracis-19038	50	10	hb	hb	X
bracis-19038	50	11	_	_	PUNCT
bracis-19038	50	12	p\mid	p\mid	VERB
bracis-19038	50	13	a	a	DET
bracis-19038	50	14	\in	\in	PROPN
bracis-19038	50	15	i\right\	i\right\	PROPN
bracis-19038	50	16	}	}	PUNCT
bracis-19038	50	17	\	\	NOUN
bracis-19038	50	18	)	)	PUNCT
bracis-19038	50	19	as	as	SCONJ
bracis-19038	50	20	the	the	DET
bracis-19038	50	21	set	set	NOUN
bracis-19038	50	22	of	of	ADP
bracis-19038	50	23	true	true	ADJ
bracis-19038	50	24	atoms	atom	NOUN
bracis-19038	50	25	w.r.t	w.r.t	VERB
bracis-19038	50	26	.	.	PUNCT
bracis-19038	51	1	i	i	PRON
bracis-19038	51	2	and	and	CCONJ
bracis-19038	51	3	to	to	PART
bracis-19038	51	4	\(f_i	\(f_i	VERB
bracis-19038	51	5	=	=	SYM
bracis-19038	51	6	\left\	\left\	PROPN
bracis-19038	51	7	{	{	PUNCT
bracis-19038	51	8	a	a	DET
bracis-19038	51	9	\in	\in	PROPN
bracis-19038	51	10	hb	hb	X
bracis-19038	51	11	_	_	PUNCT
bracis-19038	51	12	p\mid	p\mid	VERB
bracis-19038	51	13	\mathtt	\mathtt	PROPN
bracis-19038	51	14	{	{	PUNCT
bracis-19038	51	15	not\	not\	PROPN
bracis-19038	51	16	}	}	PUNCT
bracis-19038	51	17	a	a	DET
bracis-19038	51	18	\in	\in	PROPN
bracis-19038	51	19	i\right\	i\right\	PROPN
bracis-19038	51	20	}	}	PUNCT
bracis-19038	51	21	\	\	NOUN
bracis-19038	51	22	)	)	PUNCT
bracis-19038	51	23	as	as	SCONJ
bracis-19038	51	24	the	the	DET
bracis-19038	51	25	set	set	NOUN
bracis-19038	51	26	of	of	ADP
bracis-19038	51	27	false	false	ADJ
bracis-19038	51	28	atoms	atom	NOUN
bracis-19038	51	29	w.r.t	w.r.t	VERB
bracis-19038	51	30	.	.	PUNCT
bracis-19038	52	1	i.	i.	PROPN
bracis-19038	52	2	if	if	SCONJ
bracis-19038	52	3	\(a	\(a	NOUN
bracis-19038	52	4	\not	\not	ADV
bracis-19038	52	5	\in	\in	PROPN
bracis-19038	52	6	t_i	t_i	VERB
bracis-19038	52	7	\cup	\cup	VERB
bracis-19038	52	8	f_i\	f_i\	NOUN
bracis-19038	52	9	)	)	PUNCT
bracis-19038	52	10	,	,	PUNCT
bracis-19038	52	11	then	then	ADV
bracis-19038	52	12	a	a	PRON
bracis-19038	52	13	is	be	AUX
bracis-19038	52	14	undefined	undefined	ADJ
bracis-19038	52	15	w.r.t	w.r.t	NOUN
bracis-19038	52	16	.	.	PUNCT
bracis-19038	53	1	i.	i.	PROPN
bracis-19038	53	2	let	let	VERB
bracis-19038	53	3	i	i	PRON
bracis-19038	53	4	be	be	AUX
bracis-19038	53	5	a	a	DET
bracis-19038	53	6	3	3	NUM
bracis-19038	53	7	-	-	PUNCT
bracis-19038	53	8	valued	value	VERB
bracis-19038	53	9	interpretation	interpretation	NOUN
bracis-19038	53	10	of	of	ADP
bracis-19038	53	11	a	a	DET
bracis-19038	53	12	program	program	NOUN
bracis-19038	53	13	p	p	X
bracis-19038	53	14	;	;	PUNCT
bracis-19038	53	15	in	in	ADP
bracis-19038	53	16	order	order	NOUN
bracis-19038	53	17	to	to	PART
bracis-19038	53	18	define	define	VERB
bracis-19038	53	19	the	the	DET
bracis-19038	53	20	semantics	semantic	NOUN
bracis-19038	53	21	for	for	ADP
bracis-19038	53	22	normal	normal	ADJ
bracis-19038	53	23	logic	logic	NOUN
bracis-19038	53	24	programs	program	NOUN
bracis-19038	53	25	,	,	PUNCT
bracis-19038	53	26	we	we	PRON
bracis-19038	53	27	will	will	AUX
bracis-19038	53	28	resort	resort	VERB
bracis-19038	53	29	to	to	ADP
bracis-19038	53	30	the	the	DET
bracis-19038	53	31	reduct	reduct	NOUN
bracis-19038	53	32	of	of	ADP
bracis-19038	53	33	p	p	NOUN
bracis-19038	53	34	with	with	ADP
bracis-19038	53	35	respect	respect	NOUN
bracis-19038	53	36	to	to	ADP
bracis-19038	53	37	i	i	PRON
bracis-19038	53	38	(	(	PUNCT
bracis-19038	53	39	written	write	VERB
bracis-19038	53	40	as	as	ADP
bracis-19038	53	41	p	p	PROPN
bracis-19038	53	42	/	/	SYM
bracis-19038	53	43	i	i	PROPN
bracis-19038	53	44	)	)	PUNCT
bracis-19038	53	45	,	,	PUNCT
bracis-19038	53	46	which	which	PRON
bracis-19038	53	47	is	be	AUX
bracis-19038	53	48	the	the	DET
bracis-19038	53	49	definite	definite	ADJ
bracis-19038	53	50	logic	logic	NOUN
bracis-19038	53	51	program	program	NOUN
bracis-19038	53	52	built	build	VERB
bracis-19038	53	53	by	by	ADP
bracis-19038	53	54	the	the	DET
bracis-19038	53	55	execution	execution	NOUN
bracis-19038	53	56	of	of	ADP
bracis-19038	53	57	the	the	DET
bracis-19038	53	58	following	follow	VERB
bracis-19038	53	59	steps	step	NOUN
bracis-19038	53	60	:	:	PUNCT
bracis-19038	53	61	1	1	X
bracis-19038	53	62	.	.	X
bracis-19038	53	63	remove	remove	VERB
bracis-19038	53	64	any	any	DET
bracis-19038	53	65	\(a	\(a	NOUN
bracis-19038	53	66	\leftarrow	\leftarrow	PROPN
bracis-19038	53	67	a_1	a_1	NOUN
bracis-19038	53	68	,	,	PUNCT
bracis-19038	53	69	\ldots	\ldots	INTJ
bracis-19038	53	70	,	,	PUNCT
bracis-19038	53	71	a_m,\	a_m,\	ADJ
bracis-19038	53	72	)	)	PUNCT
bracis-19038	53	73	\(\mathtt	\(\mathtt	VERB
bracis-19038	53	74	{	{	PUNCT
bracis-19038	53	75	not\	not\	PROPN
bracis-19038	53	76	}	}	PUNCT
bracis-19038	53	77	b_1	b_1	PROPN
bracis-19038	53	78	,	,	PUNCT
bracis-19038	53	79	\ldots	\ldots	PROPN
bracis-19038	53	80	,	,	PUNCT
bracis-19038	53	81	\mathtt	\mathtt	PROPN
bracis-19038	53	82	{	{	PUNCT
bracis-19038	53	83	not\	not\	PROPN
bracis-19038	53	84	}	}	PUNCT
bracis-19038	53	85	b_n	b_n	ADJ
bracis-19038	53	86	\in	\in	PROPN
bracis-19038	53	87	p\	p\	NOUN
bracis-19038	53	88	)	)	PUNCT
bracis-19038	53	89	with	with	ADP
bracis-19038	53	90	\(\left\	\(\left\	PROPN
bracis-19038	53	91	{	{	PUNCT
bracis-19038	53	92	b_1	b_1	PROPN
bracis-19038	53	93	,	,	PUNCT
bracis-19038	53	94	\ldots	\ldots	PROPN
bracis-19038	53	95	,	,	PUNCT
bracis-19038	53	96	b_n\right\	b_n\right\	ADJ
bracis-19038	53	97	}	}	PUNCT
bracis-19038	53	98	\cap	\cap	NOUN
bracis-19038	53	99	i	i	PRON
bracis-19038	53	100	\ne	\ne	PROPN
bracis-19038	53	101	\emptyset	\emptyset	VERB
bracis-19038	53	102	\	\	PROPN
bracis-19038	53	103	)	)	PUNCT
bracis-19038	53	104	;	;	PUNCT
bracis-19038	53	105	2	2	X
bracis-19038	53	106	.	.	NOUN
bracis-19038	53	107	afterwards	afterwards	ADV
bracis-19038	53	108	,	,	PUNCT
bracis-19038	53	109	remove	remove	VERB
bracis-19038	53	110	any	any	DET
bracis-19038	53	111	occurrence	occurrence	NOUN
bracis-19038	53	112	of	of	ADP
bracis-19038	53	113	\(\mathtt	\(\mathtt	NOUN
bracis-19038	53	114	{	{	PUNCT
bracis-19038	53	115	not\	not\	PROPN
bracis-19038	53	116	}	}	PUNCT
bracis-19038	53	117	b_i\	b_i\	PROPN
bracis-19038	53	118	)	)	PUNCT
bracis-19038	53	119	from	from	ADP
bracis-19038	53	120	p	p	PRON
bracis-19038	53	121	such	such	ADJ
bracis-19038	53	122	that	that	SCONJ
bracis-19038	53	123	\(\mathtt	\(\mathtt	NOUN
bracis-19038	53	124	{	{	PUNCT
bracis-19038	53	125	not\	not\	PROPN
bracis-19038	53	126	}	}	PUNCT
bracis-19038	53	127	b_i	b_i	PROPN
bracis-19038	53	128	\in	\in	PROPN
bracis-19038	53	129	i\	i\	PROPN
bracis-19038	53	130	)	)	PUNCT
bracis-19038	53	131	.	.	PUNCT
bracis-19038	54	1	3	3	X
bracis-19038	54	2	.	.	X
bracis-19038	54	3	then	then	ADV
bracis-19038	54	4	,	,	PUNCT
bracis-19038	54	5	replace	replace	VERB
bracis-19038	54	6	any	any	DET
bracis-19038	54	7	occurrence	occurrence	NOUN
bracis-19038	54	8	of	of	ADP
bracis-19038	54	9	\(\mathtt	\(\mathtt	NOUN
bracis-19038	54	10	{	{	PUNCT
bracis-19038	54	11	not\	not\	PROPN
bracis-19038	54	12	}	}	PUNCT
bracis-19038	54	13	b_i\	b_i\	PROPN
bracis-19038	54	14	)	)	PUNCT
bracis-19038	54	15	left	leave	VERB
bracis-19038	54	16	by	by	ADP
bracis-19038	54	17	a	a	DET
bracis-19038	54	18	special	special	ADJ
bracis-19038	54	19	atom	atom	NOUN
bracis-19038	54	20	\(\mathbf	\(\mathbf	X
bracis-19038	54	21	{	{	PUNCT
bracis-19038	54	22	u}\	u}\	PROPN
bracis-19038	54	23	)	)	PUNCT
bracis-19038	54	24	(	(	PUNCT
bracis-19038	54	25	\(\mathbf	\(\mathbf	VERB
bracis-19038	54	26	{	{	PUNCT
bracis-19038	54	27	u	u	NOUN
bracis-19038	54	28	}	}	PUNCT
bracis-19038	54	29	\not	\not	ADV
bracis-19038	54	30	\in	\in	ADJ
bracis-19038	54	31	hb	hb	X
bracis-19038	54	32	_	_	NOUN
bracis-19038	54	33	p\	p\	NOUN
bracis-19038	54	34	)	)	PUNCT
bracis-19038	54	35	)	)	PUNCT
bracis-19038	54	36	.	.	PUNCT
bracis-19038	55	1	we	we	PRON
bracis-19038	55	2	say	say	VERB
bracis-19038	55	3	i	i	PRON
bracis-19038	55	4	is	be	AUX
bracis-19038	55	5	the	the	DET
bracis-19038	55	6	least	least	ADJ
bracis-19038	55	7	model	model	NOUN
bracis-19038	55	8	of	of	ADP
bracis-19038	55	9	a	a	DET
bracis-19038	55	10	definite	definite	ADJ
bracis-19038	55	11	logic	logic	NOUN
bracis-19038	55	12	program	program	NOUN
bracis-19038	55	13	p	p	NOUN
bracis-19038	56	1	if	if	SCONJ
bracis-19038	56	2	among	among	ADP
bracis-19038	56	3	the	the	DET
bracis-19038	56	4	models	model	NOUN
bracis-19038	56	5	of	of	ADP
bracis-19038	56	6	p	p	NOUN
bracis-19038	56	7	,	,	PUNCT
bracis-19038	56	8	\(t_i\	\(t_i\	NOUN
bracis-19038	56	9	)	)	PUNCT
bracis-19038	56	10	is	be	AUX
bracis-19038	56	11	minimal	minimal	ADJ
bracis-19038	56	12	(	(	PUNCT
bracis-19038	56	13	w.r.t	w.r.t	NOUN
bracis-19038	56	14	.	.	PUNCT
bracis-19038	57	1	set	set	PROPN
bracis-19038	57	2	inclusion	inclusion	NOUN
bracis-19038	57	3	)	)	PUNCT
bracis-19038	57	4	and	and	CCONJ
bracis-19038	57	5	\(f_i\	\(f_i\	NOUN
bracis-19038	57	6	)	)	PUNCT
bracis-19038	57	7	is	be	AUX
bracis-19038	57	8	maximal	maximal	ADJ
bracis-19038	57	9	(	(	PUNCT
bracis-19038	57	10	w.r.t	w.r.t	NOUN
bracis-19038	57	11	.	.	PUNCT
bracis-19038	58	1	set	set	VERB
bracis-19038	58	2	inclusion	inclusion	NOUN
bracis-19038	58	3	)	)	PUNCT
bracis-19038	58	4	.	.	PUNCT
bracis-19038	59	1	note	note	VERB
bracis-19038	59	2	that	that	SCONJ
bracis-19038	59	3	p	p	X
bracis-19038	59	4	/	/	X
bracis-19038	59	5	i	i	PRON
bracis-19038	59	6	is	be	AUX
bracis-19038	59	7	a	a	DET
bracis-19038	59	8	definite	definite	ADJ
bracis-19038	59	9	logic	logic	NOUN
bracis-19038	59	10	program	program	NOUN
bracis-19038	59	11	.	.	PUNCT
bracis-19038	60	1	as	as	ADP
bracis-19038	60	2	consequence	consequence	NOUN
bracis-19038	60	3	,	,	PUNCT
bracis-19038	60	4	p	p	X
bracis-19038	60	5	/	/	X
bracis-19038	60	6	i	i	PRON
bracis-19038	60	7	has	have	VERB
bracis-19038	60	8	a	a	DET
bracis-19038	60	9	unique	unique	ADJ
bracis-19038	60	10	least	least	ADJ
bracis-19038	60	11	model	model	NOUN
bracis-19038	60	12	[	[	X
bracis-19038	60	13	14	14	NUM
bracis-19038	60	14	]	]	PUNCT
bracis-19038	60	15	,	,	PUNCT
bracis-19038	60	16	denoted	denote	VERB
bracis-19038	60	17	by	by	ADP
bracis-19038	60	18	\(\varomega	\(\varomega	NOUN
bracis-19038	60	19	_	_	NOUN
bracis-19038	60	20	p(i)\	p(i)\	NOUN
bracis-19038	60	21	)	)	PUNCT
bracis-19038	60	22	,	,	PUNCT
bracis-19038	60	23	such	such	ADJ
bracis-19038	60	24	that	that	PRON
bracis-19038	60	25	for	for	ADP
bracis-19038	60	26	any	any	DET
bracis-19038	60	27	\(a	\(a	ADJ
bracis-19038	60	28	\in	\in	ADJ
bracis-19038	60	29	hb	hb	NOUN
bracis-19038	60	30	_	_	NOUN
bracis-19038	60	31	p\	p\	NOUN
bracis-19038	60	32	)	)	PUNCT
bracis-19038	60	33	\(a	\(a	NOUN
bracis-19038	60	34	\in	\in	PROPN
bracis-19038	60	35	\varomega	\varomega	PROPN
bracis-19038	60	36	_	_	NOUN
bracis-19038	60	37	p(i)\	p(i)\	NOUN
bracis-19038	60	38	)	)	PUNCT
bracis-19038	61	1	iff	iff	PROPN
bracis-19038	61	2	\(a	\(a	PROPN
bracis-19038	61	3	\leftarrow	\leftarrow	PROPN
bracis-19038	61	4	a_1	a_1	NOUN
bracis-19038	61	5	,	,	PUNCT
bracis-19038	61	6	\ldots	\ldots	PROPN
bracis-19038	61	7	,	,	PUNCT
bracis-19038	61	8	a_m	a_m	ADP
bracis-19038	61	9	\in	\in	PROPN
bracis-19038	61	10	p	p	PROPN
bracis-19038	61	11	/	/	SYM
bracis-19038	61	12	i\	i\	NOUN
bracis-19038	61	13	)	)	PUNCT
bracis-19038	61	14	and	and	CCONJ
bracis-19038	61	15	\(\left\	\(\left\	NOUN
bracis-19038	61	16	{	{	PUNCT
bracis-19038	61	17	a_1	a_1	NOUN
bracis-19038	61	18	,	,	PUNCT
bracis-19038	61	19	\ldots	\ldots	INTJ
bracis-19038	61	20	,	,	PUNCT
bracis-19038	61	21	a_m\right\	a_m\right\	ADJ
bracis-19038	61	22	}	}	PUNCT
bracis-19038	61	23	\subseteq	\subseteq	PROPN
bracis-19038	61	24	\varomega	\varomega	NOUN
bracis-19038	61	25	_	_	NOUN
bracis-19038	61	26	p(i)\	p(i)\	NOUN
bracis-19038	61	27	)	)	PUNCT
bracis-19038	61	28	;	;	PUNCT
bracis-19038	61	29	\(\mathtt	\(\mathtt	NOUN
bracis-19038	61	30	{	{	PUNCT
bracis-19038	61	31	not\	not\	PROPN
bracis-19038	61	32	}	}	PUNCT
bracis-19038	61	33	a	a	DET
bracis-19038	61	34	\in	\in	PROPN
bracis-19038	61	35	\varomega	\varomega	PROPN
bracis-19038	61	36	_	_	NOUN
bracis-19038	61	37	p(i)\	p(i)\	NOUN
bracis-19038	61	38	)	)	PUNCT
bracis-19038	61	39	iff	iff	NOUN
bracis-19038	61	40	for	for	ADP
bracis-19038	61	41	every	every	DET
bracis-19038	61	42	\(a	\(a	NOUN
bracis-19038	61	43	\leftarrow	\leftarrow	PROPN
bracis-19038	61	44	a_1	a_1	NOUN
bracis-19038	61	45	,	,	PUNCT
bracis-19038	61	46	\ldots	\ldots	PROPN
bracis-19038	61	47	,	,	PUNCT
bracis-19038	61	48	a_m	a_m	ADP
bracis-19038	61	49	\in	\in	PROPN
bracis-19038	61	50	p	p	PROPN
bracis-19038	61	51	/	/	SYM
bracis-19038	61	52	i\	i\	NOUN
bracis-19038	61	53	)	)	PUNCT
bracis-19038	61	54	,	,	PUNCT
bracis-19038	61	55	it	it	PRON
bracis-19038	61	56	holds	hold	VERB
bracis-19038	61	57	\(\{\mathtt	\(\{\mathtt	NOUN
bracis-19038	61	58	{	{	PUNCT
bracis-19038	61	59	not\	not\	PROPN
bracis-19038	61	60	}	}	PUNCT
bracis-19038	61	61	a_1	a_1	PROPN
bracis-19038	61	62	,	,	PUNCT
bracis-19038	61	63	\ldots	\ldots	PROPN
bracis-19038	61	64	,	,	PUNCT
bracis-19038	61	65	\	\	ADJ
bracis-19038	61	66	)	)	PUNCT
bracis-19038	61	67	\(\mathtt	\(\mathtt	VERB
bracis-19038	61	68	{	{	PUNCT
bracis-19038	61	69	not\	not\	PROPN
bracis-19038	61	70	}	}	PUNCT
bracis-19038	61	71	a_m	a_m	VERB
bracis-19038	61	72	\	\	ADJ
bracis-19038	61	73	}	}	PUNCT
bracis-19038	61	74	\cap	\cap	VERB
bracis-19038	61	75	\varomega	\varomega	PROPN
bracis-19038	61	76	_	_	PUNCT
bracis-19038	62	1	p(i	p(i	X
bracis-19038	62	2	)	)	PUNCT
bracis-19038	63	1	\ne	\ne	PROPN
bracis-19038	63	2	\emptyset	\emptyset	VERB
bracis-19038	63	3	\	\	NOUN
bracis-19038	63	4	)	)	PUNCT
bracis-19038	63	5	.	.	PUNCT
bracis-19038	64	1	we	we	PRON
bracis-19038	64	2	now	now	ADV
bracis-19038	64	3	specify	specify	VERB
bracis-19038	64	4	the	the	DET
bracis-19038	64	5	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	64	6	)	)	PUNCT
bracis-19038	64	7	semantics	semantic	NOUN
bracis-19038	64	8	to	to	PART
bracis-19038	64	9	be	be	AUX
bracis-19038	64	10	examined	examine	VERB
bracis-19038	64	11	in	in	ADP
bracis-19038	64	12	this	this	DET
bracis-19038	64	13	paper	paper	NOUN
bracis-19038	64	14	.	.	PUNCT
bracis-19038	65	1	definition	definition	NOUN
bracis-19038	65	2	3	3	NUM
bracis-19038	65	3	let	let	VERB
bracis-19038	65	4	p	p	PRON
bracis-19038	65	5	be	be	AUX
bracis-19038	65	6	an	an	DET
bracis-19038	65	7	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	65	8	)	)	PUNCT
bracis-19038	65	9	and	and	CCONJ
bracis-19038	65	10	i	i	PRON
bracis-19038	65	11	be	be	VERB
bracis-19038	65	12	an	an	DET
bracis-19038	65	13	interpretation	interpretation	NOUN
bracis-19038	65	14	:	:	PUNCT
bracis-19038	65	15	i	i	PRON
bracis-19038	65	16	is	be	AUX
bracis-19038	65	17	a	a	DET
bracis-19038	65	18	partial	partial	ADJ
bracis-19038	65	19	stable	stable	NOUN
bracis-19038	65	20	(	(	PUNCT
bracis-19038	65	21	\	\	PROPN
bracis-19038	65	22	(	(	PUNCT
bracis-19038	65	23	ps	ps	NOUN
bracis-19038	65	24	\	\	PROPN
bracis-19038	65	25	)	)	PUNCT
bracis-19038	65	26	)	)	PUNCT
bracis-19038	65	27	model	model	NOUN
bracis-19038	65	28	of	of	ADP
bracis-19038	65	29	p	p	X
bracis-19038	65	30	iff	iff	PROPN
bracis-19038	65	31	\(i	\(i	NOUN
bracis-19038	65	32	=	=	PUNCT
bracis-19038	65	33	\varomega	\varomega	X
bracis-19038	65	34	_	_	NOUN
bracis-19038	65	35	p(i)\	p(i)\	NOUN
bracis-19038	65	36	)	)	PUNCT
bracis-19038	66	1	[	[	X
bracis-19038	66	2	14	14	NUM
bracis-19038	66	3	]	]	PUNCT
bracis-19038	66	4	.	.	PUNCT
bracis-19038	67	1	i	i	PRON
bracis-19038	67	2	is	be	AUX
bracis-19038	67	3	a	a	DET
bracis-19038	67	4	well	well	ADV
bracis-19038	67	5	-	-	PUNCT
bracis-19038	67	6	founded	found	VERB
bracis-19038	67	7	model	model	NOUN
bracis-19038	67	8	of	of	ADP
bracis-19038	67	9	p	p	PROPN
bracis-19038	67	10	iff	iff	PROPN
bracis-19038	67	11	i	i	PRON
bracis-19038	67	12	is	be	AUX
bracis-19038	67	13	a	a	DET
bracis-19038	67	14	\	\	PROPN
bracis-19038	67	15	(	(	PUNCT
bracis-19038	67	16	ps	ps	PROPN
bracis-19038	67	17	\	\	ADJ
bracis-19038	67	18	)	)	PUNCT
bracis-19038	67	19	model	model	NOUN
bracis-19038	67	20	of	of	ADP
bracis-19038	67	21	p	p	NOUN
bracis-19038	67	22	with	with	ADP
bracis-19038	67	23	minimal	minimal	ADJ
bracis-19038	67	24	\(t_i\	\(t_i\	NOUN
bracis-19038	67	25	)	)	PUNCT
bracis-19038	68	1	[	[	X
bracis-19038	68	2	14	14	NUM
bracis-19038	68	3	]	]	PUNCT
bracis-19038	68	4	.	.	PUNCT
bracis-19038	69	1	i	i	PRON
bracis-19038	69	2	is	be	AUX
bracis-19038	69	3	a	a	DET
bracis-19038	69	4	regular	regular	ADJ
bracis-19038	69	5	model	model	NOUN
bracis-19038	69	6	of	of	ADP
bracis-19038	69	7	p	p	PROPN
bracis-19038	69	8	iff	iff	PROPN
bracis-19038	69	9	i	i	PRON
bracis-19038	69	10	is	be	AUX
bracis-19038	69	11	a	a	DET
bracis-19038	69	12	\	\	PROPN
bracis-19038	69	13	(	(	PUNCT
bracis-19038	69	14	ps	ps	PROPN
bracis-19038	69	15	\	\	ADJ
bracis-19038	69	16	)	)	PUNCT
bracis-19038	69	17	model	model	NOUN
bracis-19038	69	18	of	of	ADP
bracis-19038	69	19	p	p	NOUN
bracis-19038	69	20	with	with	ADP
bracis-19038	69	21	maximal	maximal	ADJ
bracis-19038	69	22	\(t_i\	\(t_i\	NOUN
bracis-19038	69	23	)	)	PUNCT
bracis-19038	70	1	[	[	X
bracis-19038	70	2	15	15	NUM
bracis-19038	70	3	]	]	PUNCT
bracis-19038	70	4	.	.	PUNCT
bracis-19038	71	1	i	i	PRON
bracis-19038	71	2	is	be	AUX
bracis-19038	71	3	a	a	DET
bracis-19038	71	4	stable	stable	ADJ
bracis-19038	71	5	model	model	NOUN
bracis-19038	71	6	of	of	ADP
bracis-19038	71	7	p	p	PROPN
bracis-19038	71	8	iff	iff	PROPN
bracis-19038	71	9	i	i	PRON
bracis-19038	71	10	is	be	AUX
bracis-19038	71	11	a	a	DET
bracis-19038	71	12	\	\	PROPN
bracis-19038	71	13	(	(	PUNCT
bracis-19038	71	14	ps	ps	PROPN
bracis-19038	71	15	\	\	ADJ
bracis-19038	71	16	)	)	PUNCT
bracis-19038	71	17	model	model	NOUN
bracis-19038	71	18	of	of	ADP
bracis-19038	71	19	p	p	PRON
bracis-19038	71	20	where	where	SCONJ
bracis-19038	71	21	for	for	ADP
bracis-19038	71	22	each	each	DET
bracis-19038	71	23	\(a	\(a	NOUN
bracis-19038	71	24	\in	\in	NOUN
bracis-19038	71	25	hb	hb	NOUN
bracis-19038	71	26	_	_	NOUN
bracis-19038	71	27	p\	p\	NOUN
bracis-19038	71	28	)	)	PUNCT
bracis-19038	71	29	,	,	PUNCT
bracis-19038	71	30	\(a	\(a	NOUN
bracis-19038	71	31	\in	\in	PROPN
bracis-19038	71	32	t_i	t_i	PART
bracis-19038	71	33	\cup	\cup	VERB
bracis-19038	71	34	f_i\	f_i\	NOUN
bracis-19038	71	35	)	)	PUNCT
bracis-19038	72	1	[	[	X
bracis-19038	72	2	14	14	NUM
bracis-19038	72	3	]	]	PUNCT
bracis-19038	72	4	.	.	PUNCT
bracis-19038	73	1	i	i	PRON
bracis-19038	73	2	is	be	AUX
bracis-19038	73	3	an	an	DET
bracis-19038	73	4	l	l	ADJ
bracis-19038	73	5	-	-	ADJ
bracis-19038	73	6	stable	stable	ADJ
bracis-19038	73	7	model	model	NOUN
bracis-19038	73	8	of	of	ADP
bracis-19038	73	9	p	p	PROPN
bracis-19038	73	10	iff	iff	PROPN
bracis-19038	73	11	i	i	PRON
bracis-19038	73	12	is	be	AUX
bracis-19038	73	13	a	a	DET
bracis-19038	73	14	\	\	PROPN
bracis-19038	73	15	(	(	PUNCT
bracis-19038	73	16	ps	ps	PROPN
bracis-19038	73	17	\	\	ADJ
bracis-19038	73	18	)	)	PUNCT
bracis-19038	73	19	model	model	NOUN
bracis-19038	73	20	of	of	ADP
bracis-19038	73	21	p	p	NOUN
bracis-19038	73	22	with	with	ADP
bracis-19038	73	23	minimal	minimal	ADJ
bracis-19038	73	24	(	(	PUNCT
bracis-19038	73	25	w.r.t	w.r.t	NOUN
bracis-19038	73	26	.	.	PUNCT
bracis-19038	74	1	set	set	PROPN
bracis-19038	74	2	inclusion	inclusion	NOUN
bracis-19038	74	3	)	)	PUNCT
bracis-19038	75	1	\(\left\	\(\left\	PROPN
bracis-19038	75	2	{	{	PUNCT
bracis-19038	75	3	a	a	DET
bracis-19038	75	4	\in	\in	PROPN
bracis-19038	75	5	hb	hb	X
bracis-19038	75	6	_	_	PUNCT
bracis-19038	75	7	p\mid	p\mid	VERB
bracis-19038	75	8	a	a	DET
bracis-19038	75	9	\not	\not	ADV
bracis-19038	75	10	\in	\in	PROPN
bracis-19038	75	11	t_i	t_i	VERB
bracis-19038	75	12	\cup	\cup	VERB
bracis-19038	75	13	f_i\right\	f_i\right\	NOUN
bracis-19038	75	14	}	}	PUNCT
bracis-19038	75	15	\	\	NOUN
bracis-19038	75	16	)	)	PUNCT
bracis-19038	76	1	[	[	X
bracis-19038	76	2	15	15	NUM
bracis-19038	76	3	]	]	PUNCT
bracis-19038	76	4	.	.	PUNCT
bracis-19038	76	5	example	example	NOUN
bracis-19038	76	6	1	1	NUM
bracis-19038	76	7	consider	consider	VERB
bracis-19038	76	8	the	the	DET
bracis-19038	76	9	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	76	10	)	)	PUNCT
bracis-19038	77	1	p	p	X
bracis-19038	77	2	:	:	PUNCT
bracis-19038	77	3	$	$	SYM
bracis-19038	77	4	$	$	SYM
bracis-19038	77	5	\begin{array}{lllll	\begin{array}{lllll	NOUN
bracis-19038	77	6	}	}	PUNCT
bracis-19038	77	7	a	a	DET
bracis-19038	77	8	\leftarrow	\leftarrow	PROPN
bracis-19038	77	9	\mathtt	\mathtt	PROPN
bracis-19038	77	10	{	{	PUNCT
bracis-19038	77	11	not\	not\	PROPN
bracis-19038	77	12	}	}	PUNCT
bracis-19038	77	13	b	b	NOUN
bracis-19038	77	14	\quad&b	\quad&b	NOUN
bracis-19038	77	15	\leftarrow	\leftarrow	VERB
bracis-19038	77	16	\mathtt	\mathtt	PROPN
bracis-19038	77	17	{	{	PUNCT
bracis-19038	77	18	not\	not\	PROPN
bracis-19038	77	19	}	}	PUNCT
bracis-19038	77	20	a	a	X
bracis-19038	77	21	,	,	PUNCT
bracis-19038	77	22	\mathtt	\mathtt	PROPN
bracis-19038	77	23	{	{	PUNCT
bracis-19038	77	24	not\	not\	PROPN
bracis-19038	77	25	}	}	PUNCT
bracis-19038	77	26	c	c	PROPN
bracis-19038	77	27	\quad&c	\quad&c	NOUN
bracis-19038	77	28	\leftarrow	\leftarrow	VERB
bracis-19038	77	29	\mathtt	\mathtt	PROPN
bracis-19038	77	30	{	{	PUNCT
bracis-19038	77	31	not\	not\	PROPN
bracis-19038	77	32	}	}	PUNCT
bracis-19038	77	33	b	b	PROPN
bracis-19038	77	34	,	,	PUNCT
bracis-19038	77	35	\mathtt	\mathtt	PROPN
bracis-19038	77	36	{	{	PUNCT
bracis-19038	77	37	not\	not\	PROPN
bracis-19038	77	38	}	}	PUNCT
bracis-19038	77	39	d	d	PROPN
bracis-19038	77	40	\quad&c	\quad&c	SCONJ
bracis-19038	77	41	\leftarrow	\leftarrow	VERB
bracis-19038	77	42	\mathtt	\mathtt	PROPN
bracis-19038	77	43	{	{	PUNCT
bracis-19038	77	44	not\	not\	PROPN
bracis-19038	77	45	}	}	PUNCT
bracis-19038	77	46	c	c	NOUN
bracis-19038	77	47	\quad&d	\quad&d	NOUN
bracis-19038	77	48	\leftarrow	\leftarrow	VERB
bracis-19038	77	49	\mathtt	\mathtt	PROPN
bracis-19038	77	50	{	{	PUNCT
bracis-19038	77	51	not\	not\	PROPN
bracis-19038	77	52	}	}	PUNCT
bracis-19038	77	53	c	c	NOUN
bracis-19038	77	54	\end{array	\end{array	ADV
bracis-19038	77	55	}	}	PUNCT
bracis-19038	77	56	$	$	SYM
bracis-19038	77	57	$	$	SYM
bracis-19038	77	58	with	with	ADP
bracis-19038	77	59	respect	respect	NOUN
bracis-19038	77	60	to	to	ADP
bracis-19038	77	61	p	p	PRON
bracis-19038	77	62	,	,	PUNCT
bracis-19038	77	63	we	we	PRON
bracis-19038	77	64	have	have	VERB
bracis-19038	77	65	a	a	DET
bracis-19038	77	66	)	)	PUNCT
bracis-19038	77	67	partial	partial	ADJ
bracis-19038	77	68	stable	stable	ADJ
bracis-19038	77	69	models	model	NOUN
bracis-19038	77	70	:	:	PUNCT
bracis-19038	77	71	\(i_1	\(i_1	NUM
bracis-19038	77	72	=	=	SYM
bracis-19038	77	73	\emptyset	\emptyset	VERB
bracis-19038	77	74	\	\	NOUN
bracis-19038	77	75	)	)	PUNCT
bracis-19038	77	76	,	,	PUNCT
bracis-19038	78	1	\(i_2	\(i_2	PROPN
bracis-19038	78	2	=	=	SYM
bracis-19038	78	3	\left\	\left\	PROPN
bracis-19038	78	4	{	{	PUNCT
bracis-19038	78	5	a	a	X
bracis-19038	78	6	,	,	PUNCT
bracis-19038	78	7	\mathtt	\mathtt	PROPN
bracis-19038	78	8	{	{	PUNCT
bracis-19038	78	9	not\	not\	PROPN
bracis-19038	78	10	}	}	PUNCT
bracis-19038	78	11	b\right\	b\right\	NOUN
bracis-19038	78	12	}	}	PUNCT
bracis-19038	78	13	\	\	PROPN
bracis-19038	78	14	)	)	PUNCT
bracis-19038	78	15	,	,	PUNCT
bracis-19038	78	16	\(i_3	\(i_3	PROPN
bracis-19038	78	17	=	=	SYM
bracis-19038	78	18	\left\	\left\	PROPN
bracis-19038	78	19	{	{	PUNCT
bracis-19038	78	20	d\right\	d\right\	NOUN
bracis-19038	78	21	}	}	PUNCT
bracis-19038	78	22	\	\	NOUN
bracis-19038	78	23	)	)	PUNCT
bracis-19038	78	24	,	,	PUNCT
bracis-19038	78	25	\(i_4	\(i_4	PROPN
bracis-19038	78	26	=	=	SYM
bracis-19038	78	27	\{b	\{b	PROPN
bracis-19038	78	28	,	,	PUNCT
bracis-19038	78	29	d	d	X
bracis-19038	78	30	,	,	PUNCT
bracis-19038	78	31	\mathtt	\mathtt	PROPN
bracis-19038	78	32	{	{	PUNCT
bracis-19038	78	33	not\	not\	PROPN
bracis-19038	78	34	}	}	PUNCT
bracis-19038	78	35	a	a	DET
bracis-19038	78	36	\}\	\}\	NOUN
bracis-19038	78	37	)	)	PUNCT
bracis-19038	78	38	,	,	PUNCT
bracis-19038	78	39	\(i_5	\(i_5	PROPN
bracis-19038	78	40	=	=	SYM
bracis-19038	78	41	\left\	\left\	PROPN
bracis-19038	78	42	{	{	PUNCT
bracis-19038	78	43	a	a	X
bracis-19038	78	44	,	,	PUNCT
bracis-19038	78	45	c	c	X
bracis-19038	78	46	,	,	PUNCT
bracis-19038	78	47	\mathtt	\mathtt	PROPN
bracis-19038	78	48	{	{	PUNCT
bracis-19038	78	49	not\	not\	PROPN
bracis-19038	78	50	}	}	PUNCT
bracis-19038	78	51	b	b	PROPN
bracis-19038	78	52	,	,	PUNCT
bracis-19038	78	53	\mathtt	\mathtt	PROPN
bracis-19038	78	54	{	{	PUNCT
bracis-19038	78	55	not\	not\	PROPN
bracis-19038	78	56	}	}	PUNCT
bracis-19038	78	57	d\right\	d\right\	NOUN
bracis-19038	78	58	}	}	PUNCT
bracis-19038	78	59	\	\	NOUN
bracis-19038	78	60	)	)	PUNCT
bracis-19038	78	61	and	and	CCONJ
bracis-19038	78	62	\(i_6	\(i_6	PROPN
bracis-19038	78	63	=	=	SYM
bracis-19038	78	64	\left\	\left\	PROPN
bracis-19038	78	65	{	{	PUNCT
bracis-19038	78	66	a	a	PRON
bracis-19038	78	67	,	,	PUNCT
bracis-19038	78	68	d	d	PROPN
bracis-19038	78	69	,	,	PUNCT
bracis-19038	78	70	\mathtt	\mathtt	PROPN
bracis-19038	78	71	{	{	PUNCT
bracis-19038	78	72	not\	not\	PROPN
bracis-19038	78	73	}	}	PUNCT
bracis-19038	78	74	b\right\	b\right\	NOUN
bracis-19038	78	75	}	}	PUNCT
bracis-19038	78	76	\	\	PROPN
bracis-19038	78	77	)	)	PUNCT
bracis-19038	78	78	;	;	PUNCT
bracis-19038	78	79	b	b	X
bracis-19038	78	80	)	)	PUNCT
bracis-19038	78	81	well	well	ADV
bracis-19038	78	82	-	-	PUNCT
bracis-19038	78	83	founded	found	VERB
bracis-19038	78	84	model	model	NOUN
bracis-19038	78	85	:	:	PUNCT
bracis-19038	78	86	\(i_0\	\(i_0\	NOUN
bracis-19038	78	87	)	)	PUNCT
bracis-19038	78	88	;	;	PUNCT
bracis-19038	78	89	c	c	X
bracis-19038	78	90	)	)	PUNCT
bracis-19038	78	91	regular	regular	ADJ
bracis-19038	78	92	models	model	NOUN
bracis-19038	78	93	:	:	PUNCT
bracis-19038	78	94	\(i_4\	\(i_4\	ADJ
bracis-19038	78	95	)	)	PUNCT
bracis-19038	78	96	,	,	PUNCT
bracis-19038	78	97	\(i_5\	\(i_5\	ADJ
bracis-19038	78	98	)	)	PUNCT
bracis-19038	78	99	and	and	CCONJ
bracis-19038	78	100	\(i_6\	\(i_6\	PROPN
bracis-19038	78	101	)	)	PUNCT
bracis-19038	78	102	;	;	PUNCT
bracis-19038	78	103	d	d	X
bracis-19038	78	104	)	)	PUNCT
bracis-19038	78	105	stable	stable	ADJ
bracis-19038	78	106	model	model	NOUN
bracis-19038	78	107	and	and	CCONJ
bracis-19038	78	108	l	l	ADJ
bracis-19038	78	109	-	-	ADJ
bracis-19038	78	110	stable	stable	ADJ
bracis-19038	78	111	model	model	NOUN
bracis-19038	78	112	:	:	PUNCT
bracis-19038	78	113	\(i_5\	\(i_5\	ADJ
bracis-19038	78	114	)	)	PUNCT
bracis-19038	78	115	.	.	PUNCT
bracis-19038	79	1	in	in	ADP
bracis-19038	79	2	the	the	DET
bracis-19038	79	3	next	next	ADJ
bracis-19038	79	4	section	section	NOUN
bracis-19038	79	5	,	,	PUNCT
bracis-19038	79	6	we	we	PRON
bracis-19038	79	7	will	will	AUX
bracis-19038	79	8	offer	offer	VERB
bracis-19038	79	9	a	a	DET
bracis-19038	79	10	comprehensive	comprehensive	ADJ
bracis-19038	79	11	and	and	CCONJ
bracis-19038	79	12	systematic	systematic	ADJ
bracis-19038	79	13	treatment	treatment	NOUN
bracis-19038	79	14	to	to	PART
bracis-19038	79	15	deal	deal	VERB
bracis-19038	79	16	with	with	ADP
bracis-19038	79	17	preferences	preference	NOUN
bracis-19038	79	18	in	in	ADP
bracis-19038	79	19	logic	logic	NOUN
bracis-19038	79	20	programming	programming	NOUN
bracis-19038	79	21	.	.	PUNCT
bracis-19038	80	1	3	3	NUM
bracis-19038	80	2	semantics	semantic	NOUN
bracis-19038	80	3	for	for	ADP
bracis-19038	80	4	prioritised	prioritise	VERB
bracis-19038	80	5	logic	logic	NOUN
bracis-19038	80	6	programs	program	NOUN
bracis-19038	80	7	the	the	DET
bracis-19038	80	8	semantics	semantic	NOUN
bracis-19038	80	9	of	of	ADP
bracis-19038	80	10	normal	normal	ADJ
bracis-19038	80	11	logic	logic	NOUN
bracis-19038	80	12	programs	program	NOUN
bracis-19038	80	13	seen	see	VERB
bracis-19038	80	14	in	in	ADP
bracis-19038	80	15	definition	definition	NOUN
bracis-19038	80	16	3	3	NUM
bracis-19038	80	17	have	have	VERB
bracis-19038	80	18	multiple	multiple	ADJ
bracis-19038	80	19	models	model	NOUN
bracis-19038	80	20	in	in	ADP
bracis-19038	80	21	general	general	ADJ
bracis-19038	80	22	.	.	PUNCT
bracis-19038	81	1	preference	preference	NOUN
bracis-19038	81	2	is	be	AUX
bracis-19038	81	3	then	then	ADV
bracis-19038	81	4	introduced	introduce	VERB
bracis-19038	81	5	to	to	PART
bracis-19038	81	6	select	select	VERB
bracis-19038	81	7	among	among	ADP
bracis-19038	81	8	them	they	PRON
bracis-19038	81	9	the	the	DET
bracis-19038	81	10	intended	intend	VERB
bracis-19038	81	11	models	model	NOUN
bracis-19038	81	12	of	of	ADP
bracis-19038	81	13	a	a	DET
bracis-19038	81	14	program	program	NOUN
bracis-19038	81	15	,	,	PUNCT
bracis-19038	81	16	but	but	CCONJ
bracis-19038	81	17	at	at	ADP
bracis-19038	81	18	the	the	DET
bracis-19038	81	19	semantic	semantic	ADJ
bracis-19038	81	20	level	level	NOUN
bracis-19038	81	21	.	.	PUNCT
bracis-19038	82	1	in	in	ADP
bracis-19038	82	2	[	[	X
bracis-19038	82	3	4	4	NUM
bracis-19038	82	4	]	]	PUNCT
bracis-19038	82	5	,	,	PUNCT
bracis-19038	82	6	they	they	PRON
bracis-19038	82	7	conceived	conceive	VERB
bracis-19038	82	8	the	the	DET
bracis-19038	82	9	notion	notion	NOUN
bracis-19038	82	10	of	of	ADP
bracis-19038	82	11	prioritised	prioritised	ADJ
bracis-19038	82	12	logic	logic	NOUN
bracis-19038	82	13	programs	program	NOUN
bracis-19038	82	14	(	(	PUNCT
bracis-19038	82	15	\(\textit{plp}\)s	\(\textit{plp}\)s	PROPN
bracis-19038	82	16	)	)	PUNCT
bracis-19038	82	17	by	by	ADP
bracis-19038	82	18	establishing	establish	VERB
bracis-19038	82	19	a	a	DET
bracis-19038	82	20	prioritisation	prioritisation	NOUN
bracis-19038	82	21	mechanism	mechanism	NOUN
bracis-19038	82	22	between	between	ADP
bracis-19038	82	23	literals	literal	NOUN
bracis-19038	82	24	(	(	PUNCT
bracis-19038	82	25	atoms	atom	NOUN
bracis-19038	82	26	or	or	CCONJ
bracis-19038	82	27	its	its	PRON
bracis-19038	82	28	negation	negation	NOUN
bracis-19038	82	29	)	)	PUNCT
bracis-19038	82	30	to	to	PART
bracis-19038	82	31	represent	represent	VERB
bracis-19038	82	32	and	and	CCONJ
bracis-19038	82	33	reason	reason	NOUN
bracis-19038	82	34	with	with	ADP
bracis-19038	82	35	preferences	preference	NOUN
bracis-19038	82	36	in	in	ADP
bracis-19038	82	37	logic	logic	NOUN
bracis-19038	82	38	programming	programming	NOUN
bracis-19038	82	39	at	at	ADP
bracis-19038	82	40	the	the	DET
bracis-19038	82	41	syntactic	syntactic	ADJ
bracis-19038	82	42	level	level	NOUN
bracis-19038	82	43	.	.	PUNCT
bracis-19038	83	1	here	here	ADV
bracis-19038	83	2	we	we	PRON
bracis-19038	83	3	generalise	generalise	VERB
bracis-19038	83	4	this	this	DET
bracis-19038	83	5	notion	notion	NOUN
bracis-19038	83	6	of	of	ADP
bracis-19038	83	7	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	83	8	)	)	PUNCT
bracis-19038	83	9	to	to	PART
bracis-19038	83	10	encompass	encompass	VERB
bracis-19038	83	11	not	not	PART
bracis-19038	83	12	only	only	ADV
bracis-19038	83	13	the	the	DET
bracis-19038	83	14	relation	relation	NOUN
bracis-19038	83	15	of	of	ADP
bracis-19038	83	16	priority	priority	NOUN
bracis-19038	83	17	between	between	ADP
bracis-19038	83	18	literals	literal	NOUN
bracis-19038	83	19	,	,	PUNCT
bracis-19038	83	20	but	but	CCONJ
bracis-19038	83	21	also	also	ADV
bracis-19038	83	22	sets	set	VERB
bracis-19038	83	23	of	of	ADP
bracis-19038	83	24	literals	literal	NOUN
bracis-19038	83	25	.	.	PUNCT
bracis-19038	84	1	the	the	DET
bracis-19038	84	2	idea	idea	NOUN
bracis-19038	84	3	is	be	AUX
bracis-19038	84	4	to	to	PART
bracis-19038	84	5	employ	employ	VERB
bracis-19038	84	6	these	these	DET
bracis-19038	84	7	priorities	priority	NOUN
bracis-19038	84	8	to	to	PART
bracis-19038	84	9	select	select	VERB
bracis-19038	84	10	the	the	DET
bracis-19038	84	11	most	most	ADV
bracis-19038	84	12	preferable	preferable	ADJ
bracis-19038	84	13	partial	partial	ADJ
bracis-19038	84	14	stable	stable	ADJ
bracis-19038	84	15	models	model	NOUN
bracis-19038	84	16	.	.	PUNCT
bracis-19038	85	1	we	we	PRON
bracis-19038	85	2	will	will	AUX
bracis-19038	85	3	focus	focus	VERB
bracis-19038	85	4	on	on	ADP
bracis-19038	85	5	partial	partial	ADJ
bracis-19038	85	6	stable	stable	ADJ
bracis-19038	85	7	models	model	NOUN
bracis-19038	85	8	,	,	PUNCT
bracis-19038	85	9	because	because	SCONJ
bracis-19038	85	10	it	it	PRON
bracis-19038	85	11	is	be	AUX
bracis-19038	85	12	the	the	DET
bracis-19038	85	13	base	base	NOUN
bracis-19038	85	14	to	to	PART
bracis-19038	85	15	define	define	VERB
bracis-19038	85	16	the	the	DET
bracis-19038	85	17	remaining	remain	VERB
bracis-19038	85	18	semantics	semantic	NOUN
bracis-19038	85	19	in	in	ADP
bracis-19038	85	20	definition	definition	NOUN
bracis-19038	85	21	3	3	NUM
bracis-19038	85	22	.	.	PUNCT
bracis-19038	86	1	in	in	ADP
bracis-19038	86	2	this	this	DET
bracis-19038	86	3	work	work	NOUN
bracis-19038	86	4	,	,	PUNCT
bracis-19038	86	5	the	the	DET
bracis-19038	86	6	priorities	priority	NOUN
bracis-19038	86	7	will	will	AUX
bracis-19038	86	8	be	be	AUX
bracis-19038	86	9	established	establish	VERB
bracis-19038	86	10	between	between	ADP
bracis-19038	86	11	sets	set	NOUN
bracis-19038	86	12	of	of	ADP
bracis-19038	86	13	literals	literal	NOUN
bracis-19038	86	14	,	,	PUNCT
bracis-19038	86	15	which	which	PRON
bracis-19038	86	16	we	we	PRON
bracis-19038	86	17	will	will	AUX
bracis-19038	86	18	be	be	AUX
bracis-19038	86	19	called	call	VERB
bracis-19038	86	20	as	as	ADP
bracis-19038	86	21	options	option	NOUN
bracis-19038	86	22	:	:	PUNCT
bracis-19038	86	23	definition	definition	NOUN
bracis-19038	86	24	4	4	NUM
bracis-19038	86	25	(	(	PUNCT
bracis-19038	86	26	options	option	NOUN
bracis-19038	86	27	)	)	PUNCT
bracis-19038	86	28	given	give	VERB
bracis-19038	86	29	an	an	DET
bracis-19038	86	30	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	86	31	)	)	PUNCT
bracis-19038	86	32	p	p	NOUN
bracis-19038	86	33	,	,	PUNCT
bracis-19038	86	34	an	an	DET
bracis-19038	86	35	option	option	NOUN
bracis-19038	86	36	o	o	NOUN
bracis-19038	86	37	from	from	ADP
bracis-19038	86	38	p	p	NOUN
bracis-19038	86	39	is	be	AUX
bracis-19038	86	40	a	a	DET
bracis-19038	86	41	subset	subset	NOUN
bracis-19038	86	42	of	of	ADP
bracis-19038	86	43	\	\	PROPN
bracis-19038	86	44	(	(	PUNCT
bracis-19038	86	45	lit	light	VERB
bracis-19038	86	46	_	_	PRON
bracis-19038	86	47	p\	p\	NOUN
bracis-19038	86	48	)	)	PUNCT
bracis-19038	86	49	.	.	PUNCT
bracis-19038	87	1	by	by	ADP
bracis-19038	87	2	\(\mathcal	\(\mathcal	ADJ
bracis-19038	87	3	{	{	PUNCT
bracis-19038	87	4	o}_p\	o}_p\	NOUN
bracis-19038	87	5	)	)	PUNCT
bracis-19038	87	6	we	we	PRON
bracis-19038	87	7	mean	mean	VERB
bracis-19038	87	8	the	the	DET
bracis-19038	87	9	set	set	NOUN
bracis-19038	87	10	of	of	ADP
bracis-19038	87	11	all	all	DET
bracis-19038	87	12	options	option	NOUN
bracis-19038	87	13	from	from	ADP
bracis-19038	87	14	p.	p.	NOUN
bracis-19038	87	15	we	we	PRON
bracis-19038	87	16	say	say	VERB
bracis-19038	87	17	o	o	NOUN
bracis-19038	87	18	is	be	AUX
bracis-19038	87	19	inconsistent	inconsistent	ADJ
bracis-19038	87	20	,	,	PUNCT
bracis-19038	87	21	if	if	SCONJ
bracis-19038	87	22	there	there	PRON
bracis-19038	87	23	is	be	VERB
bracis-19038	87	24	\(a	\(a	ADJ
bracis-19038	87	25	\in	\in	PROPN
bracis-19038	87	26	hb	hb	NOUN
bracis-19038	87	27	_	_	PUNCT
bracis-19038	87	28	p\	p\	NOUN
bracis-19038	87	29	)	)	PUNCT
bracis-19038	87	30	such	such	ADJ
bracis-19038	87	31	that	that	PRON
bracis-19038	87	32	\(\left\	\(\left\	PROPN
bracis-19038	87	33	{	{	PUNCT
bracis-19038	87	34	a,\mathtt	a,\mathtt	PROPN
bracis-19038	87	35	{	{	PUNCT
bracis-19038	87	36	not\	not\	PROPN
bracis-19038	87	37	}	}	PUNCT
bracis-19038	87	38	a\right\	a\right\	PROPN
bracis-19038	87	39	}	}	PUNCT
bracis-19038	87	40	\subseteq	\subseteq	PROPN
bracis-19038	87	41	o\	o\	NOUN
bracis-19038	87	42	)	)	PUNCT
bracis-19038	87	43	.	.	PUNCT
bracis-19038	88	1	otherwise	otherwise	ADV
bracis-19038	88	2	,	,	PUNCT
bracis-19038	88	3	o	o	NOUN
bracis-19038	88	4	is	be	AUX
bracis-19038	88	5	consistent	consistent	ADJ
bracis-19038	88	6	.	.	PUNCT
bracis-19038	89	1	thus	thus	ADV
bracis-19038	89	2	in	in	ADP
bracis-19038	89	3	a	a	DET
bracis-19038	89	4	program	program	NOUN
bracis-19038	89	5	representing	represent	VERB
bracis-19038	89	6	a	a	DET
bracis-19038	89	7	menu	menu	NOUN
bracis-19038	89	8	based	base	VERB
bracis-19038	89	9	on	on	ADP
bracis-19038	89	10	fish	fish	NOUN
bracis-19038	89	11	(	(	PUNCT
bracis-19038	89	12	f	f	X
bracis-19038	89	13	)	)	PUNCT
bracis-19038	89	14	,	,	PUNCT
bracis-19038	89	15	meat	meat	NOUN
bracis-19038	89	16	m	m	PROPN
bracis-19038	89	17	,	,	PUNCT
bracis-19038	89	18	white	white	ADJ
bracis-19038	89	19	wine	wine	NOUN
bracis-19038	89	20	(	(	PUNCT
bracis-19038	89	21	w	w	NOUN
bracis-19038	89	22	)	)	PUNCT
bracis-19038	89	23	,	,	PUNCT
bracis-19038	89	24	red	red	ADJ
bracis-19038	89	25	wine	wine	NOUN
bracis-19038	89	26	(	(	PUNCT
bracis-19038	89	27	r	r	NOUN
bracis-19038	89	28	)	)	PUNCT
bracis-19038	89	29	,	,	PUNCT
bracis-19038	89	30	cake	cake	NOUN
bracis-19038	89	31	(	(	PUNCT
bracis-19038	89	32	c	c	NOUN
bracis-19038	89	33	)	)	PUNCT
bracis-19038	89	34	and	and	CCONJ
bracis-19038	89	35	ice	ice	NOUN
bracis-19038	89	36	cream	cream	NOUN
bracis-19038	89	37	(	(	PUNCT
bracis-19038	89	38	i	i	NOUN
bracis-19038	89	39	)	)	PUNCT
bracis-19038	89	40	,	,	PUNCT
bracis-19038	89	41	\(\left\	\(\left\	PROPN
bracis-19038	89	42	{	{	PUNCT
bracis-19038	89	43	f	f	X
bracis-19038	89	44	,	,	PUNCT
bracis-19038	89	45	\mathtt	\mathtt	PROPN
bracis-19038	89	46	{	{	PUNCT
bracis-19038	89	47	not\	not\	PROPN
bracis-19038	89	48	}	}	PUNCT
bracis-19038	89	49	m	m	PROPN
bracis-19038	89	50	,	,	PUNCT
bracis-19038	89	51	r\right\	r\right\	VERB
bracis-19038	89	52	}	}	PUNCT
bracis-19038	89	53	\	\	NOUN
bracis-19038	89	54	)	)	PUNCT
bracis-19038	89	55	,	,	PUNCT
bracis-19038	89	56	\(\left\	\(\left\	PROPN
bracis-19038	89	57	{	{	PUNCT
bracis-19038	89	58	i	i	NOUN
bracis-19038	89	59	,	,	PUNCT
bracis-19038	89	60	\mathtt	\mathtt	PROPN
bracis-19038	89	61	{	{	PUNCT
bracis-19038	89	62	not\	not\	PROPN
bracis-19038	89	63	}	}	PUNCT
bracis-19038	89	64	i\right\	i\right\	PROPN
bracis-19038	89	65	}	}	PUNCT
bracis-19038	89	66	\	\	NOUN
bracis-19038	89	67	)	)	PUNCT
bracis-19038	89	68	and	and	CCONJ
bracis-19038	89	69	\(\emptyset	\(\emptyset	NOUN
bracis-19038	89	70	\	\	NOUN
bracis-19038	89	71	)	)	PUNCT
bracis-19038	89	72	are	be	AUX
bracis-19038	89	73	possible	possible	ADJ
bracis-19038	89	74	options	option	NOUN
bracis-19038	89	75	.	.	PUNCT
bracis-19038	90	1	not	not	PART
bracis-19038	90	2	rarely	rarely	ADV
bracis-19038	90	3	,	,	PUNCT
bracis-19038	90	4	some	some	DET
bracis-19038	90	5	options	option	NOUN
bracis-19038	90	6	have	have	VERB
bracis-19038	90	7	a	a	DET
bracis-19038	90	8	higher	high	ADJ
bracis-19038	90	9	priority	priority	NOUN
bracis-19038	90	10	than	than	ADP
bracis-19038	90	11	others	other	NOUN
bracis-19038	90	12	:	:	PUNCT
bracis-19038	90	13	definition	definition	NOUN
bracis-19038	90	14	5	5	NUM
bracis-19038	90	15	(	(	PUNCT
bracis-19038	90	16	priorities	priority	NOUN
bracis-19038	90	17	)	)	PUNCT
bracis-19038	90	18	given	give	VERB
bracis-19038	90	19	an	an	DET
bracis-19038	90	20	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	90	21	)	)	PUNCT
bracis-19038	90	22	p	p	NOUN
bracis-19038	90	23	,	,	PUNCT
bracis-19038	90	24	a	a	DET
bracis-19038	90	25	reflexive	reflexive	ADJ
bracis-19038	90	26	and	and	CCONJ
bracis-19038	90	27	transitive	transitive	ADJ
bracis-19038	90	28	relation	relation	NOUN
bracis-19038	90	29	is	be	AUX
bracis-19038	90	30	defined	define	VERB
bracis-19038	90	31	on	on	ADP
bracis-19038	90	32	\(\mathcal	\(\mathcal	ADJ
bracis-19038	90	33	{	{	PUNCT
bracis-19038	90	34	o}_p\	o}_p\	NOUN
bracis-19038	90	35	)	)	PUNCT
bracis-19038	90	36	.	.	PUNCT
bracis-19038	91	1	for	for	ADP
bracis-19038	91	2	any	any	DET
bracis-19038	91	3	\(o_1\	\(o_1\	NOUN
bracis-19038	91	4	)	)	PUNCT
bracis-19038	91	5	and	and	CCONJ
bracis-19038	91	6	\(o_2\	\(o_2\	VERB
bracis-19038	91	7	)	)	PUNCT
bracis-19038	91	8	from	from	ADP
bracis-19038	91	9	\(\mathcal	\(\mathcal	ADJ
bracis-19038	91	10	{	{	PUNCT
bracis-19038	91	11	o}_p\	o}_p\	NOUN
bracis-19038	91	12	)	)	PUNCT
bracis-19038	91	13	,	,	PUNCT
bracis-19038	91	14	\(o_1	\(o_1	PROPN
bracis-19038	91	15	\preceq	\preceq	PROPN
bracis-19038	91	16	o_2\	o_2\	PROPN
bracis-19038	91	17	)	)	PUNCT
bracis-19038	91	18	is	be	AUX
bracis-19038	91	19	called	call	VERB
bracis-19038	91	20	a	a	DET
bracis-19038	91	21	priority	priority	NOUN
bracis-19038	91	22	,	,	PUNCT
bracis-19038	91	23	and	and	CCONJ
bracis-19038	91	24	we	we	PRON
bracis-19038	91	25	say	say	VERB
bracis-19038	91	26	\(o_2\	\(o_2\	VERB
bracis-19038	91	27	)	)	PUNCT
bracis-19038	91	28	has	have	VERB
bracis-19038	91	29	a	a	DET
bracis-19038	91	30	higher	high	ADJ
bracis-19038	91	31	or	or	CCONJ
bracis-19038	91	32	equal	equal	ADJ
bracis-19038	91	33	priority	priority	NOUN
bracis-19038	91	34	than	than	ADP
bracis-19038	91	35	\(o_1\	\(o_1\	NOUN
bracis-19038	91	36	)	)	PUNCT
bracis-19038	91	37	.	.	PUNCT
bracis-19038	92	1	we	we	PRON
bracis-19038	92	2	write	write	VERB
bracis-19038	92	3	\(o_1	\(o_1	PROPN
bracis-19038	92	4	\prec	\prec	PROPN
bracis-19038	92	5	o_2\	o_2\	PROPN
bracis-19038	92	6	)	)	PUNCT
bracis-19038	92	7	if	if	SCONJ
bracis-19038	92	8	\(o_1	\(o_1	PROPN
bracis-19038	92	9	\preceq	\preceq	PROPN
bracis-19038	92	10	o_2\	o_2\	PROPN
bracis-19038	92	11	)	)	PUNCT
bracis-19038	92	12	and	and	CCONJ
bracis-19038	92	13	\(o_2	\(o_2	PROPN
bracis-19038	92	14	\not	\not	ADV
bracis-19038	92	15	\preceq	\preceq	PROPN
bracis-19038	92	16	o_1\	o_1\	NOUN
bracis-19038	92	17	)	)	PUNCT
bracis-19038	92	18	,	,	PUNCT
bracis-19038	92	19	and	and	CCONJ
bracis-19038	92	20	say	say	VERB
bracis-19038	92	21	\(o_2\	\(o_2\	PROPN
bracis-19038	92	22	)	)	PUNCT
bracis-19038	92	23	has	have	VERB
bracis-19038	92	24	a	a	DET
bracis-19038	92	25	strictly	strictly	ADV
bracis-19038	92	26	higher	high	ADJ
bracis-19038	92	27	priority	priority	NOUN
bracis-19038	92	28	than	than	ADP
bracis-19038	92	29	\(o_1\	\(o_1\	NOUN
bracis-19038	92	30	)	)	PUNCT
bracis-19038	92	31	.	.	PUNCT
bracis-19038	93	1	furthermore	furthermore	ADV
bracis-19038	93	2	,	,	PUNCT
bracis-19038	93	3	\(o_1\	\(o_1\	PROPN
bracis-19038	93	4	)	)	PUNCT
bracis-19038	93	5	is	be	AUX
bracis-19038	93	6	indifferent	indifferent	ADJ
bracis-19038	93	7	to	to	ADP
bracis-19038	93	8	\(o_2\	\(o_2\	PROPN
bracis-19038	93	9	)	)	PUNCT
bracis-19038	93	10	,	,	PUNCT
bracis-19038	93	11	denoted	denote	VERB
bracis-19038	93	12	by	by	ADP
bracis-19038	93	13	\(o_1	\(o_1	PROPN
bracis-19038	93	14	\approx	\approx	PROPN
bracis-19038	93	15	o_2\	o_2\	PROPN
bracis-19038	93	16	)	)	PUNCT
bracis-19038	93	17	,	,	PUNCT
bracis-19038	93	18	when	when	SCONJ
bracis-19038	93	19	both	both	DET
bracis-19038	93	20	\(o_1	\(o_1	PROPN
bracis-19038	93	21	\preceq	\preceq	PROPN
bracis-19038	93	22	o_2\	o_2\	PROPN
bracis-19038	93	23	)	)	PUNCT
bracis-19038	93	24	and	and	CCONJ
bracis-19038	93	25	\(o_2	\(o_2	NUM
bracis-19038	93	26	\preceq	\preceq	PROPN
bracis-19038	93	27	o_1\	o_1\	NOUN
bracis-19038	93	28	)	)	PUNCT
bracis-19038	93	29	hold	hold	NOUN
bracis-19038	93	30	.	.	PUNCT
bracis-19038	94	1	from	from	ADP
bracis-19038	94	2	an	an	DET
bracis-19038	94	3	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	94	4	)	)	PUNCT
bracis-19038	94	5	and	and	CCONJ
bracis-19038	94	6	a	a	DET
bracis-19038	94	7	set	set	NOUN
bracis-19038	94	8	of	of	ADP
bracis-19038	94	9	priorities	priority	NOUN
bracis-19038	94	10	,	,	PUNCT
bracis-19038	94	11	we	we	PRON
bracis-19038	94	12	build	build	VERB
bracis-19038	94	13	a	a	DET
bracis-19038	94	14	prioritised	prioritise	VERB
bracis-19038	94	15	logic	logic	NOUN
bracis-19038	94	16	program	program	NOUN
bracis-19038	94	17	:	:	PUNCT
bracis-19038	94	18	definition	definition	NOUN
bracis-19038	94	19	6	6	NUM
bracis-19038	94	20	(	(	PUNCT
bracis-19038	94	21	prioritised	prioritise	VERB
bracis-19038	94	22	logic	logic	NOUN
bracis-19038	94	23	programs	program	NOUN
bracis-19038	94	24	)	)	PUNCT
bracis-19038	94	25	a	a	DET
bracis-19038	94	26	prioritised	prioritise	VERB
bracis-19038	94	27	logic	logic	NOUN
bracis-19038	94	28	program	program	NOUN
bracis-19038	94	29	(	(	PUNCT
bracis-19038	94	30	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	94	31	)	)	PUNCT
bracis-19038	94	32	)	)	PUNCT
bracis-19038	94	33	is	be	AUX
bracis-19038	94	34	a	a	DET
bracis-19038	94	35	pair	pair	NOUN
bracis-19038	94	36	\((p,\varphi	\((p,\varphi	NOUN
bracis-19038	94	37	)	)	PUNCT
bracis-19038	94	38	\	\	PROPN
bracis-19038	94	39	)	)	PUNCT
bracis-19038	94	40	,	,	PUNCT
bracis-19038	94	41	where	where	SCONJ
bracis-19038	94	42	p	p	NOUN
bracis-19038	94	43	is	be	AUX
bracis-19038	94	44	an	an	DET
bracis-19038	94	45	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	94	46	)	)	PUNCT
bracis-19038	94	47	and	and	CCONJ
bracis-19038	94	48	\(\varphi	\(\varphi	PROPN
bracis-19038	94	49	\	\	NOUN
bracis-19038	94	50	)	)	PUNCT
bracis-19038	94	51	is	be	AUX
bracis-19038	94	52	a	a	DET
bracis-19038	94	53	set	set	NOUN
bracis-19038	94	54	of	of	ADP
bracis-19038	94	55	priorities	priority	NOUN
bracis-19038	94	56	on	on	ADP
bracis-19038	94	57	\(\mathcal	\(\mathcal	ADJ
bracis-19038	94	58	{	{	PUNCT
bracis-19038	94	59	o}_p\	o}_p\	NOUN
bracis-19038	94	60	)	)	PUNCT
bracis-19038	94	61	.	.	PUNCT
bracis-19038	95	1	in	in	ADP
bracis-19038	95	2	order	order	NOUN
bracis-19038	95	3	to	to	PART
bracis-19038	95	4	enforce	enforce	VERB
bracis-19038	95	5	the	the	DET
bracis-19038	95	6	priority	priority	NOUN
bracis-19038	95	7	relation	relation	NOUN
bracis-19038	95	8	in	in	ADP
bracis-19038	95	9	\(\varphi	\(\varphi	ADJ
bracis-19038	95	10	\	\	NOUN
bracis-19038	95	11	)	)	PUNCT
bracis-19038	95	12	is	be	AUX
bracis-19038	95	13	reflexive	reflexive	ADJ
bracis-19038	95	14	and	and	CCONJ
bracis-19038	95	15	transitive	transitive	ADJ
bracis-19038	95	16	,	,	PUNCT
bracis-19038	95	17	while	while	SCONJ
bracis-19038	95	18	maintaining	maintain	VERB
bracis-19038	95	19	a	a	DET
bracis-19038	95	20	compact	compact	ADJ
bracis-19038	95	21	representation	representation	NOUN
bracis-19038	95	22	of	of	ADP
bracis-19038	95	23	priorities	priority	NOUN
bracis-19038	95	24	,	,	PUNCT
bracis-19038	95	25	we	we	PRON
bracis-19038	95	26	resort	resort	VERB
bracis-19038	95	27	to	to	ADP
bracis-19038	95	28	the	the	DET
bracis-19038	95	29	closure	closure	NOUN
bracis-19038	95	30	of	of	ADP
bracis-19038	95	31	\(\varphi	\(\varphi	ADJ
bracis-19038	95	32	\	\	NOUN
bracis-19038	95	33	):	):	PUNCT
bracis-19038	95	34	definition	definition	NOUN
bracis-19038	95	35	7	7	NUM
bracis-19038	95	36	(	(	PUNCT
bracis-19038	95	37	closure	closure	NOUN
bracis-19038	95	38	of	of	ADP
bracis-19038	95	39	\(\boldsymbol{\varphi	\(\boldsymbol{\varphi	NOUN
bracis-19038	95	40	}	}	PUNCT
bracis-19038	95	41	\	\	NOUN
bracis-19038	95	42	)	)	PUNCT
bracis-19038	95	43	)	)	PUNCT
bracis-19038	95	44	.	.	PUNCT
bracis-19038	96	1	let	let	VERB
bracis-19038	96	2	\((p	\((p	NOUN
bracis-19038	96	3	,	,	PUNCT
bracis-19038	96	4	\varphi	\varphi	PROPN
bracis-19038	96	5	)	)	PUNCT
bracis-19038	96	6	\	\	NOUN
bracis-19038	96	7	)	)	PUNCT
bracis-19038	96	8	be	be	AUX
bracis-19038	96	9	a	a	DET
bracis-19038	96	10	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	96	11	)	)	PUNCT
bracis-19038	96	12	.	.	PUNCT
bracis-19038	97	1	for	for	ADP
bracis-19038	97	2	each	each	DET
bracis-19038	97	3	\(o_1	\(o_1	PROPN
bracis-19038	97	4	,	,	PUNCT
bracis-19038	97	5	o_2\	o_2\	PROPN
bracis-19038	97	6	)	)	PUNCT
bracis-19038	97	7	in	in	ADP
bracis-19038	97	8	\(\mathcal	\(\mathcal	ADJ
bracis-19038	97	9	{	{	PUNCT
bracis-19038	97	10	o}_p\	o}_p\	NOUN
bracis-19038	97	11	)	)	PUNCT
bracis-19038	97	12	,	,	PUNCT
bracis-19038	97	13	the	the	DET
bracis-19038	97	14	closure	closure	NOUN
bracis-19038	97	15	\(\varphi	\(\varphi	NOUN
bracis-19038	97	16	^*\	^*\	NUM
bracis-19038	97	17	)	)	PUNCT
bracis-19038	97	18	of	of	ADP
bracis-19038	97	19	\(\varphi	\(\varphi	PROPN
bracis-19038	97	20	\	\	NOUN
bracis-19038	97	21	)	)	PUNCT
bracis-19038	97	22	is	be	AUX
bracis-19038	97	23	defined	define	VERB
bracis-19038	97	24	as	as	SCONJ
bracis-19038	97	25	follows	follow	VERB
bracis-19038	97	26	:	:	PUNCT
bracis-19038	97	27	\(o_1	\(o_1	PROPN
bracis-19038	97	28	\preceq	\preceq	PROPN
bracis-19038	97	29	o_1	o_1	ADP
bracis-19038	97	30	\in	\in	PROPN
bracis-19038	97	31	\varphi	\varphi	PROPN
bracis-19038	97	32	^*\	^*\	NUM
bracis-19038	97	33	)	)	PUNCT
bracis-19038	97	34	;	;	PUNCT
bracis-19038	97	35	if	if	SCONJ
bracis-19038	97	36	\(o_1	\(o_1	PROPN
bracis-19038	97	37	\preceq	\preceq	PROPN
bracis-19038	97	38	o_2	o_2	PROPN
bracis-19038	97	39	\in	\in	PROPN
bracis-19038	97	40	\varphi	\varphi	PROPN
bracis-19038	97	41	\	\	NOUN
bracis-19038	97	42	)	)	PUNCT
bracis-19038	97	43	,	,	PUNCT
bracis-19038	97	44	then	then	ADV
bracis-19038	97	45	\(o_1	\(o_1	PROPN
bracis-19038	97	46	\preceq	\preceq	PROPN
bracis-19038	97	47	o_2	o_2	PROPN
bracis-19038	97	48	\in	\in	PROPN
bracis-19038	97	49	\varphi	\varphi	PROPN
bracis-19038	97	50	^*\	^*\	NUM
bracis-19038	97	51	)	)	PUNCT
bracis-19038	97	52	;	;	PUNCT
bracis-19038	97	53	if	if	SCONJ
bracis-19038	97	54	\(o_1	\(o_1	PROPN
bracis-19038	97	55	\preceq	\preceq	PROPN
bracis-19038	97	56	o_2	o_2	PROPN
bracis-19038	97	57	\in	\in	PROPN
bracis-19038	97	58	\varphi	\varphi	PROPN
bracis-19038	97	59	^*\	^*\	NUM
bracis-19038	97	60	)	)	PUNCT
bracis-19038	97	61	and	and	CCONJ
bracis-19038	97	62	\(o_2	\(o_2	NUM
bracis-19038	97	63	\preceq	\preceq	PROPN
bracis-19038	97	64	o_3	o_3	NOUN
bracis-19038	97	65	\in	\in	PROPN
bracis-19038	97	66	\varphi	\varphi	PROPN
bracis-19038	97	67	^*\	^*\	NUM
bracis-19038	97	68	)	)	PUNCT
bracis-19038	97	69	,	,	PUNCT
bracis-19038	97	70	then	then	ADV
bracis-19038	97	71	\(o_1	\(o_1	PROPN
bracis-19038	97	72	\preceq	\preceq	PROPN
bracis-19038	97	73	o_3	o_3	NOUN
bracis-19038	97	74	\in	\in	PROPN
bracis-19038	97	75	\varphi	\varphi	PROPN
bracis-19038	97	76	^*\	^*\	NUM
bracis-19038	97	77	)	)	PUNCT
bracis-19038	97	78	.	.	PUNCT
bracis-19038	98	1	\(o_1	\(o_1	PROPN
bracis-19038	98	2	\preceq	\preceq	PROPN
bracis-19038	98	3	o_2	o_2	PROPN
bracis-19038	98	4	\in	\in	PROPN
bracis-19038	98	5	\varphi	\varphi	PROPN
bracis-19038	98	6	^*\	^*\	NUM
bracis-19038	98	7	)	)	PUNCT
bracis-19038	98	8	and	and	CCONJ
bracis-19038	98	9	\(o_1	\(o_1	PROPN
bracis-19038	98	10	\ne	\ne	PROPN
bracis-19038	98	11	\emptyset	\emptyset	VERB
bracis-19038	98	12	\	\	NOUN
bracis-19038	98	13	)	)	PUNCT
bracis-19038	98	14	and	and	CCONJ
bracis-19038	98	15	\(o_2	\(o_2	PROPN
bracis-19038	98	16	\ne	\ne	PROPN
bracis-19038	98	17	\emptyset	\emptyset	VERB
bracis-19038	98	18	\	\	NOUN
bracis-19038	98	19	)	)	PUNCT
bracis-19038	98	20	and	and	CCONJ
bracis-19038	98	21	\(e	\(e	PRON
bracis-19038	98	22	\not	\not	ADV
bracis-19038	98	23	\in	\in	PROPN
bracis-19038	98	24	o_1	o_1	ADP
bracis-19038	98	25	\cup	\cup	NOUN
bracis-19038	98	26	o_2\	o_2\	NUM
bracis-19038	98	27	)	)	PUNCT
bracis-19038	98	28	,	,	PUNCT
bracis-19038	98	29	then	then	ADV
bracis-19038	98	30	\(o_1	\(o_1	PROPN
bracis-19038	98	31	\cup	\cup	VERB
bracis-19038	98	32	\left\	\left\	PROPN
bracis-19038	98	33	{	{	PUNCT
bracis-19038	98	34	e\right\	e\right\	NOUN
bracis-19038	98	35	}	}	PUNCT
bracis-19038	98	36	\preceq	\preceq	PROPN
bracis-19038	98	37	o_2	o_2	NOUN
bracis-19038	98	38	\cup	\cup	VERB
bracis-19038	98	39	\left\	\left\	PROPN
bracis-19038	98	40	{	{	PUNCT
bracis-19038	98	41	e\right\	e\right\	NOUN
bracis-19038	98	42	}	}	PUNCT
bracis-19038	98	43	\in	\in	PROPN
bracis-19038	98	44	\varphi	\varphi	PROPN
bracis-19038	98	45	^*\	^*\	NUM
bracis-19038	98	46	)	)	PUNCT
bracis-19038	98	47	.	.	PUNCT
bracis-19038	99	1	the	the	DET
bracis-19038	99	2	closure	closure	NOUN
bracis-19038	99	3	\(\varphi	\(\varphi	PROPN
bracis-19038	99	4	^*\	^*\	NUM
bracis-19038	99	5	)	)	PUNCT
bracis-19038	99	6	of	of	ADP
bracis-19038	99	7	\(\varphi	\(\varphi	PROPN
bracis-19038	99	8	\	\	NOUN
bracis-19038	99	9	)	)	PUNCT
bracis-19038	99	10	is	be	AUX
bracis-19038	99	11	the	the	DET
bracis-19038	99	12	set	set	NOUN
bracis-19038	99	13	of	of	ADP
bracis-19038	99	14	priorities	priority	NOUN
bracis-19038	99	15	derived	derive	VERB
bracis-19038	99	16	reflexively	reflexively	ADV
bracis-19038	99	17	and	and	CCONJ
bracis-19038	99	18	transitively	transitively	NOUN
bracis-19038	99	19	using	use	VERB
bracis-19038	99	20	priorities	priority	NOUN
bracis-19038	99	21	in	in	ADP
bracis-19038	99	22	\(\varphi	\(\varphi	NOUN
bracis-19038	99	23	\	\	NOUN
bracis-19038	99	24	)	)	PUNCT
bracis-19038	99	25	.	.	PUNCT
bracis-19038	100	1	besides	besides	ADV
bracis-19038	100	2	,	,	PUNCT
bracis-19038	100	3	we	we	PRON
bracis-19038	100	4	introduced	introduce	VERB
bracis-19038	100	5	in	in	ADP
bracis-19038	100	6	\(\varphi	\(\varphi	PROPN
bracis-19038	100	7	^*\	^*\	NUM
bracis-19038	100	8	)	)	PUNCT
bracis-19038	100	9	an	an	DET
bracis-19038	100	10	inertia	inertia	NOUN
bracis-19038	100	11	principle	principle	NOUN
bracis-19038	100	12	to	to	PART
bracis-19038	100	13	keep	keep	VERB
bracis-19038	100	14	the	the	DET
bracis-19038	100	15	preference	preference	NOUN
bracis-19038	100	16	representation	representation	NOUN
bracis-19038	100	17	in	in	ADP
bracis-19038	100	18	\(\varphi	\(\varphi	ADJ
bracis-19038	100	19	\	\	ADJ
bracis-19038	100	20	)	)	PUNCT
bracis-19038	100	21	compact	compact	ADJ
bracis-19038	100	22	.	.	PUNCT
bracis-19038	101	1	in	in	ADP
bracis-19038	101	2	the	the	DET
bracis-19038	101	3	remainder	remainder	NOUN
bracis-19038	101	4	of	of	ADP
bracis-19038	101	5	this	this	DET
bracis-19038	101	6	paper	paper	NOUN
bracis-19038	101	7	,	,	PUNCT
bracis-19038	101	8	when	when	SCONJ
bracis-19038	101	9	we	we	PRON
bracis-19038	101	10	say	say	VERB
bracis-19038	101	11	\(o_2	\(o_2	PROPN
bracis-19038	101	12	\not	\not	ADV
bracis-19038	101	13	\prec	\prec	ADP
bracis-19038	101	14	o_1\	o_1\	PROPN
bracis-19038	101	15	)	)	PUNCT
bracis-19038	101	16	according	accord	VERB
bracis-19038	101	17	to	to	ADP
bracis-19038	101	18	\(\varphi	\(\varphi	PROPN
bracis-19038	101	19	^*\	^*\	NUM
bracis-19038	101	20	)	)	PUNCT
bracis-19038	101	21	,	,	PUNCT
bracis-19038	101	22	we	we	PRON
bracis-19038	101	23	mean	mean	VERB
bracis-19038	101	24	\(o_2	\(o_2	NUM
bracis-19038	101	25	\preceq	\preceq	PROPN
bracis-19038	101	26	o_1	o_1	ADP
bracis-19038	101	27	\not	\not	ADV
bracis-19038	101	28	\in	\in	PROPN
bracis-19038	101	29	\varphi	\varphi	PROPN
bracis-19038	101	30	^*\	^*\	NUM
bracis-19038	101	31	)	)	PUNCT
bracis-19038	101	32	or	or	CCONJ
bracis-19038	101	33	\(o_1	\(o_1	PROPN
bracis-19038	101	34	\preceq	\preceq	PROPN
bracis-19038	101	35	o_2	o_2	PROPN
bracis-19038	101	36	\in	\in	PROPN
bracis-19038	101	37	\varphi	\varphi	PROPN
bracis-19038	101	38	^*\	^*\	NUM
bracis-19038	101	39	)	)	PUNCT
bracis-19038	101	40	.	.	PUNCT
bracis-19038	102	1	among	among	ADP
bracis-19038	102	2	the	the	DET
bracis-19038	102	3	many	many	ADJ
bracis-19038	102	4	possible	possible	ADJ
bracis-19038	102	5	options	option	NOUN
bracis-19038	102	6	,	,	PUNCT
bracis-19038	102	7	we	we	PRON
bracis-19038	102	8	are	be	AUX
bracis-19038	102	9	particularly	particularly	ADV
bracis-19038	102	10	interested	interested	ADJ
bracis-19038	102	11	in	in	ADP
bracis-19038	102	12	those	those	PRON
bracis-19038	102	13	best	good	ADJ
bracis-19038	102	14	/	/	SYM
bracis-19038	102	15	worst	worst	ADV
bracis-19038	102	16	-	-	PUNCT
bracis-19038	102	17	ranked	ranked	ADJ
bracis-19038	102	18	:	:	PUNCT
bracis-19038	102	19	definition	definition	NOUN
bracis-19038	102	20	8	8	NUM
bracis-19038	102	21	(	(	PUNCT
bracis-19038	102	22	best	well	ADV
bracis-19038	102	23	/	/	SYM
bracis-19038	102	24	worst	worst	ADV
bracis-19038	102	25	-	-	PUNCT
bracis-19038	102	26	ranked	rank	VERB
bracis-19038	102	27	option	option	NOUN
bracis-19038	102	28	)	)	PUNCT
bracis-19038	102	29	let	let	VERB
bracis-19038	102	30	\((p	\((p	NOUN
bracis-19038	102	31	,	,	PUNCT
bracis-19038	102	32	\varphi	\varphi	PROPN
bracis-19038	102	33	)	)	PUNCT
bracis-19038	102	34	\	\	NOUN
bracis-19038	102	35	)	)	PUNCT
bracis-19038	102	36	be	be	AUX
bracis-19038	102	37	a	a	DET
bracis-19038	102	38	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	102	39	)	)	PUNCT
bracis-19038	102	40	and	and	CCONJ
bracis-19038	102	41	\(i	\(i	NOUN
bracis-19038	102	42	\subseteq	\subseteq	AUX
bracis-19038	102	43	lit	light	VERB
bracis-19038	102	44	_	_	PUNCT
bracis-19038	102	45	p\	p\	NOUN
bracis-19038	102	46	)	)	PUNCT
bracis-19038	102	47	.	.	PUNCT
bracis-19038	103	1	we	we	PRON
bracis-19038	103	2	say	say	VERB
bracis-19038	103	3	o	o	NOUN
bracis-19038	103	4	is	be	AUX
bracis-19038	103	5	a	a	PRON
bracis-19038	103	6	)	)	PUNCT
bracis-19038	103	7	a	a	DET
bracis-19038	103	8	best	well	ADV
bracis-19038	103	9	-	-	PUNCT
bracis-19038	103	10	ranked	rank	VERB
bracis-19038	103	11	option	option	NOUN
bracis-19038	103	12	in	in	SCONJ
bracis-19038	103	13	i	i	PRON
bracis-19038	103	14	w.r.t	w.r.t	VERB
bracis-19038	103	15	.	.	PUNCT
bracis-19038	104	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	104	2	\	\	NOUN
bracis-19038	104	3	)	)	PUNCT
bracis-19038	104	4	iff	iff	PROPN
bracis-19038	104	5	\(o	\(o	PROPN
bracis-19038	104	6	\subseteq	\subseteq	PROPN
bracis-19038	104	7	i\	i\	PROPN
bracis-19038	104	8	)	)	PUNCT
bracis-19038	104	9	and	and	CCONJ
bracis-19038	104	10	\(\not	\(\not	ADV
bracis-19038	104	11	\exists	\exist	NOUN
bracis-19038	104	12	o	o	VERB
bracis-19038	104	13	'	'	PUNCT
bracis-19038	104	14	\subseteq	\subseteq	PROPN
bracis-19038	104	15	i\	i\	PROPN
bracis-19038	104	16	)	)	PUNCT
bracis-19038	104	17	such	such	ADJ
bracis-19038	104	18	that	that	SCONJ
bracis-19038	104	19	\(o	\(o	PRON
bracis-19038	105	1	\prec	\prec	ADV
bracis-19038	105	2	o	o	NOUN
bracis-19038	105	3	'	'	PUNCT
bracis-19038	105	4	\in	\in	PROPN
bracis-19038	105	5	\varphi	\varphi	PROPN
bracis-19038	105	6	^*\	^*\	NUM
bracis-19038	105	7	)	)	PUNCT
bracis-19038	105	8	.	.	PUNCT
bracis-19038	106	1	b	b	X
bracis-19038	106	2	)	)	PUNCT
bracis-19038	106	3	a	a	DET
bracis-19038	106	4	worst	worst	ADV
bracis-19038	106	5	-	-	PUNCT
bracis-19038	106	6	ranked	rank	VERB
bracis-19038	106	7	option	option	NOUN
bracis-19038	106	8	in	in	ADP
bracis-19038	106	9	i	i	PRON
bracis-19038	106	10	w.r.t	w.r.t	VERB
bracis-19038	106	11	.	.	PUNCT
bracis-19038	107	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	107	2	\	\	NOUN
bracis-19038	107	3	)	)	PUNCT
bracis-19038	107	4	iff	iff	PROPN
bracis-19038	107	5	\(o	\(o	PROPN
bracis-19038	107	6	\subseteq	\subseteq	PROPN
bracis-19038	107	7	i\	i\	PROPN
bracis-19038	107	8	)	)	PUNCT
bracis-19038	107	9	and	and	CCONJ
bracis-19038	107	10	\(\not	\(\not	ADV
bracis-19038	107	11	\exists	\exist	NOUN
bracis-19038	107	12	o	o	VERB
bracis-19038	107	13	'	'	PUNCT
bracis-19038	107	14	\subseteq	\subseteq	PROPN
bracis-19038	107	15	i\	i\	PROPN
bracis-19038	107	16	)	)	PUNCT
bracis-19038	107	17	such	such	ADJ
bracis-19038	107	18	that	that	SCONJ
bracis-19038	107	19	\(o	\(o	NOUN
bracis-19038	107	20	'	'	PUNCT
bracis-19038	107	21	\prec	\prec	NUM
bracis-19038	107	22	o	o	X
bracis-19038	107	23	\in	\in	PROPN
bracis-19038	107	24	\varphi	\varphi	PROPN
bracis-19038	107	25	^*\	^*\	NUM
bracis-19038	107	26	)	)	PUNCT
bracis-19038	107	27	.	.	PUNCT
bracis-19038	108	1	given	give	VERB
bracis-19038	108	2	two	two	NUM
bracis-19038	108	3	set	set	NOUN
bracis-19038	108	4	of	of	ADP
bracis-19038	108	5	options	option	NOUN
bracis-19038	108	6	,	,	PUNCT
bracis-19038	108	7	we	we	PRON
bracis-19038	108	8	have	have	VERB
bracis-19038	108	9	to	to	PART
bracis-19038	108	10	determine	determine	VERB
bracis-19038	108	11	which	which	DET
bracis-19038	108	12	one	one	PRON
bracis-19038	108	13	is	be	AUX
bracis-19038	108	14	preferable	preferable	ADJ
bracis-19038	108	15	;	;	PUNCT
bracis-19038	108	16	we	we	PRON
bracis-19038	108	17	introduce	introduce	VERB
bracis-19038	108	18	below	below	ADP
bracis-19038	108	19	four	four	NUM
bracis-19038	108	20	criteria	criterion	NOUN
bracis-19038	108	21	with	with	ADP
bracis-19038	108	22	this	this	DET
bracis-19038	108	23	purpose	purpose	NOUN
bracis-19038	108	24	:	:	PUNCT
bracis-19038	108	25	definition	definition	NOUN
bracis-19038	108	26	9	9	NUM
bracis-19038	108	27	let	let	VERB
bracis-19038	108	28	\((p	\((p	NOUN
bracis-19038	108	29	,	,	PUNCT
bracis-19038	108	30	\varphi	\varphi	PROPN
bracis-19038	108	31	)	)	PUNCT
bracis-19038	108	32	\	\	NOUN
bracis-19038	108	33	)	)	PUNCT
bracis-19038	108	34	be	be	AUX
bracis-19038	108	35	a	a	DET
bracis-19038	108	36	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	108	37	)	)	PUNCT
bracis-19038	108	38	and	and	CCONJ
bracis-19038	108	39	\(\mathcal	\(\mathcal	ADJ
bracis-19038	108	40	o_1\	o_1\	NOUN
bracis-19038	108	41	)	)	PUNCT
bracis-19038	108	42	and	and	CCONJ
bracis-19038	108	43	\(\mathcal	\(\mathcal	ADJ
bracis-19038	108	44	o_2\	o_2\	PROPN
bracis-19038	108	45	)	)	PUNCT
bracis-19038	108	46	subsets	subset	NOUN
bracis-19038	108	47	of	of	ADP
bracis-19038	108	48	\(\mathcal	\(\mathcal	ADJ
bracis-19038	108	49	{	{	PUNCT
bracis-19038	108	50	o}_p\	o}_p\	NOUN
bracis-19038	108	51	)	)	PUNCT
bracis-19038	108	52	.	.	PUNCT
bracis-19038	109	1	we	we	PRON
bracis-19038	109	2	say	say	VERB
bracis-19038	109	3	\(\mathcal	\(\mathcal	ADJ
bracis-19038	109	4	o_1	o_1	ADP
bracis-19038	109	5	\subseteq	\subseteq	PROPN
bracis-19038	109	6	^{\forall	^{\forall	NOUN
bracis-19038	110	1	\forall	\forall	PRON
bracis-19038	110	2	}	}	PUNCT
bracis-19038	110	3	\mathcal	\mathcal	ADJ
bracis-19038	110	4	o_2\	o_2\	PROPN
bracis-19038	110	5	)	)	PUNCT
bracis-19038	110	6	in	in	ADP
bracis-19038	110	7	\(\varphi	\(\varphi	ADJ
bracis-19038	110	8	\	\	NOUN
bracis-19038	110	9	)	)	PUNCT
bracis-19038	110	10	iff	iff	VERB
bracis-19038	110	11	\(\forall	\(\forall	ADV
bracis-19038	110	12	o_1	o_1	ADP
bracis-19038	110	13	\in	\in	PROPN
bracis-19038	110	14	\mathcal	\mathcal	NOUN
bracis-19038	110	15	o_1\	o_1\	NOUN
bracis-19038	110	16	)	)	PUNCT
bracis-19038	110	17	and	and	CCONJ
bracis-19038	110	18	\(\forall	\(\forall	ADV
bracis-19038	110	19	o_2	o_2	PROPN
bracis-19038	110	20	\in	\in	PROPN
bracis-19038	110	21	\mathcal	\mathcal	PROPN
bracis-19038	110	22	o_2\	o_2\	PROPN
bracis-19038	110	23	)	)	PUNCT
bracis-19038	110	24	,	,	PUNCT
bracis-19038	110	25	it	it	PRON
bracis-19038	110	26	holds	hold	VERB
bracis-19038	110	27	\(o_2	\(o_2	PROPN
bracis-19038	110	28	\not	\not	ADV
bracis-19038	110	29	\prec	\prec	ADP
bracis-19038	110	30	o_1\	o_1\	PROPN
bracis-19038	110	31	)	)	PUNCT
bracis-19038	110	32	in	in	ADP
bracis-19038	110	33	\(\varphi	\(\varphi	PROPN
bracis-19038	110	34	^*\	^*\	NUM
bracis-19038	110	35	)	)	PUNCT
bracis-19038	110	36	.	.	PUNCT
bracis-19038	111	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	111	2	o_1	o_1	ADP
bracis-19038	111	3	\subseteq	\subseteq	PROPN
bracis-19038	111	4	^{\forall	^{\forall	DET
bracis-19038	111	5	\exists	\exist	NOUN
bracis-19038	111	6	}	}	PUNCT
bracis-19038	111	7	\mathcal	\mathcal	ADJ
bracis-19038	111	8	o_2\	o_2\	PROPN
bracis-19038	111	9	)	)	PUNCT
bracis-19038	111	10	in	in	ADP
bracis-19038	111	11	\(\varphi	\(\varphi	ADJ
bracis-19038	111	12	\	\	NOUN
bracis-19038	111	13	)	)	PUNCT
bracis-19038	111	14	iff	iff	VERB
bracis-19038	111	15	\(\forall	\(\forall	ADV
bracis-19038	111	16	o_1	o_1	ADP
bracis-19038	111	17	\in	\in	PROPN
bracis-19038	111	18	\mathcal	\mathcal	PROPN
bracis-19038	111	19	o_1\	o_1\	NOUN
bracis-19038	111	20	)	)	PUNCT
bracis-19038	111	21	,	,	PUNCT
bracis-19038	111	22	it	it	PRON
bracis-19038	111	23	holds	hold	VERB
bracis-19038	111	24	\(\exists	\(\exist	NOUN
bracis-19038	111	25	o_2	o_2	PROPN
bracis-19038	111	26	\in	\in	PROPN
bracis-19038	111	27	\mathcal	\mathcal	PROPN
bracis-19038	111	28	o_2\	o_2\	PROPN
bracis-19038	111	29	)	)	PUNCT
bracis-19038	111	30	such	such	ADJ
bracis-19038	111	31	that	that	SCONJ
bracis-19038	111	32	\(o_2	\(o_2	PROPN
bracis-19038	111	33	\not	\not	ADV
bracis-19038	111	34	\prec	\prec	ADP
bracis-19038	111	35	o_1\	o_1\	PROPN
bracis-19038	111	36	)	)	PUNCT
bracis-19038	111	37	in	in	ADP
bracis-19038	111	38	\(\varphi	\(\varphi	PROPN
bracis-19038	111	39	^*\	^*\	NUM
bracis-19038	111	40	)	)	PUNCT
bracis-19038	111	41	.	.	PUNCT
bracis-19038	112	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	112	2	o_1	o_1	ADP
bracis-19038	112	3	\subseteq	\subseteq	PROPN
bracis-19038	112	4	^{\exists	^{\exist	NOUN
bracis-19038	112	5	\forall	\forall	PRON
bracis-19038	112	6	}	}	PUNCT
bracis-19038	112	7	\mathcal	\mathcal	ADJ
bracis-19038	112	8	o_2\	o_2\	PROPN
bracis-19038	112	9	)	)	PUNCT
bracis-19038	112	10	in	in	ADP
bracis-19038	112	11	\(\varphi	\(\varphi	ADJ
bracis-19038	112	12	\	\	NOUN
bracis-19038	112	13	)	)	PUNCT
bracis-19038	112	14	iff	iff	PROPN
bracis-19038	112	15	\(\exists	\(\exist	NOUN
bracis-19038	112	16	o_1	o_1	ADP
bracis-19038	112	17	\in	\in	PROPN
bracis-19038	112	18	\mathcal	\mathcal	PROPN
bracis-19038	112	19	o_1\	o_1\	NOUN
bracis-19038	112	20	)	)	PUNCT
bracis-19038	112	21	such	such	ADJ
bracis-19038	112	22	that	that	SCONJ
bracis-19038	112	23	\(\forall	\(\forall	ADV
bracis-19038	112	24	o_2	o_2	NOUN
bracis-19038	112	25	\in	\in	PROPN
bracis-19038	112	26	\mathcal	\mathcal	PROPN
bracis-19038	112	27	o_2\	o_2\	PROPN
bracis-19038	112	28	)	)	PUNCT
bracis-19038	112	29	,	,	PUNCT
bracis-19038	112	30	it	it	PRON
bracis-19038	112	31	holds	hold	VERB
bracis-19038	112	32	\(o_2	\(o_2	PROPN
bracis-19038	112	33	\not	\not	ADV
bracis-19038	112	34	\prec	\prec	ADP
bracis-19038	112	35	o_1\	o_1\	PROPN
bracis-19038	112	36	)	)	PUNCT
bracis-19038	112	37	in	in	ADP
bracis-19038	112	38	\(\varphi	\(\varphi	PROPN
bracis-19038	112	39	^*\	^*\	NUM
bracis-19038	112	40	)	)	PUNCT
bracis-19038	112	41	.	.	PUNCT
bracis-19038	113	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	113	2	o_1	o_1	ADP
bracis-19038	113	3	\subseteq	\subseteq	PROPN
bracis-19038	113	4	^{\exists	^{\exist	VERB
bracis-19038	113	5	\exists	\exist	NOUN
bracis-19038	113	6	}	}	PUNCT
bracis-19038	113	7	\mathcal	\mathcal	ADJ
bracis-19038	113	8	o_2\	o_2\	PROPN
bracis-19038	113	9	)	)	PUNCT
bracis-19038	113	10	in	in	ADP
bracis-19038	113	11	\(\varphi	\(\varphi	ADJ
bracis-19038	113	12	\	\	NOUN
bracis-19038	113	13	)	)	PUNCT
bracis-19038	113	14	iff	iff	PROPN
bracis-19038	113	15	\(\exists	\(\exist	NOUN
bracis-19038	113	16	o_1	o_1	ADP
bracis-19038	113	17	\in	\in	PROPN
bracis-19038	113	18	\mathcal	\mathcal	NOUN
bracis-19038	113	19	o_1\	o_1\	NOUN
bracis-19038	113	20	)	)	PUNCT
bracis-19038	113	21	and	and	CCONJ
bracis-19038	113	22	\(\exists	\(\exist	NOUN
bracis-19038	113	23	o_2	o_2	VERB
bracis-19038	113	24	\in	\in	PROPN
bracis-19038	113	25	\mathcal	\mathcal	PROPN
bracis-19038	113	26	o_2\	o_2\	PROPN
bracis-19038	113	27	)	)	PUNCT
bracis-19038	113	28	such	such	ADJ
bracis-19038	113	29	that	that	SCONJ
bracis-19038	113	30	\(o_2	\(o_2	PROPN
bracis-19038	113	31	\not	\not	ADV
bracis-19038	113	32	\prec	\prec	ADP
bracis-19038	113	33	o_1\	o_1\	PROPN
bracis-19038	113	34	)	)	PUNCT
bracis-19038	113	35	in	in	ADP
bracis-19038	113	36	\(\varphi	\(\varphi	PROPN
bracis-19038	113	37	^*\	^*\	NUM
bracis-19038	113	38	)	)	PUNCT
bracis-19038	113	39	.	.	PUNCT
bracis-19038	114	1	besides	besides	SCONJ
bracis-19038	114	2	,	,	PUNCT
bracis-19038	114	3	different	different	ADJ
bracis-19038	114	4	preference	preference	NOUN
bracis-19038	114	5	semantics	semantic	NOUN
bracis-19038	114	6	have	have	AUX
bracis-19038	114	7	been	be	AUX
bracis-19038	114	8	proposed	propose	VERB
bracis-19038	114	9	in	in	ADP
bracis-19038	114	10	the	the	DET
bracis-19038	114	11	literature	literature	NOUN
bracis-19038	114	12	.	.	PUNCT
bracis-19038	115	1	we	we	PRON
bracis-19038	115	2	recall	recall	VERB
bracis-19038	115	3	some	some	PRON
bracis-19038	115	4	of	of	ADP
bracis-19038	115	5	the	the	DET
bracis-19038	115	6	most	most	ADV
bracis-19038	115	7	well	well	ADV
bracis-19038	115	8	-	-	PUNCT
bracis-19038	115	9	known	know	VERB
bracis-19038	115	10	of	of	ADP
bracis-19038	115	11	them	they	PRON
bracis-19038	115	12	:	:	PUNCT
bracis-19038	115	13	definition	definition	NOUN
bracis-19038	115	14	10	10	NUM
bracis-19038	115	15	(	(	PUNCT
bracis-19038	115	16	preference	preference	NOUN
bracis-19038	115	17	relation	relation	NOUN
bracis-19038	115	18	)	)	PUNCT
bracis-19038	115	19	let	let	VERB
bracis-19038	115	20	\((p,\varphi	\((p,\varphi	NOUN
bracis-19038	115	21	)	)	PUNCT
bracis-19038	115	22	\	\	NOUN
bracis-19038	115	23	)	)	PUNCT
bracis-19038	115	24	be	be	AUX
bracis-19038	115	25	a	a	DET
bracis-19038	115	26	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	115	27	)	)	PUNCT
bracis-19038	115	28	,	,	PUNCT
bracis-19038	116	1	\(i_1\	\(i_1\	PROPN
bracis-19038	116	2	)	)	PUNCT
bracis-19038	116	3	and	and	CCONJ
bracis-19038	116	4	\(i_2\	\(i_2\	PROPN
bracis-19038	116	5	)	)	PUNCT
bracis-19038	116	6	be	be	VERB
bracis-19038	116	7	\	\	PROPN
bracis-19038	116	8	(	(	PUNCT
bracis-19038	116	9	ps	ps	NOUN
bracis-19038	116	10	\	\	ADJ
bracis-19038	116	11	)	)	PUNCT
bracis-19038	116	12	models	model	NOUN
bracis-19038	116	13	of	of	ADP
bracis-19038	116	14	p	p	X
bracis-19038	116	15	,	,	PUNCT
bracis-19038	116	16	\(\mathcal	\(\mathcal	ADJ
bracis-19038	116	17	b_1\	b_1\	NOUN
bracis-19038	116	18	)	)	PUNCT
bracis-19038	116	19	and	and	CCONJ
bracis-19038	116	20	\(\mathcal	\(\mathcal	ADJ
bracis-19038	116	21	b_2\	b_2\	PROPN
bracis-19038	116	22	)	)	PUNCT
bracis-19038	116	23	are	be	AUX
bracis-19038	116	24	respectively	respectively	ADV
bracis-19038	116	25	the	the	DET
bracis-19038	116	26	sets	set	NOUN
bracis-19038	116	27	of	of	ADP
bracis-19038	116	28	all	all	DET
bracis-19038	116	29	best	well	ADV
bracis-19038	116	30	-	-	PUNCT
bracis-19038	116	31	ranked	rank	VERB
bracis-19038	116	32	options	option	NOUN
bracis-19038	116	33	in	in	ADP
bracis-19038	116	34	\(i_1\	\(i_1\	NOUN
bracis-19038	116	35	)	)	PUNCT
bracis-19038	116	36	and	and	CCONJ
bracis-19038	116	37	\(i_2\	\(i_2\	PROPN
bracis-19038	116	38	)	)	PUNCT
bracis-19038	116	39	w.r.t	w.r.t	NOUN
bracis-19038	116	40	.	.	PUNCT
bracis-19038	117	1	\(\varphi	\(\varphi	ADJ
bracis-19038	117	2	\	\	NOUN
bracis-19038	117	3	)	)	PUNCT
bracis-19038	117	4	,	,	PUNCT
bracis-19038	117	5	and	and	CCONJ
bracis-19038	117	6	\(\mathcal	\(\mathcal	ADJ
bracis-19038	117	7	w_1\	w_1\	PROPN
bracis-19038	117	8	)	)	PUNCT
bracis-19038	117	9	and	and	CCONJ
bracis-19038	117	10	\(\mathcal	\(\mathcal	ADJ
bracis-19038	117	11	w_2\	w_2\	PROPN
bracis-19038	117	12	)	)	PUNCT
bracis-19038	117	13	are	be	AUX
bracis-19038	117	14	respectively	respectively	ADV
bracis-19038	117	15	the	the	DET
bracis-19038	117	16	sets	set	NOUN
bracis-19038	117	17	of	of	ADP
bracis-19038	117	18	all	all	DET
bracis-19038	117	19	worst	worst	ADV
bracis-19038	117	20	-	-	PUNCT
bracis-19038	117	21	ranked	rank	VERB
bracis-19038	117	22	options	option	NOUN
bracis-19038	117	23	in	in	ADP
bracis-19038	117	24	\(i_1\	\(i_1\	NOUN
bracis-19038	117	25	)	)	PUNCT
bracis-19038	117	26	and	and	CCONJ
bracis-19038	117	27	\(i_2\	\(i_2\	PROPN
bracis-19038	117	28	)	)	PUNCT
bracis-19038	117	29	w.r.t	w.r.t	NOUN
bracis-19038	117	30	.	.	PUNCT
bracis-19038	118	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	118	2	\	\	NOUN
bracis-19038	118	3	)	)	PUNCT
bracis-19038	118	4	.	.	PUNCT
bracis-19038	119	1	consider	consider	VERB
bracis-19038	119	2	also	also	ADV
bracis-19038	119	3	\(x	\(x	ADJ
bracis-19038	119	4	\in	\in	PROPN
bracis-19038	119	5	\left\	\left\	PROPN
bracis-19038	119	6	{	{	PUNCT
bracis-19038	119	7	st	st	PROPN
bracis-19038	119	8	,	,	PUNCT
bracis-19038	119	9	opt	opt	NOUN
bracis-19038	119	10	,	,	PUNCT
bracis-19038	119	11	pes	pe	NOUN
bracis-19038	119	12	,	,	PUNCT
bracis-19038	119	13	opp	opp	PROPN
bracis-19038	119	14	\right\	\right\	ADV
bracis-19038	119	15	}	}	PUNCT
bracis-19038	119	16	\	\	NOUN
bracis-19038	119	17	)	)	PUNCT
bracis-19038	119	18	and	and	CCONJ
bracis-19038	119	19	\(y	\(y	PROPN
bracis-19038	119	20	\in	\in	PROPN
bracis-19038	119	21	\left\	\left\	PROPN
bracis-19038	119	22	{	{	PUNCT
bracis-19038	119	23	\forall	\forall	INTJ
bracis-19038	120	1	\forall	\forall	INTJ
bracis-19038	120	2	,	,	PUNCT
bracis-19038	120	3	\forall	\forall	DET
bracis-19038	120	4	\exists	\exist	NOUN
bracis-19038	120	5	,	,	PUNCT
bracis-19038	120	6	\exists	\exist	NOUN
bracis-19038	120	7	\forall	\forall	ADV
bracis-19038	120	8	,	,	PUNCT
bracis-19038	120	9	\exists	\exist	NOUN
bracis-19038	120	10	\exists	\exist	NOUN
bracis-19038	120	11	\right\	\right\	ADV
bracis-19038	120	12	}	}	PUNCT
bracis-19038	120	13	\	\	NOUN
bracis-19038	120	14	)	)	PUNCT
bracis-19038	120	15	.	.	PUNCT
bracis-19038	121	1	by	by	ADP
bracis-19038	121	2	\(i_1	\(i_1	PROPN
bracis-19038	121	3	\subseteq	\subseteq	PROPN
bracis-19038	121	4	^y_x	^y_x	NUM
bracis-19038	121	5	i_2\	i_2\	NUM
bracis-19038	121	6	)	)	PUNCT
bracis-19038	121	7	w.r.t	w.r.t	NOUN
bracis-19038	121	8	.	.	PUNCT
bracis-19038	122	1	\(\varphi	\(\varphi	ADJ
bracis-19038	122	2	\	\	NOUN
bracis-19038	122	3	)	)	PUNCT
bracis-19038	122	4	,	,	PUNCT
bracis-19038	122	5	we	we	PRON
bracis-19038	122	6	mean	mean	VERB
bracis-19038	122	7	the	the	DET
bracis-19038	122	8	preference	preference	NOUN
bracis-19038	122	9	relation	relation	PROPN
bracis-19038	122	10	\(\subseteq	\(\subseteq	PROPN
bracis-19038	122	11	^y_x\	^y_x\	NUM
bracis-19038	122	12	)	)	PUNCT
bracis-19038	122	13	over	over	ADP
bracis-19038	122	14	the	the	DET
bracis-19038	122	15	set	set	NOUN
bracis-19038	122	16	of	of	ADP
bracis-19038	122	17	\	\	PROPN
bracis-19038	122	18	(	(	PUNCT
bracis-19038	122	19	ps	ps	PROPN
bracis-19038	122	20	\	\	ADJ
bracis-19038	122	21	)	)	PUNCT
bracis-19038	122	22	models	model	NOUN
bracis-19038	122	23	of	of	ADP
bracis-19038	122	24	p	p	NOUN
bracis-19038	122	25	is	be	AUX
bracis-19038	122	26	defined	define	VERB
bracis-19038	122	27	as	as	SCONJ
bracis-19038	122	28	follows	follow	VERB
bracis-19038	122	29	:	:	PUNCT
bracis-19038	122	30	1	1	X
bracis-19038	122	31	.	.	X
bracis-19038	122	32	\(i_1	\(i_1	NUM
bracis-19038	122	33	\subseteq	\subseteq	PROPN
bracis-19038	122	34	^y_x	^y_x	NUM
bracis-19038	122	35	i_1\	i_1\	PROPN
bracis-19038	122	36	)	)	PUNCT
bracis-19038	122	37	w.r.t	w.r.t	NOUN
bracis-19038	122	38	.	.	PUNCT
bracis-19038	123	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	123	2	\	\	NUM
bracis-19038	123	3	)	)	PUNCT
bracis-19038	123	4	;	;	PUNCT
bracis-19038	124	1	2	2	X
bracis-19038	124	2	.	.	X
bracis-19038	124	3	\(i_1	\(i_1	NUM
bracis-19038	124	4	\subseteq	\subseteq	PROPN
bracis-19038	124	5	^y_x	^y_x	NUM
bracis-19038	124	6	i_2\	i_2\	NUM
bracis-19038	124	7	)	)	PUNCT
bracis-19038	124	8	w.r.t	w.r.t	NOUN
bracis-19038	124	9	.	.	PUNCT
bracis-19038	125	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	125	2	\	\	NUM
bracis-19038	125	3	)	)	PUNCT
bracis-19038	125	4	a	a	X
bracis-19038	125	5	)	)	PUNCT
bracis-19038	125	6	(	(	PUNCT
bracis-19038	125	7	strong	strong	ADJ
bracis-19038	125	8	semantics	semantic	NOUN
bracis-19038	125	9	):	):	PUNCT
bracis-19038	125	10	if	if	SCONJ
bracis-19038	125	11	\(x	\(x	NOUN
bracis-19038	125	12	=	=	SYM
bracis-19038	125	13	st	st	PROPN
bracis-19038	125	14	\	\	PROPN
bracis-19038	125	15	)	)	PUNCT
bracis-19038	125	16	and	and	CCONJ
bracis-19038	125	17	\(\mathcal	\(\mathcal	PROPN
bracis-19038	125	18	b_1	b_1	PROPN
bracis-19038	125	19	\subseteq	\subseteq	PROPN
bracis-19038	125	20	^y	^y	ADJ
bracis-19038	125	21	\mathcal	\mathcal	PROPN
bracis-19038	125	22	w_2\	w_2\	PROPN
bracis-19038	125	23	)	)	PUNCT
bracis-19038	125	24	in	in	ADP
bracis-19038	125	25	\(\varphi	\(\varphi	ADJ
bracis-19038	125	26	\	\	NOUN
bracis-19038	125	27	)	)	PUNCT
bracis-19038	125	28	.	.	PUNCT
bracis-19038	126	1	b	b	X
bracis-19038	126	2	)	)	PUNCT
bracis-19038	126	3	(	(	PUNCT
bracis-19038	126	4	optimistic	optimistic	ADJ
bracis-19038	126	5	semantics	semantic	NOUN
bracis-19038	126	6	):	):	PUNCT
bracis-19038	126	7	if	if	SCONJ
bracis-19038	126	8	\(x	\(x	NOUN
bracis-19038	126	9	=	=	SYM
bracis-19038	126	10	opt	opt	PROPN
bracis-19038	126	11	\	\	NOUN
bracis-19038	126	12	)	)	PUNCT
bracis-19038	126	13	and	and	CCONJ
bracis-19038	126	14	\(\mathcal	\(\mathcal	PROPN
bracis-19038	126	15	b_1	b_1	PROPN
bracis-19038	126	16	\subseteq	\subseteq	PROPN
bracis-19038	126	17	^y	^y	ADJ
bracis-19038	126	18	\mathcal	\mathcal	PROPN
bracis-19038	126	19	b_2\	b_2\	PROPN
bracis-19038	126	20	)	)	PUNCT
bracis-19038	126	21	in	in	ADP
bracis-19038	126	22	\(\varphi	\(\varphi	NOUN
bracis-19038	126	23	\	\	NOUN
bracis-19038	126	24	)	)	PUNCT
bracis-19038	126	25	.	.	PUNCT
bracis-19038	127	1	c	c	X
bracis-19038	127	2	)	)	PUNCT
bracis-19038	127	3	(	(	PUNCT
bracis-19038	127	4	pessimistic	pessimistic	ADJ
bracis-19038	127	5	semantics	semantic	NOUN
bracis-19038	127	6	):	):	PUNCT
bracis-19038	127	7	if	if	SCONJ
bracis-19038	127	8	\(x	\(x	NOUN
bracis-19038	127	9	=	=	SYM
bracis-19038	127	10	pes	pes	X
bracis-19038	127	11	\	\	PROPN
bracis-19038	127	12	)	)	PUNCT
bracis-19038	127	13	and	and	CCONJ
bracis-19038	127	14	\(\mathcal	\(\mathcal	ADJ
bracis-19038	127	15	w_1	w_1	PROPN
bracis-19038	127	16	\subseteq	\subseteq	PROPN
bracis-19038	127	17	^y	^y	ADJ
bracis-19038	127	18	\mathcal	\mathcal	PROPN
bracis-19038	127	19	w_2\	w_2\	PROPN
bracis-19038	127	20	)	)	PUNCT
bracis-19038	127	21	in	in	ADP
bracis-19038	127	22	\(\varphi	\(\varphi	NOUN
bracis-19038	127	23	\	\	NOUN
bracis-19038	127	24	)	)	PUNCT
bracis-19038	127	25	.	.	PUNCT
bracis-19038	128	1	d	d	X
bracis-19038	128	2	)	)	PUNCT
bracis-19038	128	3	(	(	PUNCT
bracis-19038	128	4	opportunistic	opportunistic	ADJ
bracis-19038	128	5	semantics	semantic	NOUN
bracis-19038	128	6	):	):	PUNCT
bracis-19038	128	7	if	if	SCONJ
bracis-19038	128	8	\(x	\(x	NOUN
bracis-19038	128	9	=	=	PUNCT
bracis-19038	128	10	opp	opp	PROPN
bracis-19038	128	11	\	\	PROPN
bracis-19038	128	12	)	)	PUNCT
bracis-19038	128	13	and	and	CCONJ
bracis-19038	128	14	\(\mathcal	\(\mathcal	ADJ
bracis-19038	128	15	w_1	w_1	PROPN
bracis-19038	128	16	\subseteq	\subseteq	PROPN
bracis-19038	128	17	^y	^y	ADJ
bracis-19038	128	18	\mathcal	\mathcal	PROPN
bracis-19038	128	19	b_2\	b_2\	PROPN
bracis-19038	128	20	)	)	PUNCT
bracis-19038	128	21	in	in	ADP
bracis-19038	128	22	\(\varphi	\(\varphi	NOUN
bracis-19038	128	23	\	\	NOUN
bracis-19038	128	24	)	)	PUNCT
bracis-19038	128	25	.	.	PUNCT
bracis-19038	129	1	3	3	X
bracis-19038	129	2	.	.	X
bracis-19038	130	1	if	if	SCONJ
bracis-19038	130	2	\(i_1	\(i_1	PROPN
bracis-19038	130	3	\subseteq	\subseteq	PROPN
bracis-19038	130	4	^y_x	^y_x	NUM
bracis-19038	130	5	i_2\	i_2\	NUM
bracis-19038	130	6	)	)	PUNCT
bracis-19038	130	7	w.r.t	w.r.t	NOUN
bracis-19038	130	8	.	.	PUNCT
bracis-19038	131	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	131	2	\	\	NUM
bracis-19038	131	3	)	)	PUNCT
bracis-19038	131	4	and	and	CCONJ
bracis-19038	131	5	\(i_2	\(i_2	PROPN
bracis-19038	131	6	\subseteq	\subseteq	PROPN
bracis-19038	131	7	^y_x	^y_x	NUM
bracis-19038	131	8	i_3\	i_3\	NOUN
bracis-19038	131	9	)	)	PUNCT
bracis-19038	131	10	w.r.t	w.r.t	NOUN
bracis-19038	131	11	.	.	PUNCT
bracis-19038	132	1	\(\varphi	\(\varphi	ADJ
bracis-19038	132	2	\	\	NOUN
bracis-19038	132	3	)	)	PUNCT
bracis-19038	132	4	,	,	PUNCT
bracis-19038	132	5	then	then	ADV
bracis-19038	132	6	\(i_1	\(i_1	PROPN
bracis-19038	132	7	\subseteq	\subseteq	PROPN
bracis-19038	132	8	^y_x	^y_x	NUM
bracis-19038	132	9	i_3\	i_3\	PROPN
bracis-19038	132	10	)	)	PUNCT
bracis-19038	132	11	w.r.t	w.r.t	NOUN
bracis-19038	132	12	.	.	PUNCT
bracis-19038	133	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	133	2	\	\	NUM
bracis-19038	133	3	)	)	PUNCT
bracis-19038	133	4	.	.	PUNCT
bracis-19038	134	1	when	when	SCONJ
bracis-19038	134	2	it	it	PRON
bracis-19038	134	3	is	be	AUX
bracis-19038	134	4	clear	clear	ADJ
bracis-19038	134	5	from	from	ADP
bracis-19038	134	6	the	the	DET
bracis-19038	134	7	context	context	NOUN
bracis-19038	134	8	,	,	PUNCT
bracis-19038	134	9	we	we	PRON
bracis-19038	134	10	will	will	AUX
bracis-19038	134	11	drop	drop	VERB
bracis-19038	134	12	the	the	DET
bracis-19038	134	13	reference	reference	NOUN
bracis-19038	134	14	to	to	ADP
bracis-19038	134	15	\(\varphi	\(\varphi	ADJ
bracis-19038	134	16	\	\	NOUN
bracis-19038	134	17	)	)	PUNCT
bracis-19038	134	18	and	and	CCONJ
bracis-19038	134	19	say	say	VERB
bracis-19038	134	20	\(\mathcal	\(\mathcal	ADJ
bracis-19038	134	21	o_1	o_1	ADP
bracis-19038	134	22	\subseteq	\subseteq	PROPN
bracis-19038	134	23	^{\forall	^{\forall	NOUN
bracis-19038	134	24	\forall	\forall	PRON
bracis-19038	134	25	}	}	PUNCT
bracis-19038	134	26	\mathcal	\mathcal	ADJ
bracis-19038	134	27	o_2\	o_2\	PROPN
bracis-19038	134	28	)	)	PUNCT
bracis-19038	134	29	and	and	CCONJ
bracis-19038	134	30	\(i_1	\(i_1	NUM
bracis-19038	134	31	\subseteq	\subseteq	PROPN
bracis-19038	134	32	^y_x	^y_x	NUM
bracis-19038	134	33	i_2\	i_2\	NUM
bracis-19038	134	34	)	)	PUNCT
bracis-19038	134	35	.	.	PUNCT
bracis-19038	135	1	inspired	inspire	VERB
bracis-19038	135	2	by	by	ADP
bracis-19038	135	3	[	[	X
bracis-19038	135	4	4	4	NUM
bracis-19038	135	5	]	]	PUNCT
bracis-19038	135	6	,	,	PUNCT
bracis-19038	135	7	we	we	PRON
bracis-19038	135	8	can	can	AUX
bracis-19038	135	9	define	define	VERB
bracis-19038	135	10	a	a	DET
bracis-19038	135	11	preference	preference	NOUN
bracis-19038	135	12	relation	relation	NOUN
bracis-19038	135	13	\(i_1	\(i_1	PROPN
bracis-19038	135	14	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	135	15	^y_x	^y_x	NUM
bracis-19038	135	16	i_2\	i_2\	NUM
bracis-19038	135	17	)	)	PUNCT
bracis-19038	135	18	which	which	PRON
bracis-19038	135	19	consider	consider	VERB
bracis-19038	135	20	just	just	ADV
bracis-19038	135	21	their	their	PRON
bracis-19038	135	22	exclusive	exclusive	ADJ
bracis-19038	135	23	portions	portion	NOUN
bracis-19038	135	24	given	give	VERB
bracis-19038	135	25	by	by	ADP
bracis-19038	135	26	\(i_1	\(i_1	NUM
bracis-19038	135	27	i_2\	i_2\	NUM
bracis-19038	135	28	)	)	PUNCT
bracis-19038	135	29	and	and	CCONJ
bracis-19038	135	30	\(i_2	\(i_2	PROPN
bracis-19038	135	31	i_1\	i_1\	PROPN
bracis-19038	135	32	)	)	PUNCT
bracis-19038	135	33	.	.	PUNCT
bracis-19038	136	1	1	1	X
bracis-19038	136	2	.	.	X
bracis-19038	137	1	\(i_1	\(i_1	NUM
bracis-19038	137	2	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	137	3	^y_x	^y_x	NUM
bracis-19038	137	4	i_2\	i_2\	NUM
bracis-19038	137	5	)	)	PUNCT
bracis-19038	137	6	iff	iff	VERB
bracis-19038	137	7	\(i_1	\(i_1	PROPN
bracis-19038	137	8	i_2	i_2	VERB
bracis-19038	137	9	\subseteq	\subseteq	PROPN
bracis-19038	137	10	^y_x	^y_x	NUM
bracis-19038	137	11	i_2	i_2	PROPN
bracis-19038	137	12	i_1\	i_1\	PROPN
bracis-19038	137	13	)	)	PUNCT
bracis-19038	137	14	.	.	PUNCT
bracis-19038	138	1	2	2	X
bracis-19038	138	2	.	.	X
bracis-19038	139	1	if	if	SCONJ
bracis-19038	139	2	\(i_1	\(i_1	PROPN
bracis-19038	139	3	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	139	4	^y_x	^y_x	NUM
bracis-19038	139	5	i_2\	i_2\	NUM
bracis-19038	139	6	)	)	PUNCT
bracis-19038	139	7	and	and	CCONJ
bracis-19038	139	8	\(i_2	\(i_2	PROPN
bracis-19038	139	9	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	139	10	^y_x	^y_x	NUM
bracis-19038	139	11	i_3\	i_3\	PROPN
bracis-19038	139	12	)	)	PUNCT
bracis-19038	139	13	,	,	PUNCT
bracis-19038	139	14	then	then	ADV
bracis-19038	139	15	\(i_1	\(i_1	PROPN
bracis-19038	139	16	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	139	17	^y_x	^y_x	NUM
bracis-19038	139	18	i_3\	i_3\	PROPN
bracis-19038	139	19	)	)	PUNCT
bracis-19038	139	20	.	.	PUNCT
bracis-19038	140	1	note	note	VERB
bracis-19038	140	2	we	we	PRON
bracis-19038	140	3	have	have	VERB
bracis-19038	140	4	four	four	NUM
bracis-19038	140	5	criteria	criterion	NOUN
bracis-19038	140	6	to	to	PART
bracis-19038	140	7	choose	choose	VERB
bracis-19038	140	8	the	the	DET
bracis-19038	140	9	best	good	ADJ
bracis-19038	140	10	/	/	SYM
bracis-19038	140	11	worst	worst	ADV
bracis-19038	140	12	-	-	PUNCT
bracis-19038	140	13	ranked	rank	VERB
bracis-19038	140	14	options	option	NOUN
bracis-19038	140	15	(	(	PUNCT
bracis-19038	140	16	definition	definition	NOUN
bracis-19038	140	17	9	9	NUM
bracis-19038	140	18	)	)	PUNCT
bracis-19038	140	19	,	,	PUNCT
bracis-19038	140	20	four	four	NUM
bracis-19038	140	21	criteria	criterion	NOUN
bracis-19038	140	22	to	to	PART
bracis-19038	140	23	choose	choose	VERB
bracis-19038	140	24	the	the	DET
bracis-19038	140	25	most	most	ADV
bracis-19038	140	26	preferable	preferable	ADJ
bracis-19038	140	27	semantics	semantic	NOUN
bracis-19038	140	28	(	(	PUNCT
bracis-19038	140	29	definition	definition	NOUN
bracis-19038	140	30	10	10	NUM
bracis-19038	140	31	)	)	PUNCT
bracis-19038	140	32	.	.	PUNCT
bracis-19038	141	1	we	we	PRON
bracis-19038	141	2	also	also	ADV
bracis-19038	141	3	can	can	AUX
bracis-19038	141	4	decide	decide	VERB
bracis-19038	141	5	if	if	SCONJ
bracis-19038	141	6	a	a	DET
bracis-19038	141	7	\	\	PROPN
bracis-19038	141	8	(	(	PUNCT
bracis-19038	141	9	ps	ps	PROPN
bracis-19038	141	10	\	\	ADJ
bracis-19038	141	11	)	)	PUNCT
bracis-19038	141	12	model	model	NOUN
bracis-19038	141	13	\(i_1\	\(i_1\	PROPN
bracis-19038	141	14	)	)	PUNCT
bracis-19038	141	15	is	be	AUX
bracis-19038	141	16	preferred	prefer	VERB
bracis-19038	141	17	to	to	ADP
bracis-19038	141	18	a	a	DET
bracis-19038	141	19	\	\	PROPN
bracis-19038	141	20	(	(	PUNCT
bracis-19038	141	21	ps	ps	PROPN
bracis-19038	141	22	\	\	ADJ
bracis-19038	141	23	)	)	PUNCT
bracis-19038	141	24	model	model	NOUN
bracis-19038	141	25	\(i_2\	\(i_2\	PROPN
bracis-19038	141	26	)	)	PUNCT
bracis-19038	141	27	by	by	ADP
bracis-19038	141	28	regarding	regard	VERB
bracis-19038	141	29	the	the	DET
bracis-19038	141	30	whole	whole	ADJ
bracis-19038	141	31	models	model	NOUN
bracis-19038	141	32	or	or	CCONJ
bracis-19038	141	33	just	just	ADV
bracis-19038	141	34	their	their	PRON
bracis-19038	141	35	exclusive	exclusive	ADJ
bracis-19038	141	36	portions	portion	NOUN
bracis-19038	141	37	given	give	VERB
bracis-19038	141	38	by	by	ADP
bracis-19038	141	39	\(i_1	\(i_1	NUM
bracis-19038	141	40	i_2\	i_2\	NUM
bracis-19038	141	41	)	)	PUNCT
bracis-19038	141	42	and	and	CCONJ
bracis-19038	141	43	\(i_2	\(i_2	PROPN
bracis-19038	141	44	i_1\	i_1\	PROPN
bracis-19038	141	45	)	)	PUNCT
bracis-19038	141	46	.	.	PUNCT
bracis-19038	142	1	hence	hence	ADV
bracis-19038	142	2	,	,	PUNCT
bracis-19038	142	3	we	we	PRON
bracis-19038	142	4	have	have	VERB
bracis-19038	142	5	at	at	ADP
bracis-19038	142	6	disposal	disposal	NOUN
bracis-19038	142	7	32	32	NUM
bracis-19038	142	8	manners	manner	NOUN
bracis-19038	142	9	of	of	ADP
bracis-19038	142	10	selecting	select	VERB
bracis-19038	142	11	the	the	DET
bracis-19038	142	12	preferred	preferred	ADJ
bracis-19038	142	13	partial	partial	ADJ
bracis-19038	142	14	stable	stable	ADJ
bracis-19038	142	15	models	model	NOUN
bracis-19038	142	16	:	:	PUNCT
bracis-19038	142	17	definition	definition	NOUN
bracis-19038	142	18	11	11	NUM
bracis-19038	142	19	(	(	PUNCT
bracis-19038	142	20	preferred	prefer	VERB
bracis-19038	142	21	partial	partial	ADJ
bracis-19038	142	22	stable	stable	ADJ
bracis-19038	142	23	model	model	NOUN
bracis-19038	142	24	)	)	PUNCT
bracis-19038	142	25	let	let	VERB
bracis-19038	142	26	\((p,\varphi	\((p,\varphi	NOUN
bracis-19038	142	27	)	)	PUNCT
bracis-19038	142	28	\	\	NOUN
bracis-19038	142	29	)	)	PUNCT
bracis-19038	142	30	be	be	AUX
bracis-19038	142	31	a	a	DET
bracis-19038	142	32	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	142	33	)	)	PUNCT
bracis-19038	142	34	.	.	PUNCT
bracis-19038	143	1	a	a	DET
bracis-19038	143	2	\	\	PROPN
bracis-19038	143	3	(	(	PUNCT
bracis-19038	143	4	ps	ps	PROPN
bracis-19038	143	5	\	\	ADJ
bracis-19038	143	6	)	)	PUNCT
bracis-19038	143	7	model	model	NOUN
bracis-19038	143	8	i	i	PRON
bracis-19038	143	9	of	of	ADP
bracis-19038	143	10	p	p	PROPN
bracis-19038	143	11	is	be	AUX
bracis-19038	143	12	a	a	DET
bracis-19038	143	13	preferred	preferred	ADJ
bracis-19038	143	14	partial	partial	ADJ
bracis-19038	143	15	stable	stable	ADJ
bracis-19038	143	16	model	model	NOUN
bracis-19038	143	17	(	(	PUNCT
bracis-19038	143	18	or	or	CCONJ
bracis-19038	143	19	\	\	PROPN
bracis-19038	143	20	(	(	PUNCT
bracis-19038	143	21	pps	pps	NOUN
bracis-19038	143	22	\	\	ADJ
bracis-19038	143	23	)	)	PUNCT
bracis-19038	143	24	model	model	NOUN
bracis-19038	143	25	,	,	PUNCT
bracis-19038	143	26	for	for	ADP
bracis-19038	143	27	short	short	ADJ
bracis-19038	143	28	)	)	PUNCT
bracis-19038	143	29	of	of	ADP
bracis-19038	143	30	\((p,\varphi	\((p,\varphi	NOUN
bracis-19038	143	31	)	)	PUNCT
bracis-19038	143	32	\	\	NOUN
bracis-19038	143	33	)	)	PUNCT
bracis-19038	143	34	w.r.t	w.r.t	NOUN
bracis-19038	143	35	.	.	PUNCT
bracis-19038	144	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	144	2	^y_x\	^y_x\	NUM
bracis-19038	144	3	)	)	PUNCT
bracis-19038	144	4	(	(	PUNCT
bracis-19038	144	5	resp	resp	NOUN
bracis-19038	144	6	.	.	PUNCT
bracis-19038	145	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	145	2	^y_x\	^y_x\	NUM
bracis-19038	145	3	)	)	PUNCT
bracis-19038	145	4	)	)	PUNCT
bracis-19038	146	1	if	if	SCONJ
bracis-19038	146	2	\(i	\(i	PRON
bracis-19038	146	3	\subseteq	\subseteq	PROPN
bracis-19038	146	4	^y_x	^y_x	NUM
bracis-19038	146	5	i'\	i'\	PROPN
bracis-19038	146	6	)	)	PUNCT
bracis-19038	146	7	(	(	PUNCT
bracis-19038	146	8	resp	resp	NOUN
bracis-19038	146	9	.	.	PUNCT
bracis-19038	147	1	\(i	\(i	PROPN
bracis-19038	147	2	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	147	3	^y_x	^y_x	NUM
bracis-19038	147	4	i'\	i'\	PROPN
bracis-19038	147	5	)	)	PUNCT
bracis-19038	147	6	)	)	PUNCT
bracis-19038	147	7	implies	imply	VERB
bracis-19038	147	8	\(i	\(i	NOUN
bracis-19038	147	9	'	'	PUNCT
bracis-19038	147	10	\subseteq	\subseteq	PROPN
bracis-19038	147	11	^y_x	^y_x	NUM
bracis-19038	147	12	i\	i\	NOUN
bracis-19038	147	13	)	)	PUNCT
bracis-19038	147	14	(	(	PUNCT
bracis-19038	147	15	resp	resp	NOUN
bracis-19038	147	16	.	.	PUNCT
bracis-19038	148	1	\(i	\(i	PROPN
bracis-19038	148	2	'	'	PUNCT
bracis-19038	148	3	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	148	4	^y_x	^y_x	NUM
bracis-19038	148	5	i\	i\	PROPN
bracis-19038	148	6	)	)	PUNCT
bracis-19038	148	7	)	)	PUNCT
bracis-19038	149	1	(	(	PUNCT
bracis-19038	149	2	w.r.t	w.r.t	VERB
bracis-19038	149	3	\(\varphi	\(\varphi	PUNCT
bracis-19038	149	4	\	\	NOUN
bracis-19038	149	5	)	)	PUNCT
bracis-19038	149	6	)	)	PUNCT
bracis-19038	149	7	for	for	ADP
bracis-19038	149	8	any	any	DET
bracis-19038	149	9	\	\	NOUN
bracis-19038	149	10	(	(	PUNCT
bracis-19038	149	11	ps	ps	PROPN
bracis-19038	149	12	\	\	ADJ
bracis-19038	149	13	)	)	PUNCT
bracis-19038	149	14	model	model	NOUN
bracis-19038	149	15	\(i'\	\(i'\	NOUN
bracis-19038	149	16	)	)	PUNCT
bracis-19038	149	17	of	of	ADP
bracis-19038	149	18	p.	p.	NOUN
bracis-19038	149	19	the	the	DET
bracis-19038	149	20	set	set	NOUN
bracis-19038	149	21	of	of	ADP
bracis-19038	149	22	all	all	DET
bracis-19038	149	23	\	\	PROPN
bracis-19038	149	24	(	(	PUNCT
bracis-19038	149	25	pps	pps	PROPN
bracis-19038	149	26	\	\	PROPN
bracis-19038	149	27	)	)	PUNCT
bracis-19038	149	28	of	of	ADP
bracis-19038	149	29	\((p,\varphi	\((p,\varphi	NOUN
bracis-19038	149	30	)	)	PUNCT
bracis-19038	149	31	\	\	NOUN
bracis-19038	149	32	)	)	PUNCT
bracis-19038	149	33	w.r.t	w.r.t	NOUN
bracis-19038	149	34	.	.	PUNCT
bracis-19038	150	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	150	2	^y_x\	^y_x\	NUM
bracis-19038	150	3	)	)	PUNCT
bracis-19038	150	4	(	(	PUNCT
bracis-19038	150	5	resp	resp	NOUN
bracis-19038	150	6	.	.	PUNCT
bracis-19038	151	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	151	2	^y_x\	^y_x\	NUM
bracis-19038	151	3	)	)	PUNCT
bracis-19038	151	4	)	)	PUNCT
bracis-19038	152	1	is	be	AUX
bracis-19038	152	2	written	write	VERB
bracis-19038	152	3	as	as	ADP
bracis-19038	152	4	\(\mathcal	\(\mathcal	ADJ
bracis-19038	152	5	{	{	PUNCT
bracis-19038	152	6	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	152	7	)	)	PUNCT
bracis-19038	153	1	_	_	PRON
bracis-19038	153	2	{	{	PUNCT
bracis-19038	153	3	\subseteq	\subseteq	PROPN
bracis-19038	153	4	^y_x}\	^y_x}\	NUM
bracis-19038	153	5	)	)	PUNCT
bracis-19038	153	6	(	(	PUNCT
bracis-19038	153	7	resp	resp	NOUN
bracis-19038	153	8	.	.	PUNCT
bracis-19038	154	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	154	2	{	{	PUNCT
bracis-19038	154	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	154	4	)	)	PUNCT
bracis-19038	155	1	_	_	PRON
bracis-19038	155	2	{	{	PUNCT
bracis-19038	155	3	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	155	4	^y_x}\	^y_x}\	NUM
bracis-19038	155	5	)	)	PUNCT
bracis-19038	155	6	)	)	PUNCT
bracis-19038	155	7	.	.	PUNCT
bracis-19038	156	1	as	as	SCONJ
bracis-19038	156	2	the	the	DET
bracis-19038	156	3	remaining	remain	VERB
bracis-19038	156	4	semantics	semantic	NOUN
bracis-19038	156	5	for	for	ADP
bracis-19038	156	6	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	156	7	)	)	PUNCT
bracis-19038	156	8	seen	see	VERB
bracis-19038	156	9	in	in	ADP
bracis-19038	156	10	this	this	DET
bracis-19038	156	11	paper	paper	NOUN
bracis-19038	156	12	are	be	AUX
bracis-19038	156	13	based	base	VERB
bracis-19038	156	14	on	on	ADP
bracis-19038	156	15	\	\	PROPN
bracis-19038	156	16	(	(	PUNCT
bracis-19038	156	17	ps	ps	PROPN
bracis-19038	156	18	\	\	ADJ
bracis-19038	156	19	)	)	PUNCT
bracis-19038	156	20	models	model	NOUN
bracis-19038	156	21	(	(	PUNCT
bracis-19038	156	22	definition	definition	NOUN
bracis-19038	156	23	3	3	NUM
bracis-19038	156	24	)	)	PUNCT
bracis-19038	156	25	,	,	PUNCT
bracis-19038	156	26	we	we	PRON
bracis-19038	156	27	are	be	AUX
bracis-19038	156	28	equipped	equip	VERB
bracis-19038	156	29	with	with	ADP
bracis-19038	156	30	32	32	NUM
bracis-19038	156	31	different	different	ADJ
bracis-19038	156	32	manners	manner	NOUN
bracis-19038	156	33	of	of	ADP
bracis-19038	156	34	selecting	select	VERB
bracis-19038	156	35	the	the	DET
bracis-19038	156	36	most	most	ADV
bracis-19038	156	37	preferred	preferred	ADJ
bracis-19038	156	38	models	model	NOUN
bracis-19038	156	39	according	accord	VERB
bracis-19038	156	40	to	to	ADP
bracis-19038	156	41	them	they	PRON
bracis-19038	156	42	.	.	PUNCT
bracis-19038	157	1	definition	definition	NOUN
bracis-19038	157	2	12	12	NUM
bracis-19038	157	3	let	let	VERB
bracis-19038	157	4	\((p	\((p	NOUN
bracis-19038	157	5	,	,	PUNCT
bracis-19038	157	6	\varphi	\varphi	PROPN
bracis-19038	157	7	)	)	PUNCT
bracis-19038	157	8	\	\	NOUN
bracis-19038	157	9	)	)	PUNCT
bracis-19038	157	10	be	be	AUX
bracis-19038	157	11	an	an	DET
bracis-19038	157	12	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	157	13	)	)	PUNCT
bracis-19038	157	14	and	and	CCONJ
bracis-19038	157	15	i	i	PRON
bracis-19038	157	16	be	be	VERB
bracis-19038	157	17	an	an	DET
bracis-19038	157	18	interpretation	interpretation	NOUN
bracis-19038	157	19	:	:	PUNCT
bracis-19038	157	20	i	i	PRON
bracis-19038	157	21	is	be	AUX
bracis-19038	157	22	a	a	DET
bracis-19038	157	23	preferential	preferential	ADJ
bracis-19038	157	24	well	well	ADV
bracis-19038	157	25	-	-	PUNCT
bracis-19038	157	26	founded	found	VERB
bracis-19038	157	27	model	model	NOUN
bracis-19038	157	28	of	of	ADP
bracis-19038	157	29	\((p	\((p	NOUN
bracis-19038	157	30	,	,	PUNCT
bracis-19038	157	31	\varphi	\varphi	PROPN
bracis-19038	157	32	)	)	PUNCT
bracis-19038	157	33	\	\	NOUN
bracis-19038	157	34	)	)	PUNCT
bracis-19038	157	35	w.r.t	w.r.t	NOUN
bracis-19038	157	36	.	.	PUNCT
bracis-19038	158	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	158	2	^y_x\	^y_x\	NUM
bracis-19038	158	3	)	)	PUNCT
bracis-19038	158	4	(	(	PUNCT
bracis-19038	158	5	resp	resp	NOUN
bracis-19038	158	6	.	.	PUNCT
bracis-19038	159	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	159	2	^y_x\	^y_x\	NUM
bracis-19038	159	3	)	)	PUNCT
bracis-19038	159	4	)	)	PUNCT
bracis-19038	160	1	iff	iff	PROPN
bracis-19038	160	2	i	i	PRON
bracis-19038	160	3	is	be	AUX
bracis-19038	160	4	a	a	DET
bracis-19038	160	5	\	\	PROPN
bracis-19038	160	6	(	(	PUNCT
bracis-19038	160	7	pps	pps	PROPN
bracis-19038	160	8	\	\	ADJ
bracis-19038	160	9	)	)	PUNCT
bracis-19038	160	10	model	model	NOUN
bracis-19038	160	11	of	of	ADP
bracis-19038	160	12	\((p	\((p	NOUN
bracis-19038	160	13	,	,	PUNCT
bracis-19038	160	14	\varphi	\varphi	PROPN
bracis-19038	160	15	)	)	PUNCT
bracis-19038	160	16	\	\	NOUN
bracis-19038	160	17	)	)	PUNCT
bracis-19038	160	18	w.r.t	w.r.t	NOUN
bracis-19038	160	19	.	.	PUNCT
bracis-19038	161	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	161	2	^y_x\	^y_x\	NUM
bracis-19038	161	3	)	)	PUNCT
bracis-19038	161	4	(	(	PUNCT
bracis-19038	161	5	resp	resp	NOUN
bracis-19038	161	6	.	.	PUNCT
bracis-19038	162	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	162	2	^y_x\	^y_x\	NUM
bracis-19038	162	3	)	)	PUNCT
bracis-19038	162	4	)	)	PUNCT
bracis-19038	163	1	with	with	ADP
bracis-19038	163	2	minimal	minimal	ADJ
bracis-19038	163	3	\(t_i\	\(t_i\	NOUN
bracis-19038	163	4	)	)	PUNCT
bracis-19038	163	5	.	.	PUNCT
bracis-19038	164	1	i	i	PRON
bracis-19038	164	2	is	be	AUX
bracis-19038	164	3	a	a	DET
bracis-19038	164	4	preferential	preferential	ADJ
bracis-19038	164	5	regular	regular	ADJ
bracis-19038	164	6	model	model	NOUN
bracis-19038	164	7	of	of	ADP
bracis-19038	164	8	\((p	\((p	NOUN
bracis-19038	164	9	,	,	PUNCT
bracis-19038	164	10	\varphi	\varphi	PROPN
bracis-19038	164	11	)	)	PUNCT
bracis-19038	164	12	\	\	NOUN
bracis-19038	164	13	)	)	PUNCT
bracis-19038	164	14	w.r.t	w.r.t	NOUN
bracis-19038	164	15	.	.	PUNCT
bracis-19038	165	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	165	2	^y_x\	^y_x\	NUM
bracis-19038	165	3	)	)	PUNCT
bracis-19038	165	4	(	(	PUNCT
bracis-19038	165	5	resp	resp	NOUN
bracis-19038	165	6	.	.	PUNCT
bracis-19038	166	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	166	2	^y_x\	^y_x\	NUM
bracis-19038	166	3	)	)	PUNCT
bracis-19038	166	4	)	)	PUNCT
bracis-19038	167	1	iff	iff	PROPN
bracis-19038	167	2	i	i	PRON
bracis-19038	167	3	is	be	AUX
bracis-19038	167	4	a	a	DET
bracis-19038	167	5	\	\	PROPN
bracis-19038	167	6	(	(	PUNCT
bracis-19038	167	7	pps	pps	PROPN
bracis-19038	167	8	\	\	ADJ
bracis-19038	167	9	)	)	PUNCT
bracis-19038	167	10	model	model	NOUN
bracis-19038	167	11	of	of	ADP
bracis-19038	167	12	\((p	\((p	NOUN
bracis-19038	167	13	,	,	PUNCT
bracis-19038	167	14	\varphi	\varphi	PROPN
bracis-19038	167	15	)	)	PUNCT
bracis-19038	167	16	\	\	NOUN
bracis-19038	167	17	)	)	PUNCT
bracis-19038	167	18	w.r.t	w.r.t	NOUN
bracis-19038	167	19	.	.	PUNCT
bracis-19038	168	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	168	2	^y_x\	^y_x\	NUM
bracis-19038	168	3	)	)	PUNCT
bracis-19038	168	4	(	(	PUNCT
bracis-19038	168	5	resp	resp	NOUN
bracis-19038	168	6	.	.	PUNCT
bracis-19038	169	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	169	2	^y_x\	^y_x\	NUM
bracis-19038	169	3	)	)	PUNCT
bracis-19038	169	4	)	)	PUNCT
bracis-19038	170	1	with	with	ADP
bracis-19038	170	2	maximal	maximal	ADJ
bracis-19038	170	3	\(t_i\	\(t_i\	NOUN
bracis-19038	170	4	)	)	PUNCT
bracis-19038	170	5	.	.	PUNCT
bracis-19038	171	1	i	i	PRON
bracis-19038	171	2	is	be	AUX
bracis-19038	171	3	a	a	DET
bracis-19038	171	4	preferential	preferential	ADJ
bracis-19038	171	5	stable	stable	ADJ
bracis-19038	171	6	model	model	NOUN
bracis-19038	171	7	of	of	ADP
bracis-19038	171	8	\((p	\((p	NOUN
bracis-19038	171	9	,	,	PUNCT
bracis-19038	171	10	\varphi	\varphi	PROPN
bracis-19038	171	11	)	)	PUNCT
bracis-19038	171	12	\	\	NOUN
bracis-19038	171	13	)	)	PUNCT
bracis-19038	171	14	w.r.t	w.r.t	NOUN
bracis-19038	171	15	.	.	PUNCT
bracis-19038	172	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	172	2	^y_x\	^y_x\	NUM
bracis-19038	172	3	)	)	PUNCT
bracis-19038	172	4	(	(	PUNCT
bracis-19038	172	5	resp	resp	NOUN
bracis-19038	172	6	.	.	PUNCT
bracis-19038	173	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	173	2	^y_x\	^y_x\	NUM
bracis-19038	173	3	)	)	PUNCT
bracis-19038	173	4	)	)	PUNCT
bracis-19038	174	1	iff	iff	PROPN
bracis-19038	174	2	i	i	PRON
bracis-19038	174	3	is	be	AUX
bracis-19038	174	4	a	a	DET
bracis-19038	174	5	\	\	PROPN
bracis-19038	174	6	(	(	PUNCT
bracis-19038	174	7	pps	pps	PROPN
bracis-19038	174	8	\	\	ADJ
bracis-19038	174	9	)	)	PUNCT
bracis-19038	174	10	model	model	NOUN
bracis-19038	174	11	of	of	ADP
bracis-19038	174	12	\((p	\((p	NOUN
bracis-19038	174	13	,	,	PUNCT
bracis-19038	174	14	\varphi	\varphi	PROPN
bracis-19038	174	15	)	)	PUNCT
bracis-19038	174	16	\	\	NOUN
bracis-19038	174	17	)	)	PUNCT
bracis-19038	174	18	w.r.t	w.r.t	NOUN
bracis-19038	174	19	.	.	PUNCT
bracis-19038	175	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	175	2	^y_x\	^y_x\	NUM
bracis-19038	175	3	)	)	PUNCT
bracis-19038	175	4	(	(	PUNCT
bracis-19038	175	5	resp	resp	NOUN
bracis-19038	175	6	.	.	PUNCT
bracis-19038	176	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	176	2	^y_x\	^y_x\	NUM
bracis-19038	176	3	)	)	PUNCT
bracis-19038	176	4	)	)	PUNCT
bracis-19038	177	1	where	where	SCONJ
bracis-19038	177	2	for	for	ADP
bracis-19038	177	3	each	each	DET
bracis-19038	177	4	\(a	\(a	NOUN
bracis-19038	177	5	\in	\in	NOUN
bracis-19038	177	6	hb	hb	NOUN
bracis-19038	177	7	_	_	NOUN
bracis-19038	177	8	p\	p\	NOUN
bracis-19038	177	9	)	)	PUNCT
bracis-19038	177	10	,	,	PUNCT
bracis-19038	177	11	\(a	\(a	NOUN
bracis-19038	177	12	\in	\in	PROPN
bracis-19038	177	13	t_i	t_i	VERB
bracis-19038	177	14	\cup	\cup	VERB
bracis-19038	177	15	f_i\	f_i\	NOUN
bracis-19038	177	16	)	)	PUNCT
bracis-19038	177	17	.	.	PUNCT
bracis-19038	178	1	i	i	PRON
bracis-19038	178	2	is	be	AUX
bracis-19038	178	3	a	a	DET
bracis-19038	178	4	preferential	preferential	ADJ
bracis-19038	178	5	l	l	ADJ
bracis-19038	178	6	-	-	ADJ
bracis-19038	178	7	stable	stable	ADJ
bracis-19038	178	8	model	model	NOUN
bracis-19038	178	9	of	of	ADP
bracis-19038	178	10	\((p,\varphi	\((p,\varphi	NOUN
bracis-19038	178	11	)	)	PUNCT
bracis-19038	178	12	\	\	NOUN
bracis-19038	178	13	)	)	PUNCT
bracis-19038	178	14	w.r.t	w.r.t	NOUN
bracis-19038	178	15	.	.	PUNCT
bracis-19038	179	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	179	2	^y_x\	^y_x\	NUM
bracis-19038	179	3	)	)	PUNCT
bracis-19038	179	4	(	(	PUNCT
bracis-19038	179	5	resp	resp	NOUN
bracis-19038	179	6	.	.	PUNCT
bracis-19038	180	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	180	2	^y_x\	^y_x\	NUM
bracis-19038	180	3	)	)	PUNCT
bracis-19038	180	4	)	)	PUNCT
bracis-19038	181	1	iff	iff	PROPN
bracis-19038	181	2	i	i	PRON
bracis-19038	181	3	is	be	AUX
bracis-19038	181	4	a	a	DET
bracis-19038	181	5	a	a	DET
bracis-19038	181	6	\	\	PROPN
bracis-19038	181	7	(	(	PUNCT
bracis-19038	181	8	pps	pps	PROPN
bracis-19038	181	9	\	\	ADJ
bracis-19038	181	10	)	)	PUNCT
bracis-19038	181	11	model	model	NOUN
bracis-19038	181	12	of	of	ADP
bracis-19038	181	13	\((p	\((p	NOUN
bracis-19038	181	14	,	,	PUNCT
bracis-19038	181	15	\varphi	\varphi	PROPN
bracis-19038	181	16	)	)	PUNCT
bracis-19038	181	17	\	\	NOUN
bracis-19038	181	18	)	)	PUNCT
bracis-19038	181	19	w.r.t	w.r.t	NOUN
bracis-19038	181	20	.	.	PUNCT
bracis-19038	182	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	182	2	^y_x\	^y_x\	NUM
bracis-19038	182	3	)	)	PUNCT
bracis-19038	182	4	(	(	PUNCT
bracis-19038	182	5	resp	resp	NOUN
bracis-19038	182	6	.	.	PUNCT
bracis-19038	183	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	183	2	^y_x\	^y_x\	NUM
bracis-19038	183	3	)	)	PUNCT
bracis-19038	183	4	)	)	PUNCT
bracis-19038	184	1	with	with	ADP
bracis-19038	184	2	minimal	minimal	ADJ
bracis-19038	184	3	(	(	PUNCT
bracis-19038	184	4	w.r.t	w.r.t	NOUN
bracis-19038	184	5	.	.	PUNCT
bracis-19038	185	1	set	set	PROPN
bracis-19038	185	2	inclusion	inclusion	NOUN
bracis-19038	185	3	)	)	PUNCT
bracis-19038	186	1	\(\left\	\(\left\	PROPN
bracis-19038	186	2	{	{	PUNCT
bracis-19038	186	3	a	a	DET
bracis-19038	186	4	\in	\in	PROPN
bracis-19038	186	5	hb	hb	X
bracis-19038	186	6	_	_	PUNCT
bracis-19038	186	7	p\mid	p\mid	VERB
bracis-19038	186	8	a	a	DET
bracis-19038	186	9	\not	\not	ADV
bracis-19038	186	10	\in	\in	PROPN
bracis-19038	186	11	t_i	t_i	VERB
bracis-19038	186	12	\cup	\cup	VERB
bracis-19038	186	13	f_i\right\	f_i\right\	NOUN
bracis-19038	186	14	}	}	PUNCT
bracis-19038	186	15	\	\	NOUN
bracis-19038	186	16	)	)	PUNCT
bracis-19038	187	1	\(\left\	\(\left\	INTJ
bracis-19038	187	2	{	{	PUNCT
bracis-19038	187	3	a	a	DET
bracis-19038	187	4	\in	\in	PROPN
bracis-19038	187	5	hb	hb	X
bracis-19038	187	6	_	_	PUNCT
bracis-19038	187	7	p\mid	p\mid	PROPN
bracis-19038	187	8	m(a	m(a	NOUN
bracis-19038	187	9	)	)	PUNCT
bracis-19038	187	10	=	=	SYM
bracis-19038	187	11	\mathbf	\mathbf	PROPN
bracis-19038	187	12	{	{	PUNCT
bracis-19038	187	13	u}\right\	u}\right\	PROPN
bracis-19038	187	14	}	}	PUNCT
bracis-19038	187	15	\	\	NOUN
bracis-19038	187	16	)	)	PUNCT
bracis-19038	187	17	.	.	PUNCT
bracis-19038	188	1	let	let	VERB
bracis-19038	188	2	us	we	PRON
bracis-19038	188	3	consider	consider	VERB
bracis-19038	188	4	the	the	DET
bracis-19038	188	5	following	follow	VERB
bracis-19038	188	6	example	example	NOUN
bracis-19038	188	7	:	:	PUNCT
bracis-19038	188	8	example	example	NOUN
bracis-19038	188	9	2	2	NUM
bracis-19038	188	10	let	let	VERB
bracis-19038	188	11	p	p	PRON
bracis-19038	188	12	be	be	AUX
bracis-19038	188	13	the	the	DET
bracis-19038	188	14	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	188	15	)	)	PUNCT
bracis-19038	188	16	in	in	ADP
bracis-19038	188	17	example	example	NOUN
bracis-19038	188	18	1	1	NUM
bracis-19038	188	19	and	and	CCONJ
bracis-19038	188	20	\(\varphi	\(\varphi	NOUN
bracis-19038	188	21	=	=	SYM
bracis-19038	188	22	\{\emptyset	\{\emptyset	NUM
bracis-19038	188	23	\preceq	\preceq	PROPN
bracis-19038	188	24	\left\	\left\	PROPN
bracis-19038	188	25	{	{	PUNCT
bracis-19038	188	26	a\right\	a\right\	PROPN
bracis-19038	188	27	}	}	PUNCT
bracis-19038	188	28	,	,	PUNCT
bracis-19038	188	29	\left\	\left\	PROPN
bracis-19038	188	30	{	{	PUNCT
bracis-19038	188	31	a\right\	a\right\	PROPN
bracis-19038	188	32	}	}	PUNCT
bracis-19038	188	33	\preceq	\preceq	PROPN
bracis-19038	188	34	\left\	\left\	PROPN
bracis-19038	188	35	{	{	PUNCT
bracis-19038	188	36	d\right\	d\right\	NOUN
bracis-19038	188	37	}	}	PUNCT
bracis-19038	188	38	,	,	PUNCT
bracis-19038	188	39	\left\	\left\	PROPN
bracis-19038	188	40	{	{	PUNCT
bracis-19038	188	41	d\right\	d\right\	NOUN
bracis-19038	188	42	}	}	PUNCT
bracis-19038	188	43	\preceq	\preceq	PROPN
bracis-19038	188	44	\left\	\left\	PROPN
bracis-19038	188	45	{	{	PUNCT
bracis-19038	188	46	b\right\	b\right\	NOUN
bracis-19038	188	47	}	}	PUNCT
bracis-19038	188	48	,	,	PUNCT
bracis-19038	188	49	\left\	\left\	PROPN
bracis-19038	188	50	{	{	PUNCT
bracis-19038	188	51	b	b	NOUN
bracis-19038	188	52	,	,	PUNCT
bracis-19038	188	53	d\right\	d\right\	NOUN
bracis-19038	188	54	}	}	PUNCT
bracis-19038	188	55	\preceq	\preceq	PROPN
bracis-19038	188	56	\left\	\left\	PROPN
bracis-19038	188	57	{	{	PUNCT
bracis-19038	188	58	b\right\	b\right\	NOUN
bracis-19038	188	59	}	}	PUNCT
bracis-19038	188	60	,	,	PUNCT
bracis-19038	188	61	\left\	\left\	PROPN
bracis-19038	188	62	{	{	PUNCT
bracis-19038	188	63	b	b	NOUN
bracis-19038	188	64	,	,	PUNCT
bracis-19038	188	65	\mathtt	\mathtt	PROPN
bracis-19038	188	66	{	{	PUNCT
bracis-19038	188	67	not\	not\	PROPN
bracis-19038	188	68	}	}	PUNCT
bracis-19038	188	69	a\right\	a\right\	PROPN
bracis-19038	188	70	}	}	PUNCT
bracis-19038	188	71	\preceq	\preceq	PROPN
bracis-19038	188	72	\left\	\left\	PROPN
bracis-19038	188	73	{	{	PUNCT
bracis-19038	188	74	\mathtt	\mathtt	PROPN
bracis-19038	188	75	{	{	PUNCT
bracis-19038	188	76	not\	not\	PROPN
bracis-19038	188	77	}	}	PUNCT
bracis-19038	188	78	a\right\	a\right\	PROPN
bracis-19038	188	79	}	}	PUNCT
bracis-19038	188	80	,	,	PUNCT
bracis-19038	188	81	\left\	\left\	PROPN
bracis-19038	188	82	{	{	PUNCT
bracis-19038	188	83	a	a	PRON
bracis-19038	188	84	,	,	PUNCT
bracis-19038	188	85	d\right\	d\right\	NOUN
bracis-19038	188	86	}	}	PUNCT
bracis-19038	188	87	\preceq	\preceq	PROPN
bracis-19038	188	88	\left\	\left\	PROPN
bracis-19038	188	89	{	{	PUNCT
bracis-19038	188	90	d\right\	d\right\	NOUN
bracis-19038	188	91	}	}	PUNCT
bracis-19038	188	92	\}\	\}\	NOUN
bracis-19038	188	93	)	)	PUNCT
bracis-19038	188	94	.	.	PUNCT
bracis-19038	189	1	then	then	ADV
bracis-19038	189	2	the	the	DET
bracis-19038	189	3	best	well	ADV
bracis-19038	189	4	-	-	PUNCT
bracis-19038	189	5	ranked	rank	VERB
bracis-19038	189	6	options	option	NOUN
bracis-19038	189	7	for	for	ADP
bracis-19038	189	8	\(i_1	\(i_1	PROPN
bracis-19038	189	9	,	,	PUNCT
bracis-19038	189	10	i_2	i_2	PROPN
bracis-19038	189	11	,	,	PUNCT
bracis-19038	189	12	i_3	i_3	PROPN
bracis-19038	189	13	,	,	PUNCT
bracis-19038	189	14	i_4	i_4	PROPN
bracis-19038	189	15	,	,	PUNCT
bracis-19038	189	16	i_5\	i_5\	PROPN
bracis-19038	189	17	)	)	PUNCT
bracis-19038	189	18	and	and	CCONJ
bracis-19038	189	19	\	\	PROPN
bracis-19038	189	20	(	(	PUNCT
bracis-19038	189	21	i_6\	i_6\	NOUN
bracis-19038	189	22	)	)	PUNCT
bracis-19038	189	23	are	be	AUX
bracis-19038	189	24	respectively	respectively	ADV
bracis-19038	189	25	\(\mathcal	\(\mathcal	ADJ
bracis-19038	189	26	b_1	b_1	NOUN
bracis-19038	189	27	=	=	PUNCT
bracis-19038	189	28	\emptyset	\emptyset	VERB
bracis-19038	189	29	,	,	PUNCT
bracis-19038	189	30	\mathcal	\mathcal	PROPN
bracis-19038	189	31	b_2	b_2	PROPN
bracis-19038	189	32	=	=	SYM
bracis-19038	189	33	\	\	PROPN
bracis-19038	189	34	{	{	PUNCT
bracis-19038	189	35	\left\	\left\	PROPN
bracis-19038	189	36	{	{	PUNCT
bracis-19038	189	37	a\right\	a\right\	PROPN
bracis-19038	189	38	}	}	PUNCT
bracis-19038	189	39	,	,	PUNCT
bracis-19038	190	1	\left\	\left\	PROPN
bracis-19038	190	2	{	{	PUNCT
bracis-19038	190	3	\mathtt	\mathtt	PROPN
bracis-19038	190	4	{	{	PUNCT
bracis-19038	190	5	not\	not\	PROPN
bracis-19038	190	6	}	}	PUNCT
bracis-19038	190	7	b\right\	b\right\	PROPN
bracis-19038	190	8	}	}	PUNCT
bracis-19038	190	9	,	,	PUNCT
bracis-19038	190	10	\	\	PROPN
bracis-19038	190	11	)	)	PUNCT
bracis-19038	191	1	\(\left\	\(\left\	PROPN
bracis-19038	191	2	{	{	PUNCT
bracis-19038	191	3	a	a	NOUN
bracis-19038	191	4	,	,	PUNCT
bracis-19038	191	5	\mathtt	\mathtt	PROPN
bracis-19038	191	6	{	{	PUNCT
bracis-19038	191	7	not\	not\	PROPN
bracis-19038	191	8	}	}	PUNCT
bracis-19038	191	9	b\right\	b\right\	NOUN
bracis-19038	191	10	}	}	PUNCT
bracis-19038	191	11	\	\	NOUN
bracis-19038	191	12	}	}	PUNCT
bracis-19038	191	13	,	,	PUNCT
bracis-19038	191	14	\mathcal	\mathcal	PROPN
bracis-19038	191	15	b_3	b_3	PROPN
bracis-19038	191	16	=	=	PROPN
bracis-19038	191	17	\left\	\left\	PROPN
bracis-19038	191	18	{	{	PUNCT
bracis-19038	191	19	\left\	\left\	PROPN
bracis-19038	191	20	{	{	PUNCT
bracis-19038	191	21	d\right\	d\right\	NOUN
bracis-19038	191	22	}	}	PUNCT
bracis-19038	191	23	\right\	\right\	ADJ
bracis-19038	191	24	}	}	PUNCT
bracis-19038	191	25	,	,	PUNCT
bracis-19038	191	26	\mathcal	\mathcal	PROPN
bracis-19038	191	27	b_4	b_4	PROPN
bracis-19038	191	28	=	=	SYM
bracis-19038	191	29	\left\	\left\	PROPN
bracis-19038	191	30	{	{	PUNCT
bracis-19038	191	31	\left\	\left\	PROPN
bracis-19038	191	32	{	{	PUNCT
bracis-19038	191	33	b\right\	b\right\	NOUN
bracis-19038	191	34	}	}	PUNCT
bracis-19038	191	35	,	,	PUNCT
bracis-19038	191	36	\left\	\left\	PROPN
bracis-19038	191	37	{	{	PUNCT
bracis-19038	191	38	\mathtt	\mathtt	PROPN
bracis-19038	191	39	{	{	PUNCT
bracis-19038	191	40	not\	not\	PROPN
bracis-19038	191	41	}	}	PUNCT
bracis-19038	191	42	a\right\	a\right\	VERB
bracis-19038	191	43	}	}	PUNCT
bracis-19038	191	44	\right\	\right\	ADV
bracis-19038	191	45	}	}	PUNCT
bracis-19038	191	46	,	,	PUNCT
bracis-19038	191	47	\mathcal	\mathcal	PROPN
bracis-19038	191	48	b_5	b_5	PROPN
bracis-19038	191	49	=	=	SYM
bracis-19038	191	50	2^{i_5}\	2^{i_5}\	NUM
bracis-19038	191	51	)	)	PUNCT
bracis-19038	191	52	and	and	CCONJ
bracis-19038	191	53	\(\mathcal	\(\mathcal	ADJ
bracis-19038	191	54	b_6	b_6	PROPN
bracis-19038	191	55	=	=	SYM
bracis-19038	191	56	\	\	PROPN
bracis-19038	191	57	{	{	PUNCT
bracis-19038	191	58	\left\	\left\	PROPN
bracis-19038	191	59	{	{	PUNCT
bracis-19038	191	60	d\right\	d\right\	NOUN
bracis-19038	191	61	}	}	PUNCT
bracis-19038	191	62	,	,	PUNCT
bracis-19038	191	63	\left\	\left\	PROPN
bracis-19038	191	64	{	{	PUNCT
bracis-19038	191	65	\mathtt	\mathtt	PROPN
bracis-19038	191	66	{	{	PUNCT
bracis-19038	191	67	not\	not\	PROPN
bracis-19038	191	68	}	}	PUNCT
bracis-19038	191	69	b\right\	b\right\	PROPN
bracis-19038	191	70	}	}	PUNCT
bracis-19038	191	71	,	,	PUNCT
bracis-19038	191	72	\	\	PROPN
bracis-19038	191	73	)	)	PUNCT
bracis-19038	192	1	\(\left\	\(\left\	PROPN
bracis-19038	192	2	{	{	PUNCT
bracis-19038	192	3	d	d	NOUN
bracis-19038	192	4	,	,	PUNCT
bracis-19038	192	5	\mathtt	\mathtt	PROPN
bracis-19038	192	6	{	{	PUNCT
bracis-19038	192	7	not\	not\	PROPN
bracis-19038	192	8	}	}	PUNCT
bracis-19038	192	9	b\right\	b\right\	NOUN
bracis-19038	192	10	}	}	PUNCT
bracis-19038	192	11	\}\	\}\	NUM
bracis-19038	192	12	)	)	PUNCT
bracis-19038	192	13	.	.	PUNCT
bracis-19038	193	1	regarding	regard	VERB
bracis-19038	193	2	only	only	ADV
bracis-19038	193	3	the	the	DET
bracis-19038	193	4	optimistic	optimistic	ADJ
bracis-19038	193	5	approach	approach	NOUN
bracis-19038	193	6	for	for	ADP
bracis-19038	193	7	illustrative	illustrative	ADJ
bracis-19038	193	8	purposes	purpose	NOUN
bracis-19038	193	9	,	,	PUNCT
bracis-19038	193	10	we	we	PRON
bracis-19038	193	11	have	have	VERB
bracis-19038	193	12	\(\mathcal	\(\mathcal	ADJ
bracis-19038	193	13	{	{	PUNCT
bracis-19038	193	14	pps}(p,\varphi	pps}(p,\varphi	NOUN
bracis-19038	193	15	)	)	PUNCT
bracis-19038	194	1	_	_	PUNCT
bracis-19038	194	2	{	{	PUNCT
bracis-19038	194	3	\subseteq	\subseteq	PROPN
bracis-19038	194	4	^{\forall	^{\forall	NOUN
bracis-19038	194	5	\forall	\forall	PRON
bracis-19038	194	6	}	}	PUNCT
bracis-19038	194	7	_	_	PUNCT
bracis-19038	194	8	opt	opt	NOUN
bracis-19038	194	9	}	}	PUNCT
bracis-19038	194	10	=	=	SYM
bracis-19038	194	11	\left\	\left\	PROPN
bracis-19038	194	12	{	{	PUNCT
bracis-19038	194	13	i_4\right\	i_4\right\	NOUN
bracis-19038	194	14	}	}	PUNCT
bracis-19038	194	15	\	\	NOUN
bracis-19038	194	16	)	)	PUNCT
bracis-19038	194	17	;	;	PUNCT
bracis-19038	194	18	\(\mathcal	\(\mathcal	ADJ
bracis-19038	194	19	{	{	PUNCT
bracis-19038	194	20	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	194	21	)	)	PUNCT
bracis-19038	195	1	_	_	PRON
bracis-19038	195	2	{	{	PUNCT
bracis-19038	195	3	\subseteq	\subseteq	PROPN
bracis-19038	195	4	^{\forall	^{\forall	PRON
bracis-19038	195	5	\exists	\exist	NOUN
bracis-19038	195	6	}	}	PUNCT
bracis-19038	195	7	_	_	PUNCT
bracis-19038	195	8	opt	opt	ADJ
bracis-19038	195	9	}	}	PUNCT
bracis-19038	195	10	=	=	SYM
bracis-19038	195	11	\left\	\left\	PROPN
bracis-19038	195	12	{	{	PUNCT
bracis-19038	195	13	i_2	i_2	PROPN
bracis-19038	195	14	,	,	PUNCT
bracis-19038	195	15	i_4	i_4	PROPN
bracis-19038	195	16	,	,	PUNCT
bracis-19038	195	17	i_5	i_5	PROPN
bracis-19038	195	18	,	,	PUNCT
bracis-19038	195	19	i_6\right\	i_6\right\	PROPN
bracis-19038	195	20	}	}	PUNCT
bracis-19038	195	21	\	\	NOUN
bracis-19038	195	22	)	)	PUNCT
bracis-19038	195	23	;	;	PUNCT
bracis-19038	195	24	\(\mathcal	\(\mathcal	ADJ
bracis-19038	195	25	{	{	PUNCT
bracis-19038	195	26	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	195	27	)	)	PUNCT
bracis-19038	196	1	_	_	PRON
bracis-19038	196	2	{	{	PUNCT
bracis-19038	196	3	\subseteq	\subseteq	PROPN
bracis-19038	196	4	^{\exists	^{\exist	NOUN
bracis-19038	196	5	\forall	\forall	PRON
bracis-19038	196	6	}	}	PUNCT
bracis-19038	196	7	_	_	PUNCT
bracis-19038	196	8	opt	opt	NOUN
bracis-19038	196	9	}	}	PUNCT
bracis-19038	196	10	=	=	SYM
bracis-19038	196	11	\left\	\left\	PROPN
bracis-19038	196	12	{	{	PUNCT
bracis-19038	196	13	i_3	i_3	ADJ
bracis-19038	196	14	,	,	PUNCT
bracis-19038	196	15	i_4	i_4	PROPN
bracis-19038	196	16	,	,	PUNCT
bracis-19038	196	17	i_6\right\	i_6\right\	PROPN
bracis-19038	196	18	}	}	PUNCT
bracis-19038	196	19	\	\	NOUN
bracis-19038	196	20	)	)	PUNCT
bracis-19038	196	21	and	and	CCONJ
bracis-19038	196	22	\(\mathcal	\(\mathcal	ADJ
bracis-19038	196	23	{	{	PUNCT
bracis-19038	196	24	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	196	25	)	)	PUNCT
bracis-19038	197	1	_	_	PRON
bracis-19038	197	2	{	{	PUNCT
bracis-19038	197	3	\subseteq	\subseteq	PROPN
bracis-19038	197	4	^{\exists	^{\exist	VERB
bracis-19038	197	5	\exists	\exist	NOUN
bracis-19038	197	6	}	}	PUNCT
bracis-19038	197	7	_	_	PUNCT
bracis-19038	197	8	opt	opt	ADJ
bracis-19038	197	9	}	}	PUNCT
bracis-19038	197	10	=	=	SYM
bracis-19038	197	11	\left\	\left\	PROPN
bracis-19038	197	12	{	{	PUNCT
bracis-19038	197	13	i_2	i_2	PROPN
bracis-19038	197	14	,	,	PUNCT
bracis-19038	197	15	i_3	i_3	PROPN
bracis-19038	197	16	,	,	PUNCT
bracis-19038	197	17	i_4	i_4	PROPN
bracis-19038	197	18	,	,	PUNCT
bracis-19038	197	19	i_5	i_5	PROPN
bracis-19038	197	20	,	,	PUNCT
bracis-19038	197	21	i_6\right\	i_6\right\	PROPN
bracis-19038	197	22	}	}	PUNCT
bracis-19038	197	23	\	\	NOUN
bracis-19038	197	24	)	)	PUNCT
bracis-19038	197	25	.	.	PUNCT
bracis-19038	198	1	in	in	ADP
bracis-19038	198	2	this	this	DET
bracis-19038	198	3	example	example	NOUN
bracis-19038	198	4	,	,	PUNCT
bracis-19038	198	5	notice	notice	VERB
bracis-19038	198	6	at	at	ADV
bracis-19038	198	7	least	least	ADV
bracis-19038	198	8	one	one	NUM
bracis-19038	198	9	\	\	NOUN
bracis-19038	198	10	(	(	PUNCT
bracis-19038	198	11	ps	ps	NOUN
bracis-19038	198	12	\	\	ADJ
bracis-19038	198	13	)	)	PUNCT
bracis-19038	198	14	model	model	NOUN
bracis-19038	198	15	of	of	ADP
bracis-19038	198	16	p	p	PROPN
bracis-19038	198	17	is	be	AUX
bracis-19038	198	18	discarded	discard	VERB
bracis-19038	198	19	in	in	ADP
bracis-19038	198	20	\(\mathcal	\(\mathcal	ADJ
bracis-19038	198	21	{	{	PUNCT
bracis-19038	198	22	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	198	23	)	)	PUNCT
bracis-19038	199	1	_	_	PRON
bracis-19038	199	2	{	{	PUNCT
bracis-19038	199	3	\subseteq	\subseteq	PROPN
bracis-19038	199	4	^y	^y	X
bracis-19038	199	5	_	_	PRON
bracis-19038	199	6	opt	opt	ADJ
bracis-19038	199	7	}	}	PUNCT
bracis-19038	199	8	\	\	NOUN
bracis-19038	199	9	)	)	PUNCT
bracis-19038	199	10	for	for	ADP
bracis-19038	199	11	any	any	DET
bracis-19038	199	12	\(y	\(y	NUM
bracis-19038	199	13	\in	\in	PROPN
bracis-19038	199	14	\left\	\left\	PROPN
bracis-19038	199	15	{	{	PUNCT
bracis-19038	199	16	\forall	\forall	INTJ
bracis-19038	199	17	\forall	\forall	INTJ
bracis-19038	199	18	,	,	PUNCT
bracis-19038	199	19	\forall	\forall	DET
bracis-19038	199	20	\exists	\exist	NOUN
bracis-19038	199	21	,	,	PUNCT
bracis-19038	199	22	\exists	\exist	NOUN
bracis-19038	199	23	\forall	\forall	ADV
bracis-19038	199	24	,	,	PUNCT
bracis-19038	199	25	\exists	\exist	VERB
bracis-19038	199	26	\exists	\exist	NOUN
bracis-19038	199	27	\right\	\right\	ADV
bracis-19038	199	28	}	}	PUNCT
bracis-19038	199	29	\	\	NOUN
bracis-19038	199	30	)	)	PUNCT
bracis-19038	199	31	.	.	PUNCT
bracis-19038	200	1	many	many	ADJ
bracis-19038	200	2	attempts	attempt	NOUN
bracis-19038	200	3	have	have	AUX
bracis-19038	200	4	been	be	AUX
bracis-19038	200	5	made	make	VERB
bracis-19038	200	6	to	to	PART
bracis-19038	200	7	empower	empower	VERB
bracis-19038	200	8	logic	logic	NOUN
bracis-19038	200	9	programming	programming	NOUN
bracis-19038	200	10	with	with	ADP
bracis-19038	200	11	preferences	preference	NOUN
bracis-19038	200	12	.	.	PUNCT
bracis-19038	201	1	the	the	DET
bracis-19038	201	2	distinguishing	distinguish	VERB
bracis-19038	201	3	aspect	aspect	NOUN
bracis-19038	201	4	of	of	ADP
bracis-19038	201	5	our	our	PRON
bracis-19038	201	6	work	work	NOUN
bracis-19038	201	7	is	be	AUX
bracis-19038	201	8	that	that	SCONJ
bracis-19038	201	9	we	we	PRON
bracis-19038	201	10	offer	offer	VERB
bracis-19038	201	11	a	a	DET
bracis-19038	201	12	comprehensive	comprehensive	ADJ
bracis-19038	201	13	and	and	CCONJ
bracis-19038	201	14	systematic	systematic	ADJ
bracis-19038	201	15	way	way	NOUN
bracis-19038	201	16	of	of	ADP
bracis-19038	201	17	dealing	deal	VERB
bracis-19038	201	18	with	with	ADP
bracis-19038	201	19	preferences	preference	NOUN
bracis-19038	201	20	in	in	ADP
bracis-19038	201	21	logic	logic	NOUN
bracis-19038	201	22	programming	programming	NOUN
bracis-19038	201	23	inspired	inspire	VERB
bracis-19038	201	24	by	by	ADP
bracis-19038	201	25	well	well	ADV
bracis-19038	201	26	-	-	PUNCT
bracis-19038	201	27	known	know	VERB
bracis-19038	201	28	criteria	criterion	NOUN
bracis-19038	201	29	found	find	VERB
bracis-19038	201	30	in	in	ADP
bracis-19038	201	31	the	the	DET
bracis-19038	201	32	literature	literature	NOUN
bracis-19038	201	33	on	on	ADP
bracis-19038	201	34	preference	preference	NOUN
bracis-19038	201	35	.	.	PUNCT
bracis-19038	202	1	in	in	ADP
bracis-19038	202	2	the	the	DET
bracis-19038	202	3	next	next	ADJ
bracis-19038	202	4	section	section	NOUN
bracis-19038	202	5	,	,	PUNCT
bracis-19038	202	6	we	we	PRON
bracis-19038	202	7	will	will	AUX
bracis-19038	202	8	examine	examine	VERB
bracis-19038	202	9	how	how	SCONJ
bracis-19038	202	10	expressive	expressive	ADJ
bracis-19038	202	11	our	our	PRON
bracis-19038	202	12	proposal	proposal	NOUN
bracis-19038	202	13	is	be	AUX
bracis-19038	202	14	.	.	PUNCT
bracis-19038	203	1	4	4	NUM
bracis-19038	203	2	expressing	express	VERB
bracis-19038	203	3	priorities	priority	NOUN
bracis-19038	203	4	in	in	ADP
bracis-19038	203	5	\(\textit{plp}\)s	\(\textit{plp}\)s	NOUN
bracis-19038	203	6	as	as	SCONJ
bracis-19038	203	7	it	it	PRON
bracis-19038	203	8	is	be	AUX
bracis-19038	203	9	not	not	PART
bracis-19038	203	10	feasible	feasible	ADJ
bracis-19038	203	11	in	in	ADP
bracis-19038	203	12	general	general	ADJ
bracis-19038	203	13	when	when	SCONJ
bracis-19038	203	14	expressing	express	VERB
bracis-19038	203	15	preferences	preference	NOUN
bracis-19038	203	16	to	to	PART
bracis-19038	203	17	compare	compare	VERB
bracis-19038	203	18	all	all	DET
bracis-19038	203	19	possible	possible	ADJ
bracis-19038	203	20	pairs	pair	NOUN
bracis-19038	203	21	of	of	ADP
bracis-19038	203	22	options	option	NOUN
bracis-19038	203	23	or	or	CCONJ
bracis-19038	203	24	evaluate	evaluate	VERB
bracis-19038	203	25	them	they	PRON
bracis-19038	203	26	individually	individually	ADV
bracis-19038	203	27	(	(	PUNCT
bracis-19038	203	28	the	the	DET
bracis-19038	203	29	number	number	NOUN
bracis-19038	203	30	of	of	ADP
bracis-19038	203	31	options	option	NOUN
bracis-19038	203	32	increases	increase	VERB
bracis-19038	203	33	exponentially	exponentially	ADV
bracis-19038	203	34	with	with	ADP
bracis-19038	203	35	the	the	DET
bracis-19038	203	36	number	number	NOUN
bracis-19038	203	37	of	of	ADP
bracis-19038	203	38	variables	variable	NOUN
bracis-19038	203	39	)	)	PUNCT
bracis-19038	203	40	,	,	PUNCT
bracis-19038	203	41	we	we	PRON
bracis-19038	203	42	have	have	VERB
bracis-19038	203	43	to	to	PART
bracis-19038	203	44	resort	resort	VERB
bracis-19038	203	45	to	to	ADP
bracis-19038	203	46	compact	compact	ADJ
bracis-19038	203	47	preference	preference	NOUN
bracis-19038	203	48	representation	representation	NOUN
bracis-19038	203	49	languages	language	NOUN
bracis-19038	203	50	to	to	PART
bracis-19038	203	51	represent	represent	VERB
bracis-19038	203	52	these	these	DET
bracis-19038	203	53	partial	partial	ADJ
bracis-19038	203	54	descriptions	description	NOUN
bracis-19038	203	55	preferences	preference	NOUN
bracis-19038	203	56	.	.	PUNCT
bracis-19038	204	1	now	now	ADV
bracis-19038	204	2	we	we	PRON
bracis-19038	204	3	will	will	AUX
bracis-19038	204	4	show	show	VERB
bracis-19038	204	5	our	our	PRON
bracis-19038	204	6	preference	preference	NOUN
bracis-19038	204	7	representation	representation	NOUN
bracis-19038	204	8	language	language	NOUN
bracis-19038	204	9	although	although	SCONJ
bracis-19038	204	10	compact	compact	ADJ
bracis-19038	204	11	is	be	AUX
bracis-19038	204	12	robust	robust	ADJ
bracis-19038	204	13	enough	enough	ADV
bracis-19038	204	14	to	to	PART
bracis-19038	204	15	express	express	VERB
bracis-19038	204	16	well	well	ADV
bracis-19038	204	17	-	-	PUNCT
bracis-19038	204	18	known	know	VERB
bracis-19038	204	19	complex	complex	ADJ
bracis-19038	204	20	forms	form	NOUN
bracis-19038	204	21	of	of	ADP
bracis-19038	204	22	preferences	preference	NOUN
bracis-19038	204	23	.	.	PUNCT
bracis-19038	205	1	in	in	ADP
bracis-19038	205	2	subsects	subsect	NOUN
bracis-19038	205	3	.	.	PUNCT
bracis-19038	205	4	 	 	SPACE
bracis-19038	205	5	4.1	4.1	NUM
bracis-19038	205	6	,	,	PUNCT
bracis-19038	205	7	4.2	4.2	NUM
bracis-19038	205	8	,	,	PUNCT
bracis-19038	205	9	4.3	4.3	NUM
bracis-19038	205	10	,	,	PUNCT
bracis-19038	205	11	4.4	4.4	NUM
bracis-19038	205	12	and	and	CCONJ
bracis-19038	205	13	4.5	4.5	NUM
bracis-19038	205	14	,	,	PUNCT
bracis-19038	205	15	we	we	PRON
bracis-19038	205	16	will	will	AUX
bracis-19038	205	17	tackle	tackle	VERB
bracis-19038	205	18	respectively	respectively	ADV
bracis-19038	205	19	how	how	SCONJ
bracis-19038	205	20	to	to	PART
bracis-19038	205	21	represent	represent	VERB
bracis-19038	205	22	priorities	priority	NOUN
bracis-19038	205	23	between	between	ADP
bracis-19038	205	24	conjunctive	conjunctive	ADJ
bracis-19038	205	25	knowledge	knowledge	NOUN
bracis-19038	205	26	,	,	PUNCT
bracis-19038	205	27	priorities	priority	NOUN
bracis-19038	205	28	between	between	ADP
bracis-19038	205	29	disjunctive	disjunctive	ADJ
bracis-19038	205	30	knowledge	knowledge	NOUN
bracis-19038	205	31	,	,	PUNCT
bracis-19038	205	32	conditional	conditional	ADJ
bracis-19038	205	33	priorities	priority	NOUN
bracis-19038	205	34	,	,	PUNCT
bracis-19038	205	35	priorities	priority	NOUN
bracis-19038	205	36	between	between	ADP
bracis-19038	205	37	rules	rule	NOUN
bracis-19038	205	38	and	and	CCONJ
bracis-19038	205	39	bipolar	bipolar	ADJ
bracis-19038	205	40	priorities	priority	NOUN
bracis-19038	205	41	.	.	PUNCT
bracis-19038	206	1	4.1	4.1	NUM
bracis-19038	206	2	priorities	priority	NOUN
bracis-19038	206	3	between	between	ADP
bracis-19038	206	4	conjunctive	conjunctive	ADJ
bracis-19038	206	5	knowledge	knowledge	NOUN
bracis-19038	206	6	users	user	NOUN
bracis-19038	206	7	may	may	AUX
bracis-19038	206	8	also	also	ADV
bracis-19038	206	9	express	express	VERB
bracis-19038	206	10	their	their	PRON
bracis-19038	206	11	partial	partial	ADJ
bracis-19038	206	12	preferences	preference	NOUN
bracis-19038	206	13	in	in	ADP
bracis-19038	206	14	term	term	NOUN
bracis-19038	206	15	of	of	ADP
bracis-19038	206	16	comparative	comparative	ADJ
bracis-19038	206	17	statements	statement	NOUN
bracis-19038	206	18	(	(	PUNCT
bracis-19038	206	19	as	as	SCONJ
bracis-19038	206	20	in	in	ADP
bracis-19038	206	21	“	"	PUNCT
bracis-19038	206	22	i	i	PRON
bracis-19038	206	23	prefer	prefer	VERB
bracis-19038	206	24	white	white	ADJ
bracis-19038	206	25	wine	wine	NOUN
bracis-19038	206	26	to	to	ADP
bracis-19038	206	27	red	red	ADJ
bracis-19038	206	28	wine	wine	NOUN
bracis-19038	206	29	"	"	PUNCT
bracis-19038	206	30	)	)	PUNCT
bracis-19038	206	31	;	;	PUNCT
bracis-19038	206	32	this	this	DET
bracis-19038	206	33	preference	preference	NOUN
bracis-19038	206	34	can	can	AUX
bracis-19038	206	35	be	be	AUX
bracis-19038	206	36	altered	alter	VERB
bracis-19038	206	37	when	when	SCONJ
bracis-19038	206	38	interacting	interact	VERB
bracis-19038	206	39	with	with	ADP
bracis-19038	206	40	other	other	ADJ
bracis-19038	206	41	options	option	NOUN
bracis-19038	206	42	(	(	PUNCT
bracis-19038	206	43	as	as	SCONJ
bracis-19038	206	44	in	in	ADP
bracis-19038	206	45	“	"	PUNCT
bracis-19038	206	46	i	i	PRON
bracis-19038	206	47	prefer	prefer	VERB
bracis-19038	206	48	meat	meat	NOUN
bracis-19038	206	49	accompanied	accompany	VERB
bracis-19038	206	50	by	by	ADP
bracis-19038	206	51	a	a	DET
bracis-19038	206	52	red	red	ADJ
bracis-19038	206	53	wine	wine	NOUN
bracis-19038	206	54	to	to	ADP
bracis-19038	206	55	meat	meat	NOUN
bracis-19038	206	56	accompanied	accompany	VERB
bracis-19038	206	57	by	by	ADP
bracis-19038	206	58	a	a	DET
bracis-19038	206	59	white	white	ADJ
bracis-19038	206	60	wine	wine	NOUN
bracis-19038	206	61	"	"	PUNCT
bracis-19038	206	62	)	)	PUNCT
bracis-19038	206	63	;	;	PUNCT
bracis-19038	206	64	the	the	DET
bracis-19038	206	65	preference	preference	NOUN
bracis-19038	206	66	for	for	ADP
bracis-19038	206	67	white	white	ADJ
bracis-19038	206	68	wine	wine	NOUN
bracis-19038	206	69	can	can	AUX
bracis-19038	206	70	even	even	ADV
bracis-19038	206	71	be	be	AUX
bracis-19038	206	72	regained	regain	VERB
bracis-19038	206	73	with	with	ADP
bracis-19038	206	74	the	the	DET
bracis-19038	206	75	addition	addition	NOUN
bracis-19038	206	76	of	of	ADP
bracis-19038	206	77	more	more	ADJ
bracis-19038	206	78	options	option	NOUN
bracis-19038	206	79	(	(	PUNCT
bracis-19038	206	80	as	as	SCONJ
bracis-19038	206	81	in	in	ADP
bracis-19038	206	82	“	"	PUNCT
bracis-19038	206	83	i	i	PRON
bracis-19038	206	84	prefer	prefer	VERB
bracis-19038	206	85	meat	meat	NOUN
bracis-19038	206	86	and	and	CCONJ
bracis-19038	206	87	cheesecake	cheesecake	NOUN
bracis-19038	206	88	accompanied	accompany	VERB
bracis-19038	206	89	by	by	ADP
bracis-19038	206	90	a	a	DET
bracis-19038	206	91	white	white	ADJ
bracis-19038	206	92	wine	wine	NOUN
bracis-19038	206	93	to	to	PART
bracis-19038	206	94	meat	meat	VERB
bracis-19038	206	95	and	and	CCONJ
bracis-19038	206	96	cheesecake	cheesecake	NOUN
bracis-19038	206	97	accompanied	accompany	VERB
bracis-19038	206	98	by	by	ADP
bracis-19038	206	99	a	a	DET
bracis-19038	206	100	red	red	ADJ
bracis-19038	206	101	wine	wine	NOUN
bracis-19038	206	102	"	"	PUNCT
bracis-19038	206	103	)	)	PUNCT
bracis-19038	206	104	.	.	PUNCT
bracis-19038	207	1	thus	thus	ADV
bracis-19038	207	2	,	,	PUNCT
bracis-19038	207	3	the	the	DET
bracis-19038	207	4	conjunction	conjunction	NOUN
bracis-19038	207	5	of	of	ADP
bracis-19038	207	6	options	option	NOUN
bracis-19038	207	7	can	can	AUX
bracis-19038	207	8	interfere	interfere	VERB
bracis-19038	207	9	with	with	ADP
bracis-19038	207	10	the	the	DET
bracis-19038	207	11	users	user	NOUN
bracis-19038	207	12	’	’	PART
bracis-19038	207	13	preference	preference	NOUN
bracis-19038	207	14	and	and	CCONJ
bracis-19038	207	15	change	change	VERB
bracis-19038	207	16	the	the	DET
bracis-19038	207	17	overall	overall	ADJ
bracis-19038	207	18	outcome	outcome	NOUN
bracis-19038	207	19	.	.	PUNCT
bracis-19038	208	1	in	in	ADP
bracis-19038	208	2	[	[	X
bracis-19038	208	3	4	4	NUM
bracis-19038	208	4	]	]	PUNCT
bracis-19038	208	5	,	,	PUNCT
bracis-19038	208	6	conjunctive	conjunctive	ADJ
bracis-19038	208	7	preferences	preference	NOUN
bracis-19038	208	8	\((e_1	\((e_1	VERB
bracis-19038	208	9	,	,	PUNCT
bracis-19038	208	10	\ldots	\ldots	PROPN
bracis-19038	208	11	,	,	PUNCT
bracis-19038	208	12	e_m	e_m	PROPN
bracis-19038	208	13	)	)	PUNCT
bracis-19038	208	14	\preceq	\preceq	PROPN
bracis-19038	208	15	(	(	PUNCT
bracis-19038	208	16	e_1	e_1	NOUN
bracis-19038	208	17	'	'	NUM
bracis-19038	208	18	,	,	PUNCT
bracis-19038	208	19	\ldots	\ldots	INTJ
bracis-19038	208	20	,	,	PUNCT
bracis-19038	208	21	e_n')\	e_n')\	PROPN
bracis-19038	208	22	)	)	PUNCT
bracis-19038	208	23	can	can	AUX
bracis-19038	208	24	not	not	PART
bracis-19038	208	25	in	in	ADP
bracis-19038	208	26	general	general	ADJ
bracis-19038	208	27	be	be	AUX
bracis-19038	208	28	expressed	express	VERB
bracis-19038	208	29	directly	directly	ADV
bracis-19038	208	30	as	as	SCONJ
bracis-19038	208	31	the	the	DET
bracis-19038	208	32	preference	preference	NOUN
bracis-19038	208	33	relation	relation	NOUN
bracis-19038	208	34	applied	apply	VERB
bracis-19038	208	35	there	there	ADV
bracis-19038	208	36	only	only	ADV
bracis-19038	208	37	involves	involve	VERB
bracis-19038	208	38	a	a	DET
bracis-19038	208	39	pair	pair	NOUN
bracis-19038	208	40	of	of	ADP
bracis-19038	208	41	individual	individual	ADJ
bracis-19038	208	42	literals	literal	NOUN
bracis-19038	208	43	.	.	PUNCT
bracis-19038	209	1	in	in	ADP
bracis-19038	209	2	order	order	NOUN
bracis-19038	209	3	to	to	PART
bracis-19038	209	4	represent	represent	VERB
bracis-19038	209	5	these	these	DET
bracis-19038	209	6	conjunctive	conjunctive	ADJ
bracis-19038	209	7	preferences	preference	NOUN
bracis-19038	209	8	in	in	ADP
bracis-19038	209	9	a	a	DET
bracis-19038	209	10	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	209	11	)	)	PUNCT
bracis-19038	209	12	\((p	\((p	NOUN
bracis-19038	209	13	,	,	PUNCT
bracis-19038	209	14	\varphi	\varphi	PROPN
bracis-19038	209	15	)	)	PUNCT
bracis-19038	209	16	\	\	PROPN
bracis-19038	209	17	)	)	PUNCT
bracis-19038	209	18	,	,	PUNCT
bracis-19038	209	19	the	the	DET
bracis-19038	209	20	authors	author	NOUN
bracis-19038	209	21	have	have	VERB
bracis-19038	209	22	to	to	PART
bracis-19038	209	23	add	add	VERB
bracis-19038	209	24	the	the	DET
bracis-19038	209	25	rules	rule	NOUN
bracis-19038	209	26	\(e_0	\(e_0	PROPN
bracis-19038	209	27	\leftarrow	\leftarrow	PROPN
bracis-19038	209	28	e_1	e_1	NOUN
bracis-19038	209	29	,	,	PUNCT
bracis-19038	209	30	\ldots	\ldots	PROPN
bracis-19038	209	31	e_m\	e_m\	NOUN
bracis-19038	209	32	)	)	PUNCT
bracis-19038	209	33	and	and	CCONJ
bracis-19038	209	34	\(e_0	\(e_0	NOUN
bracis-19038	209	35	'	'	PART
bracis-19038	209	36	\leftarrow	\leftarrow	PROPN
bracis-19038	209	37	e_1	e_1	NOUN
bracis-19038	209	38	'	'	PUNCT
bracis-19038	209	39	,	,	PUNCT
bracis-19038	209	40	\ldots	\ldots	ADP
bracis-19038	209	41	e_n'\	e_n'\	NOUN
bracis-19038	209	42	)	)	PUNCT
bracis-19038	209	43	to	to	ADP
bracis-19038	209	44	p	p	NOUN
bracis-19038	209	45	with	with	ADP
bracis-19038	209	46	the	the	DET
bracis-19038	209	47	newly	newly	ADV
bracis-19038	209	48	introduced	introduce	VERB
bracis-19038	209	49	atoms	atom	NOUN
bracis-19038	209	50	\(e_0\	\(e_0\	NOUN
bracis-19038	209	51	)	)	PUNCT
bracis-19038	209	52	and	and	CCONJ
bracis-19038	209	53	\(e_0'\	\(e_0'\	NOUN
bracis-19038	209	54	)	)	PUNCT
bracis-19038	209	55	,	,	PUNCT
bracis-19038	209	56	and	and	CCONJ
bracis-19038	209	57	the	the	DET
bracis-19038	209	58	priority	priority	NOUN
bracis-19038	209	59	\((e_0	\((e_0	VERB
bracis-19038	209	60	\preceq	\preceq	PROPN
bracis-19038	209	61	e_0')\	e_0')\	NOUN
bracis-19038	209	62	)	)	PUNCT
bracis-19038	209	63	to	to	ADP
bracis-19038	209	64	\(\varphi	\(\varphi	ADJ
bracis-19038	209	65	\	\	PROPN
bracis-19038	209	66	)	)	PUNCT
bracis-19038	209	67	.	.	PUNCT
bracis-19038	210	1	in	in	ADP
bracis-19038	210	2	short	short	ADJ
bracis-19038	210	3	,	,	PUNCT
bracis-19038	210	4	conjunctive	conjunctive	ADJ
bracis-19038	210	5	preferences	preference	NOUN
bracis-19038	210	6	are	be	AUX
bracis-19038	210	7	represented	represent	VERB
bracis-19038	210	8	in	in	ADP
bracis-19038	210	9	[	[	X
bracis-19038	210	10	4	4	X
bracis-19038	210	11	]	]	PUNCT
bracis-19038	210	12	by	by	ADP
bracis-19038	210	13	changing	change	VERB
bracis-19038	210	14	the	the	DET
bracis-19038	210	15	program	program	NOUN
bracis-19038	210	16	p	p	NOUN
bracis-19038	210	17	with	with	ADP
bracis-19038	210	18	two	two	NUM
bracis-19038	210	19	new	new	ADJ
bracis-19038	210	20	atoms	atom	NOUN
bracis-19038	210	21	and	and	CCONJ
bracis-19038	210	22	two	two	NUM
bracis-19038	210	23	new	new	ADJ
bracis-19038	210	24	rules	rule	NOUN
bracis-19038	210	25	before	before	ADP
bracis-19038	210	26	introducing	introduce	VERB
bracis-19038	210	27	\((e_0	\((e_0	PRON
bracis-19038	210	28	\preceq	\preceq	PROPN
bracis-19038	210	29	e_0')\	e_0')\	NOUN
bracis-19038	210	30	)	)	PUNCT
bracis-19038	210	31	,	,	PUNCT
bracis-19038	210	32	which	which	PRON
bracis-19038	210	33	expresses	express	VERB
bracis-19038	210	34	indirectly	indirectly	ADV
bracis-19038	210	35	the	the	DET
bracis-19038	210	36	desired	desire	VERB
bracis-19038	210	37	conjunctive	conjunctive	ADJ
bracis-19038	210	38	preference	preference	NOUN
bracis-19038	210	39	.	.	PUNCT
bracis-19038	211	1	in	in	ADP
bracis-19038	211	2	our	our	PRON
bracis-19038	211	3	approach	approach	NOUN
bracis-19038	211	4	,	,	PUNCT
bracis-19038	211	5	we	we	PRON
bracis-19038	211	6	neither	neither	CCONJ
bracis-19038	211	7	need	need	VERB
bracis-19038	211	8	to	to	PART
bracis-19038	211	9	change	change	VERB
bracis-19038	211	10	the	the	DET
bracis-19038	211	11	program	program	NOUN
bracis-19038	211	12	p	p	NOUN
bracis-19038	211	13	nor	nor	CCONJ
bracis-19038	211	14	to	to	PART
bracis-19038	211	15	add	add	VERB
bracis-19038	211	16	new	new	ADJ
bracis-19038	211	17	artificial	artificial	ADJ
bracis-19038	211	18	atoms	atom	NOUN
bracis-19038	211	19	to	to	PART
bracis-19038	211	20	express	express	VERB
bracis-19038	211	21	conjunctive	conjunctive	ADJ
bracis-19038	211	22	preferences	preference	NOUN
bracis-19038	211	23	.	.	PUNCT
bracis-19038	212	1	preferences	preference	NOUN
bracis-19038	212	2	as	as	ADP
bracis-19038	212	3	\((e_1	\((e_1	NOUN
bracis-19038	212	4	,	,	PUNCT
bracis-19038	212	5	\ldots	\ldots	PROPN
bracis-19038	212	6	,	,	PUNCT
bracis-19038	212	7	e_m	e_m	PROPN
bracis-19038	212	8	)	)	PUNCT
bracis-19038	212	9	\preceq	\preceq	PROPN
bracis-19038	212	10	(	(	PUNCT
bracis-19038	212	11	e_1	e_1	NOUN
bracis-19038	212	12	'	'	NUM
bracis-19038	212	13	,	,	PUNCT
bracis-19038	212	14	\ldots	\ldots	INTJ
bracis-19038	212	15	,	,	PUNCT
bracis-19038	212	16	e_n')\	e_n')\	PROPN
bracis-19038	212	17	)	)	PUNCT
bracis-19038	212	18	can	can	AUX
bracis-19038	212	19	just	just	ADV
bracis-19038	212	20	be	be	AUX
bracis-19038	212	21	represented	represent	VERB
bracis-19038	212	22	as	as	ADP
bracis-19038	212	23	\(\left\	\(\left\	PROPN
bracis-19038	212	24	{	{	PUNCT
bracis-19038	212	25	e_1	e_1	NOUN
bracis-19038	212	26	,	,	PUNCT
bracis-19038	212	27	\ldots	\ldots	INTJ
bracis-19038	212	28	,	,	PUNCT
bracis-19038	212	29	e_m\right\	e_m\right\	VERB
bracis-19038	212	30	}	}	PUNCT
bracis-19038	212	31	\preceq	\preceq	PROPN
bracis-19038	212	32	\left\	\left\	PROPN
bracis-19038	212	33	{	{	PUNCT
bracis-19038	212	34	e_1	e_1	VERB
bracis-19038	212	35	'	'	PROPN
bracis-19038	212	36	,	,	PUNCT
bracis-19038	212	37	\ldots	\ldots	INTJ
bracis-19038	212	38	,	,	PUNCT
bracis-19038	212	39	e_n'\right\	e_n'\right\	ADV
bracis-19038	212	40	}	}	PUNCT
bracis-19038	212	41	\	\	NOUN
bracis-19038	212	42	)	)	PUNCT
bracis-19038	212	43	and	and	CCONJ
bracis-19038	212	44	included	include	VERB
bracis-19038	212	45	straightforwardly	straightforwardly	ADV
bracis-19038	212	46	in	in	ADP
bracis-19038	212	47	\(\varphi	\(\varphi	ADJ
bracis-19038	212	48	\	\	NOUN
bracis-19038	212	49	)	)	PUNCT
bracis-19038	212	50	.	.	PUNCT
bracis-19038	213	1	4.2	4.2	NUM
bracis-19038	213	2	priorities	priority	NOUN
bracis-19038	213	3	between	between	ADP
bracis-19038	213	4	disjunctive	disjunctive	ADJ
bracis-19038	213	5	knowledge	knowledge	NOUN
bracis-19038	213	6	disjunctive	disjunctive	ADJ
bracis-19038	213	7	preferences	preference	NOUN
bracis-19038	213	8	as	as	ADP
bracis-19038	213	9	\((e_1	\((e_1	VERB
bracis-19038	213	10	\vee	\vee	PROPN
bracis-19038	213	11	\cdots	\cdot	NOUN
bracis-19038	213	12	\vee	\vee	PROPN
bracis-19038	213	13	e_m	e_m	NOUN
bracis-19038	213	14	)	)	PUNCT
bracis-19038	213	15	\preceq	\preceq	PROPN
bracis-19038	213	16	(	(	PUNCT
bracis-19038	213	17	e_1	e_1	NOUN
bracis-19038	213	18	'	'	PART
bracis-19038	213	19	\vee	\vee	PROPN
bracis-19038	213	20	\cdots	\cdots	PROPN
bracis-19038	213	21	\vee	\vee	PROPN
bracis-19038	213	22	e_n')\	e_n')\	PROPN
bracis-19038	213	23	)	)	PUNCT
bracis-19038	213	24	can	can	AUX
bracis-19038	213	25	be	be	AUX
bracis-19038	213	26	represented	represent	VERB
bracis-19038	213	27	in	in	ADP
bracis-19038	213	28	a	a	DET
bracis-19038	213	29	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	213	30	)	)	PUNCT
bracis-19038	213	31	\((p	\((p	NOUN
bracis-19038	213	32	,	,	PUNCT
bracis-19038	213	33	\varphi	\varphi	PROPN
bracis-19038	213	34	)	)	PUNCT
bracis-19038	213	35	\	\	NOUN
bracis-19038	213	36	)	)	PUNCT
bracis-19038	213	37	by	by	ADP
bracis-19038	213	38	ensuing	ensue	VERB
bracis-19038	213	39	\(\varphi	\(\varphi	NOUN
bracis-19038	213	40	'	'	PUNCT
bracis-19038	213	41	\subseteq	\subseteq	PROPN
bracis-19038	213	42	\varphi	\varphi	PROPN
bracis-19038	213	43	\	\	NOUN
bracis-19038	213	44	)	)	PUNCT
bracis-19038	213	45	and	and	CCONJ
bracis-19038	213	46	\(\varphi	\(\varphi	NOUN
bracis-19038	213	47	'	'	PUNCT
bracis-19038	213	48	=	=	SYM
bracis-19038	213	49	\left\	\left\	PROPN
bracis-19038	213	50	{	{	PUNCT
bracis-19038	213	51	e_i	e_i	PUNCT
bracis-19038	213	52	\preceq	\preceq	PROPN
bracis-19038	213	53	e_j	e_j	PUNCT
bracis-19038	213	54	'	'	PUNCT
bracis-19038	213	55	\mid	\mid	ADP
bracis-19038	213	56	1	1	NUM
bracis-19038	213	57	\le	\le	NOUN
bracis-19038	213	58	i	i	PRON
bracis-19038	213	59	\le	\le	PROPN
bracis-19038	213	60	m	m	VERB
bracis-19038	213	61	\textit	\textit	NOUN
bracis-19038	213	62	{	{	PUNCT
bracis-19038	213	63	and	and	CCONJ
bracis-19038	213	64	}	}	SYM
bracis-19038	213	65	1	1	NUM
bracis-19038	213	66	\le	\le	PROPN
bracis-19038	213	67	j	j	PROPN
bracis-19038	213	68	\le	\le	PROPN
bracis-19038	213	69	n\right\	n\right\	NOUN
bracis-19038	213	70	}	}	PUNCT
bracis-19038	213	71	\	\	NOUN
bracis-19038	213	72	)	)	PUNCT
bracis-19038	213	73	.	.	PUNCT
bracis-19038	214	1	4.3	4.3	NUM
bracis-19038	214	2	conditional	conditional	ADJ
bracis-19038	214	3	priorities	priority	NOUN
bracis-19038	214	4	it	it	PRON
bracis-19038	214	5	is	be	AUX
bracis-19038	214	6	not	not	PART
bracis-19038	214	7	always	always	ADV
bracis-19038	214	8	the	the	DET
bracis-19038	214	9	case	case	NOUN
bracis-19038	214	10	a	a	DET
bracis-19038	214	11	preference	preference	NOUN
bracis-19038	214	12	is	be	AUX
bracis-19038	214	13	absolute	absolute	ADJ
bracis-19038	214	14	.	.	PUNCT
bracis-19038	215	1	in	in	ADP
bracis-19038	215	2	the	the	DET
bracis-19038	215	3	so	so	ADV
bracis-19038	215	4	-	-	PUNCT
bracis-19038	215	5	called	call	VERB
bracis-19038	215	6	conditional	conditional	ADJ
bracis-19038	215	7	preference	preference	NOUN
bracis-19038	215	8	,	,	PUNCT
bracis-19038	215	9	users	user	NOUN
bracis-19038	215	10	may	may	AUX
bracis-19038	215	11	also	also	ADV
bracis-19038	215	12	wish	wish	VERB
bracis-19038	215	13	to	to	PART
bracis-19038	215	14	express	express	VERB
bracis-19038	215	15	specific	specific	ADJ
bracis-19038	215	16	preferences	preference	NOUN
bracis-19038	215	17	in	in	ADP
bracis-19038	215	18	particular	particular	ADJ
bracis-19038	215	19	contexts	context	NOUN
bracis-19038	215	20	(	(	PUNCT
bracis-19038	215	21	e.g.	e.g.	ADV
bracis-19038	215	22	,	,	PUNCT
bracis-19038	215	23	if	if	SCONJ
bracis-19038	215	24	red	red	ADJ
bracis-19038	215	25	wine	wine	NOUN
bracis-19038	215	26	is	be	AUX
bracis-19038	215	27	served	serve	VERB
bracis-19038	215	28	,	,	PUNCT
bracis-19038	215	29	i	i	PRON
bracis-19038	215	30	prefer	prefer	VERB
bracis-19038	215	31	meat	meat	NOUN
bracis-19038	215	32	to	to	ADP
bracis-19038	215	33	fish	fish	VERB
bracis-19038	215	34	)	)	PUNCT
bracis-19038	215	35	.	.	PUNCT
bracis-19038	216	1	it	it	PRON
bracis-19038	216	2	is	be	AUX
bracis-19038	216	3	denoted	denote	VERB
bracis-19038	216	4	by	by	ADP
bracis-19038	216	5	\(\gamma	\(\gamma	NOUN
bracis-19038	216	6	:	:	PUNCT
bracis-19038	216	7	\phi	\phi	PROPN
bracis-19038	216	8	\preceq	\preceq	PROPN
bracis-19038	216	9	\psi	\psi	PROPN
bracis-19038	216	10	\	\	PROPN
bracis-19038	216	11	)	)	PUNCT
bracis-19038	216	12	and	and	CCONJ
bracis-19038	216	13	interpreted	interpret	VERB
bracis-19038	216	14	as	as	ADP
bracis-19038	216	15	“	"	PUNCT
bracis-19038	216	16	given	give	VERB
bracis-19038	216	17	a	a	DET
bracis-19038	216	18	context	context	NOUN
bracis-19038	216	19	\(\gamma	\(\gamma	NOUN
bracis-19038	216	20	\	\	NOUN
bracis-19038	216	21	)	)	PUNCT
bracis-19038	216	22	,	,	PUNCT
bracis-19038	216	23	prefer	prefer	VERB
bracis-19038	216	24	\(\psi	\(\psi	VERB
bracis-19038	216	25	\	\	NOUN
bracis-19038	216	26	)	)	PUNCT
bracis-19038	216	27	to	to	ADP
bracis-19038	216	28	\(\phi	\(\phi	ADJ
bracis-19038	216	29	\	\	NOUN
bracis-19038	216	30	)	)	PUNCT
bracis-19038	216	31	"	"	PUNCT
bracis-19038	216	32	.	.	PUNCT
bracis-19038	217	1	assuming	assume	VERB
bracis-19038	217	2	\(\gamma	\(\gamma	ADP
bracis-19038	217	3	=	=	SYM
bracis-19038	217	4	c_1	c_1	PROPN
bracis-19038	217	5	\wedge	\wedge	PROPN
bracis-19038	217	6	\cdots	\cdots	PROPN
bracis-19038	217	7	\wedge	\wedge	PROPN
bracis-19038	217	8	c_o\	c_o\	NOUN
bracis-19038	217	9	)	)	PUNCT
bracis-19038	217	10	,	,	PUNCT
bracis-19038	217	11	\(\phi	\(\phi	NOUN
bracis-19038	217	12	=	=	PUNCT
bracis-19038	217	13	e_1	e_1	X
bracis-19038	217	14	\wedge	\wedge	PROPN
bracis-19038	217	15	\cdots	\cdots	PROPN
bracis-19038	217	16	\wedge	\wedge	PROPN
bracis-19038	217	17	e_m\	e_m\	NOUN
bracis-19038	217	18	)	)	PUNCT
bracis-19038	217	19	and	and	CCONJ
bracis-19038	217	20	\(\psi	\(\psi	VERB
bracis-19038	217	21	=	=	PUNCT
bracis-19038	218	1	e_1	e_1	NOUN
bracis-19038	218	2	'	'	PART
bracis-19038	218	3	\wedge	\wedge	PROPN
bracis-19038	218	4	\cdots	\cdots	PROPN
bracis-19038	218	5	\wedge	\wedge	PROPN
bracis-19038	218	6	e_n'\	e_n'\	NOUN
bracis-19038	218	7	)	)	PUNCT
bracis-19038	218	8	,	,	PUNCT
bracis-19038	218	9	we	we	PRON
bracis-19038	218	10	can	can	AUX
bracis-19038	218	11	represent	represent	VERB
bracis-19038	218	12	the	the	DET
bracis-19038	218	13	conditional	conditional	ADJ
bracis-19038	218	14	preference	preference	NOUN
bracis-19038	218	15	\(\gamma	\(\gamma	NOUN
bracis-19038	218	16	:	:	PUNCT
bracis-19038	219	1	\phi	\phi	PROPN
bracis-19038	219	2	\preceq	\preceq	PROPN
bracis-19038	219	3	\psi	\psi	PROPN
bracis-19038	219	4	\	\	NOUN
bracis-19038	219	5	)	)	PUNCT
bracis-19038	219	6	as	as	ADP
bracis-19038	219	7	the	the	DET
bracis-19038	219	8	conjunctive	conjunctive	ADJ
bracis-19038	219	9	preference	preference	NOUN
bracis-19038	219	10	\(\left\	\(\left\	PROPN
bracis-19038	219	11	{	{	PUNCT
bracis-19038	219	12	c_1	c_1	PROPN
bracis-19038	219	13	,	,	PUNCT
bracis-19038	219	14	\ldots	\ldots	INTJ
bracis-19038	219	15	,	,	PUNCT
bracis-19038	219	16	c_o	c_o	PROPN
bracis-19038	219	17	,	,	PUNCT
bracis-19038	219	18	e_1	e_1	X
bracis-19038	219	19	,	,	PUNCT
bracis-19038	219	20	\ldots	\ldots	INTJ
bracis-19038	219	21	,	,	PUNCT
bracis-19038	219	22	e_m\right\	e_m\right\	VERB
bracis-19038	219	23	}	}	PUNCT
bracis-19038	219	24	\preceq	\preceq	PROPN
bracis-19038	219	25	\left\	\left\	PROPN
bracis-19038	219	26	{	{	PUNCT
bracis-19038	219	27	c_1	c_1	PROPN
bracis-19038	219	28	,	,	PUNCT
bracis-19038	219	29	\ldots	\ldots	INTJ
bracis-19038	219	30	,	,	PUNCT
bracis-19038	219	31	c_o	c_o	PROPN
bracis-19038	219	32	,	,	PUNCT
bracis-19038	219	33	e_1	e_1	VERB
bracis-19038	219	34	'	'	PUNCT
bracis-19038	219	35	,	,	PUNCT
bracis-19038	219	36	\ldots	\ldots	INTJ
bracis-19038	219	37	,	,	PUNCT
bracis-19038	219	38	e_n'\right\	e_n'\right\	ADV
bracis-19038	219	39	}	}	PUNCT
bracis-19038	219	40	\	\	NOUN
bracis-19038	219	41	)	)	PUNCT
bracis-19038	219	42	in	in	ADP
bracis-19038	219	43	\(\varphi	\(\varphi	ADJ
bracis-19038	219	44	\	\	NOUN
bracis-19038	219	45	)	)	PUNCT
bracis-19038	219	46	.	.	PUNCT
bracis-19038	220	1	conditional	conditional	ADJ
bracis-19038	220	2	preferences	preference	NOUN
bracis-19038	220	3	can	can	AUX
bracis-19038	220	4	occur	occur	VERB
bracis-19038	220	5	disguised	disguise	VERB
bracis-19038	220	6	as	as	ADP
bracis-19038	220	7	in	in	ADP
bracis-19038	220	8	“	"	PUNCT
bracis-19038	220	9	if	if	SCONJ
bracis-19038	220	10	\(\gamma	\(\gamma	ADP
bracis-19038	220	11	=	=	SYM
bracis-19038	220	12	c_1	c_1	PROPN
bracis-19038	220	13	\wedge	\wedge	PROPN
bracis-19038	220	14	\cdots	\cdots	PROPN
bracis-19038	220	15	\wedge	\wedge	PROPN
bracis-19038	220	16	c_o\	c_o\	NOUN
bracis-19038	220	17	)	)	PUNCT
bracis-19038	220	18	is	be	AUX
bracis-19038	220	19	true	true	ADJ
bracis-19038	220	20	,	,	PUNCT
bracis-19038	220	21	then	then	ADV
bracis-19038	220	22	prefer	prefer	VERB
bracis-19038	220	23	\(\psi	\(\psi	NOUN
bracis-19038	221	1	=	=	PUNCT
bracis-19038	221	2	e_1	e_1	NOUN
bracis-19038	221	3	'	'	PART
bracis-19038	221	4	\wedge	\wedge	PROPN
bracis-19038	221	5	\cdots	\cdots	PROPN
bracis-19038	221	6	\wedge	\wedge	PROPN
bracis-19038	221	7	e_n'\	e_n'\	NOUN
bracis-19038	221	8	)	)	PUNCT
bracis-19038	221	9	"	"	PUNCT
bracis-19038	221	10	;	;	PUNCT
bracis-19038	221	11	it	it	PRON
bracis-19038	221	12	interpreted	interpret	VERB
bracis-19038	221	13	as	as	ADP
bracis-19038	221	14	if	if	SCONJ
bracis-19038	221	15	\(\gamma	\(\gamma	ADP
bracis-19038	221	16	\	\	NOUN
bracis-19038	221	17	)	)	PUNCT
bracis-19038	221	18	is	be	AUX
bracis-19038	221	19	true	true	ADJ
bracis-19038	221	20	,	,	PUNCT
bracis-19038	221	21	then	then	ADV
bracis-19038	221	22	prefer	prefer	VERB
bracis-19038	221	23	\(\psi	\(\psi	VERB
bracis-19038	221	24	\	\	NOUN
bracis-19038	221	25	)	)	PUNCT
bracis-19038	221	26	to	to	ADP
bracis-19038	221	27	\(\mathtt	\(\mathtt	NOUN
bracis-19038	221	28	{	{	PUNCT
bracis-19038	221	29	not\	not\	PROPN
bracis-19038	221	30	}	}	PUNCT
bracis-19038	221	31	e_j'\	e_j'\	PROPN
bracis-19038	221	32	)	)	PUNCT
bracis-19038	221	33	with	with	ADP
bracis-19038	221	34	\(1	\(1	PROPN
bracis-19038	221	35	\le	\le	PROPN
bracis-19038	221	36	j	j	PROPN
bracis-19038	221	37	\le	\le	PROPN
bracis-19038	221	38	n\	n\	PROPN
bracis-19038	221	39	)	)	PUNCT
bracis-19038	221	40	.	.	PUNCT
bracis-19038	222	1	this	this	PRON
bracis-19038	222	2	is	be	AUX
bracis-19038	222	3	a	a	DET
bracis-19038	222	4	particular	particular	ADJ
bracis-19038	222	5	case	case	NOUN
bracis-19038	222	6	of	of	ADP
bracis-19038	222	7	our	our	PRON
bracis-19038	222	8	representation	representation	NOUN
bracis-19038	222	9	when	when	SCONJ
bracis-19038	222	10	\(\phi	\(\phi	ADJ
bracis-19038	222	11	=	=	SYM
bracis-19038	222	12	\mathtt	\mathtt	PROPN
bracis-19038	222	13	{	{	PUNCT
bracis-19038	222	14	not\	not\	PROPN
bracis-19038	222	15	}	}	PUNCT
bracis-19038	222	16	e_j'\	e_j'\	PROPN
bracis-19038	222	17	)	)	PUNCT
bracis-19038	222	18	,	,	PUNCT
bracis-19038	222	19	i.e.	i.e.	X
bracis-19038	222	20	,	,	PUNCT
bracis-19038	222	21	such	such	DET
bracis-19038	222	22	a	a	DET
bracis-19038	222	23	preference	preference	NOUN
bracis-19038	222	24	can	can	AUX
bracis-19038	222	25	be	be	AUX
bracis-19038	222	26	represented	represent	VERB
bracis-19038	222	27	in	in	ADP
bracis-19038	222	28	\((p	\((p	NOUN
bracis-19038	222	29	,	,	PUNCT
bracis-19038	222	30	\varphi	\varphi	PROPN
bracis-19038	222	31	)	)	PUNCT
bracis-19038	222	32	\	\	NOUN
bracis-19038	222	33	)	)	PUNCT
bracis-19038	222	34	by	by	ADP
bracis-19038	222	35	including	include	VERB
bracis-19038	222	36	in	in	ADP
bracis-19038	222	37	\(\varphi	\(\varphi	PROPN
bracis-19038	222	38	\	\	NOUN
bracis-19038	222	39	)	)	PUNCT
bracis-19038	222	40	the	the	DET
bracis-19038	222	41	preferences	preference	NOUN
bracis-19038	222	42	\(\left\	\(\left\	VERB
bracis-19038	222	43	{	{	PUNCT
bracis-19038	222	44	c_1	c_1	PROPN
bracis-19038	222	45	,	,	PUNCT
bracis-19038	222	46	\ldots	\ldots	INTJ
bracis-19038	222	47	,	,	PUNCT
bracis-19038	222	48	c_o	c_o	PROPN
bracis-19038	222	49	,	,	PUNCT
bracis-19038	222	50	\mathtt	\mathtt	PROPN
bracis-19038	222	51	{	{	PUNCT
bracis-19038	222	52	not\	not\	PROPN
bracis-19038	222	53	}	}	PUNCT
bracis-19038	222	54	e_j'\right\	e_j'\right\	ADJ
bracis-19038	222	55	}	}	PUNCT
bracis-19038	222	56	\preceq	\preceq	PROPN
bracis-19038	222	57	\left\	\left\	PROPN
bracis-19038	222	58	{	{	PUNCT
bracis-19038	222	59	c_1	c_1	PROPN
bracis-19038	222	60	,	,	PUNCT
bracis-19038	222	61	\ldots	\ldots	INTJ
bracis-19038	222	62	,	,	PUNCT
bracis-19038	222	63	c_o	c_o	PROPN
bracis-19038	222	64	,	,	PUNCT
bracis-19038	222	65	e_1	e_1	VERB
bracis-19038	222	66	'	'	PUNCT
bracis-19038	222	67	,	,	PUNCT
bracis-19038	222	68	\ldots	\ldots	INTJ
bracis-19038	222	69	,	,	PUNCT
bracis-19038	222	70	e_n'\right\	e_n'\right\	ADV
bracis-19038	222	71	}	}	PUNCT
bracis-19038	222	72	\	\	NOUN
bracis-19038	222	73	)	)	PUNCT
bracis-19038	222	74	with	with	ADP
bracis-19038	222	75	\(1	\(1	PROPN
bracis-19038	222	76	\le	\le	PROPN
bracis-19038	222	77	j	j	PROPN
bracis-19038	222	78	\le	\le	PROPN
bracis-19038	222	79	n\	n\	PROPN
bracis-19038	222	80	)	)	PUNCT
bracis-19038	222	81	.	.	PUNCT
bracis-19038	223	1	4.4	4.4	NUM
bracis-19038	223	2	priorities	priority	NOUN
bracis-19038	223	3	between	between	ADP
bracis-19038	223	4	rules	rule	NOUN
bracis-19038	223	5	preferences	preference	NOUN
bracis-19038	223	6	can	can	AUX
bracis-19038	223	7	also	also	ADV
bracis-19038	223	8	be	be	AUX
bracis-19038	223	9	established	establish	VERB
bracis-19038	223	10	between	between	ADP
bracis-19038	223	11	(	(	PUNCT
bracis-19038	223	12	conflicting	conflict	VERB
bracis-19038	223	13	)	)	PUNCT
bracis-19038	223	14	rules	rule	NOUN
bracis-19038	223	15	as	as	ADP
bracis-19038	223	16	in	in	ADP
bracis-19038	223	17	\(e	\(e	PROPN
bracis-19038	223	18	\leftarrow	\leftarrow	PROPN
bracis-19038	223	19	e_1	e_1	NOUN
bracis-19038	223	20	,	,	PUNCT
bracis-19038	223	21	\ldots	\ldots	INTJ
bracis-19038	223	22	,	,	PUNCT
bracis-19038	223	23	e_m\	e_m\	PROPN
bracis-19038	223	24	)	)	PUNCT
bracis-19038	223	25	\(\preceq	\(\preceq	X
bracis-19038	223	26	e	e	X
bracis-19038	223	27	'	'	PUNCT
bracis-19038	223	28	\leftarrow	\leftarrow	PROPN
bracis-19038	223	29	e_1	e_1	NOUN
bracis-19038	223	30	'	'	PROPN
bracis-19038	223	31	,	,	PUNCT
bracis-19038	223	32	\ldots	\ldots	INTJ
bracis-19038	223	33	,	,	PUNCT
bracis-19038	223	34	e_n'\	e_n'\	NOUN
bracis-19038	223	35	)	)	PUNCT
bracis-19038	223	36	.	.	PUNCT
bracis-19038	224	1	its	its	PRON
bracis-19038	224	2	intended	intend	VERB
bracis-19038	224	3	meaning	meaning	NOUN
bracis-19038	224	4	is	be	AUX
bracis-19038	224	5	the	the	DET
bracis-19038	224	6	conclusion	conclusion	NOUN
bracis-19038	224	7	of	of	ADP
bracis-19038	224	8	\(e'\	\(e'\	PROPN
bracis-19038	224	9	)	)	PUNCT
bracis-19038	224	10	via	via	ADP
bracis-19038	224	11	\(e	\(e	NOUN
bracis-19038	224	12	'	'	PUNCT
bracis-19038	224	13	\leftarrow	\leftarrow	PROPN
bracis-19038	224	14	e_1	e_1	NOUN
bracis-19038	224	15	'	'	PUNCT
bracis-19038	224	16	,	,	PUNCT
bracis-19038	224	17	\ldots	\ldots	INTJ
bracis-19038	224	18	,	,	PUNCT
bracis-19038	224	19	e_n'\	e_n'\	NOUN
bracis-19038	224	20	)	)	PUNCT
bracis-19038	224	21	will	will	AUX
bracis-19038	224	22	block	block	VERB
bracis-19038	224	23	the	the	DET
bracis-19038	224	24	conclusion	conclusion	NOUN
bracis-19038	224	25	of	of	ADP
bracis-19038	224	26	e	e	PROPN
bracis-19038	224	27	via	via	ADP
bracis-19038	224	28	\(e	\(e	PROPN
bracis-19038	224	29	\leftarrow	\leftarrow	PROPN
bracis-19038	224	30	e_1	e_1	NOUN
bracis-19038	224	31	,	,	PUNCT
bracis-19038	224	32	\ldots	\ldots	INTJ
bracis-19038	224	33	,	,	PUNCT
bracis-19038	224	34	e_m\	e_m\	PROPN
bracis-19038	224	35	)	)	PUNCT
bracis-19038	224	36	.	.	PUNCT
bracis-19038	225	1	such	such	DET
bracis-19038	225	2	a	a	DET
bracis-19038	225	3	preference	preference	NOUN
bracis-19038	225	4	can	can	AUX
bracis-19038	225	5	be	be	AUX
bracis-19038	225	6	represented	represent	VERB
bracis-19038	225	7	in	in	ADP
bracis-19038	225	8	\((p	\((p	NOUN
bracis-19038	225	9	,	,	PUNCT
bracis-19038	225	10	\varphi	\varphi	PROPN
bracis-19038	225	11	)	)	PUNCT
bracis-19038	225	12	\	\	NOUN
bracis-19038	225	13	)	)	PUNCT
bracis-19038	225	14	by	by	ADP
bracis-19038	225	15	including	include	VERB
bracis-19038	225	16	\(\left\	\(\left\	PROPN
bracis-19038	225	17	{	{	PUNCT
bracis-19038	225	18	e_1	e_1	NOUN
bracis-19038	225	19	,	,	PUNCT
bracis-19038	225	20	\ldots	\ldots	INTJ
bracis-19038	225	21	,	,	PUNCT
bracis-19038	225	22	e_m\right\	e_m\right\	VERB
bracis-19038	225	23	}	}	PUNCT
bracis-19038	225	24	\preceq	\preceq	PROPN
bracis-19038	225	25	\left\	\left\	PROPN
bracis-19038	225	26	{	{	PUNCT
bracis-19038	225	27	e_1	e_1	VERB
bracis-19038	225	28	'	'	PROPN
bracis-19038	225	29	,	,	PUNCT
bracis-19038	225	30	\ldots	\ldots	INTJ
bracis-19038	225	31	,	,	PUNCT
bracis-19038	225	32	e_n'\right\	e_n'\right\	ADV
bracis-19038	225	33	}	}	PUNCT
bracis-19038	225	34	\	\	NOUN
bracis-19038	225	35	)	)	PUNCT
bracis-19038	225	36	in	in	ADP
bracis-19038	225	37	\(\varphi	\(\varphi	ADJ
bracis-19038	225	38	\	\	NOUN
bracis-19038	225	39	)	)	PUNCT
bracis-19038	225	40	.	.	PUNCT
bracis-19038	226	1	4.5	4.5	NUM
bracis-19038	226	2	bipolar	bipolar	ADJ
bracis-19038	226	3	preferences	preference	NOUN
bracis-19038	226	4	preferences	preference	NOUN
bracis-19038	226	5	can	can	AUX
bracis-19038	226	6	express	express	VERB
bracis-19038	226	7	not	not	PART
bracis-19038	226	8	only	only	ADV
bracis-19038	226	9	what	what	PRON
bracis-19038	226	10	is	be	AUX
bracis-19038	226	11	satisfactory	satisfactory	ADJ
bracis-19038	226	12	(	(	PUNCT
bracis-19038	226	13	positive	positive	ADJ
bracis-19038	226	14	preferences	preference	NOUN
bracis-19038	226	15	)	)	PUNCT
bracis-19038	226	16	,	,	PUNCT
bracis-19038	226	17	but	but	CCONJ
bracis-19038	226	18	also	also	ADV
bracis-19038	226	19	what	what	PRON
bracis-19038	226	20	can	can	AUX
bracis-19038	226	21	be	be	AUX
bracis-19038	226	22	considered	consider	VERB
bracis-19038	226	23	tolerable	tolerable	ADJ
bracis-19038	226	24	or	or	CCONJ
bracis-19038	226	25	unacceptable	unacceptable	ADJ
bracis-19038	226	26	(	(	PUNCT
bracis-19038	226	27	negative	negative	ADJ
bracis-19038	226	28	preferences	preference	NOUN
bracis-19038	226	29	)	)	PUNCT
bracis-19038	226	30	.	.	PUNCT
bracis-19038	227	1	these	these	DET
bracis-19038	227	2	two	two	NUM
bracis-19038	227	3	forms	form	NOUN
bracis-19038	227	4	of	of	ADP
bracis-19038	227	5	preferences	preference	NOUN
bracis-19038	227	6	(	(	PUNCT
bracis-19038	227	7	bipolar	bipolar	ADJ
bracis-19038	227	8	preferences	preference	NOUN
bracis-19038	227	9	)	)	PUNCT
bracis-19038	227	10	have	have	AUX
bracis-19038	227	11	been	be	AUX
bracis-19038	227	12	conjointly	conjointly	ADV
bracis-19038	227	13	and	and	CCONJ
bracis-19038	227	14	compactly	compactly	ADV
bracis-19038	227	15	expressed	express	VERB
bracis-19038	227	16	in	in	ADP
bracis-19038	227	17	various	various	ADJ
bracis-19038	227	18	works	work	NOUN
bracis-19038	227	19	[	[	X
bracis-19038	227	20	16,17,18,19,20,21	16,17,18,19,20,21	NUM
bracis-19038	227	21	]	]	X
bracis-19038	227	22	.	.	PUNCT
bracis-19038	228	1	roughly	roughly	ADV
bracis-19038	228	2	speaking	speak	VERB
bracis-19038	228	3	,	,	PUNCT
bracis-19038	228	4	the	the	DET
bracis-19038	228	5	intended	intend	VERB
bracis-19038	228	6	meaning	meaning	NOUN
bracis-19038	228	7	of	of	ADP
bracis-19038	228	8	introducing	introduce	VERB
bracis-19038	228	9	positive	positive	ADJ
bracis-19038	228	10	preferences	preference	NOUN
bracis-19038	228	11	is	be	AUX
bracis-19038	228	12	to	to	PART
bracis-19038	228	13	express	express	VERB
bracis-19038	228	14	wishes	wish	NOUN
bracis-19038	228	15	which	which	PRON
bracis-19038	228	16	should	should	AUX
bracis-19038	228	17	be	be	AUX
bracis-19038	228	18	satisfied	satisfied	ADJ
bracis-19038	228	19	as	as	ADV
bracis-19038	228	20	best	good	ADJ
bracis-19038	228	21	as	as	ADP
bracis-19038	228	22	possible	possible	ADJ
bracis-19038	228	23	,	,	PUNCT
bracis-19038	228	24	whilst	whilst	SCONJ
bracis-19038	228	25	negative	negative	ADJ
bracis-19038	228	26	preferences	preference	NOUN
bracis-19038	228	27	are	be	AUX
bracis-19038	228	28	intended	intend	VERB
bracis-19038	228	29	to	to	PART
bracis-19038	228	30	enhance	enhance	VERB
bracis-19038	228	31	the	the	DET
bracis-19038	228	32	idea	idea	NOUN
bracis-19038	228	33	that	that	SCONJ
bracis-19038	228	34	what	what	PRON
bracis-19038	228	35	is	be	AUX
bracis-19038	228	36	not	not	PART
bracis-19038	228	37	rejected	reject	VERB
bracis-19038	228	38	or	or	CCONJ
bracis-19038	228	39	excluded	exclude	VERB
bracis-19038	228	40	is	be	AUX
bracis-19038	228	41	tolerated	tolerate	VERB
bracis-19038	228	42	.	.	PUNCT
bracis-19038	229	1	thus	thus	ADV
bracis-19038	229	2	,	,	PUNCT
bracis-19038	229	3	when	when	SCONJ
bracis-19038	229	4	interpreting	interpret	VERB
bracis-19038	229	5	\(\preceq	\(\preceq	X
bracis-19038	229	6	\	\	NOUN
bracis-19038	229	7	)	)	PUNCT
bracis-19038	229	8	as	as	ADP
bracis-19038	229	9	a	a	DET
bracis-19038	229	10	bipolar	bipolar	ADJ
bracis-19038	229	11	priority	priority	NOUN
bracis-19038	229	12	by	by	ADP
bracis-19038	229	13	\(\left\	\(\left\	PROPN
bracis-19038	229	14	{	{	PUNCT
bracis-19038	229	15	e_1	e_1	NOUN
bracis-19038	229	16	,	,	PUNCT
bracis-19038	229	17	\ldots	\ldots	INTJ
bracis-19038	229	18	,	,	PUNCT
bracis-19038	229	19	e_m\right\	e_m\right\	VERB
bracis-19038	229	20	}	}	PUNCT
bracis-19038	229	21	\preceq	\preceq	PROPN
bracis-19038	229	22	\left\	\left\	PROPN
bracis-19038	229	23	{	{	PUNCT
bracis-19038	229	24	e_1	e_1	VERB
bracis-19038	229	25	'	'	PROPN
bracis-19038	229	26	,	,	PUNCT
bracis-19038	229	27	\ldots	\ldots	INTJ
bracis-19038	229	28	,	,	PUNCT
bracis-19038	229	29	e_n'\right\	e_n'\right\	ADV
bracis-19038	229	30	}	}	PUNCT
bracis-19038	229	31	\	\	NOUN
bracis-19038	229	32	)	)	PUNCT
bracis-19038	229	33	,	,	PUNCT
bracis-19038	229	34	we	we	PRON
bracis-19038	229	35	mean	mean	VERB
bracis-19038	229	36	we	we	PRON
bracis-19038	229	37	are	be	AUX
bracis-19038	229	38	giving	give	VERB
bracis-19038	229	39	priority	priority	NOUN
bracis-19038	229	40	not	not	PART
bracis-19038	229	41	only	only	ADV
bracis-19038	229	42	to	to	ADP
bracis-19038	229	43	outcomes	outcome	NOUN
bracis-19038	229	44	satisfying	satisfy	VERB
bracis-19038	229	45	\(\left\	\(\left\	PROPN
bracis-19038	229	46	{	{	PUNCT
bracis-19038	229	47	e_1	e_1	NOUN
bracis-19038	229	48	,	,	PUNCT
bracis-19038	229	49	\ldots	\ldots	INTJ
bracis-19038	229	50	,	,	PUNCT
bracis-19038	229	51	e_m\right\	e_m\right\	VERB
bracis-19038	229	52	}	}	PUNCT
bracis-19038	229	53	\preceq	\preceq	PROPN
bracis-19038	229	54	\left\	\left\	PROPN
bracis-19038	229	55	{	{	PUNCT
bracis-19038	229	56	e_1	e_1	VERB
bracis-19038	229	57	'	'	PROPN
bracis-19038	229	58	,	,	PUNCT
bracis-19038	229	59	\ldots	\ldots	INTJ
bracis-19038	229	60	,	,	PUNCT
bracis-19038	229	61	e_n'\right\	e_n'\right\	ADV
bracis-19038	229	62	}	}	PUNCT
bracis-19038	229	63	\	\	NOUN
bracis-19038	229	64	)	)	PUNCT
bracis-19038	229	65	,	,	PUNCT
bracis-19038	229	66	but	but	CCONJ
bracis-19038	229	67	to	to	ADP
bracis-19038	229	68	those	those	PRON
bracis-19038	229	69	not	not	PART
bracis-19038	229	70	falsifying	falsify	VERB
bracis-19038	229	71	\(\left\	\(\left\	PROPN
bracis-19038	229	72	{	{	PUNCT
bracis-19038	229	73	e_1	e_1	NOUN
bracis-19038	229	74	,	,	PUNCT
bracis-19038	229	75	\ldots	\ldots	INTJ
bracis-19038	229	76	,	,	PUNCT
bracis-19038	229	77	e_m\right\	e_m\right\	VERB
bracis-19038	229	78	}	}	PUNCT
bracis-19038	229	79	\preceq	\preceq	PROPN
bracis-19038	229	80	\left\	\left\	PROPN
bracis-19038	229	81	{	{	PUNCT
bracis-19038	229	82	e_1	e_1	VERB
bracis-19038	229	83	'	'	PROPN
bracis-19038	229	84	,	,	PUNCT
bracis-19038	229	85	\ldots	\ldots	INTJ
bracis-19038	229	86	,	,	PUNCT
bracis-19038	229	87	e_n'\right\	e_n'\right\	ADV
bracis-19038	229	88	}	}	PUNCT
bracis-19038	229	89	\	\	NOUN
bracis-19038	229	90	)	)	PUNCT
bracis-19038	229	91	,	,	PUNCT
bracis-19038	229	92	i.e.	i.e.	X
bracis-19038	229	93	,	,	PUNCT
bracis-19038	229	94	it	it	PRON
bracis-19038	229	95	either	either	CCONJ
bracis-19038	229	96	should	should	AUX
bracis-19038	229	97	contain	contain	VERB
bracis-19038	229	98	\(\left\	\(\left\	PROPN
bracis-19038	229	99	{	{	PUNCT
bracis-19038	229	100	e_1	e_1	NOUN
bracis-19038	229	101	'	'	NUM
bracis-19038	229	102	,	,	PUNCT
bracis-19038	229	103	\ldots	\ldots	INTJ
bracis-19038	229	104	,	,	PUNCT
bracis-19038	229	105	e_n'\right\	e_n'\right\	ADV
bracis-19038	229	106	}	}	PUNCT
bracis-19038	229	107	\	\	NOUN
bracis-19038	229	108	)	)	PUNCT
bracis-19038	229	109	,	,	PUNCT
bracis-19038	229	110	but	but	CCONJ
bracis-19038	229	111	not	not	PART
bracis-19038	229	112	\(\left\	\(\left\	ADV
bracis-19038	229	113	{	{	PUNCT
bracis-19038	229	114	e_1	e_1	NOUN
bracis-19038	229	115	,	,	PUNCT
bracis-19038	229	116	\ldots	\ldots	INTJ
bracis-19038	229	117	,	,	PUNCT
bracis-19038	229	118	e_m\right\	e_m\right\	VERB
bracis-19038	229	119	}	}	PUNCT
bracis-19038	229	120	\	\	NOUN
bracis-19038	229	121	)	)	PUNCT
bracis-19038	229	122	(	(	PUNCT
bracis-19038	229	123	positive	positive	ADJ
bracis-19038	229	124	preference	preference	NOUN
bracis-19038	229	125	)	)	PUNCT
bracis-19038	229	126	,	,	PUNCT
bracis-19038	229	127	or	or	CCONJ
bracis-19038	229	128	should	should	AUX
bracis-19038	229	129	contain	contain	VERB
bracis-19038	229	130	\(\left\	\(\left\	PROPN
bracis-19038	229	131	{	{	PUNCT
bracis-19038	229	132	\mathtt	\mathtt	PROPN
bracis-19038	229	133	{	{	PUNCT
bracis-19038	229	134	not\	not\	PROPN
bracis-19038	229	135	}	}	PUNCT
bracis-19038	229	136	e_i\right\	e_i\right\	ADJ
bracis-19038	229	137	}	}	PUNCT
bracis-19038	229	138	\	\	NOUN
bracis-19038	229	139	)	)	PUNCT
bracis-19038	229	140	,	,	PUNCT
bracis-19038	229	141	but	but	CCONJ
bracis-19038	229	142	not	not	PART
bracis-19038	229	143	\(\left\	\(\left\	ADV
bracis-19038	229	144	{	{	PUNCT
bracis-19038	229	145	\mathtt	\mathtt	PROPN
bracis-19038	229	146	{	{	PUNCT
bracis-19038	229	147	not\	not\	PROPN
bracis-19038	229	148	}	}	PUNCT
bracis-19038	229	149	e_j'\right\	e_j'\right\	ADJ
bracis-19038	229	150	}	}	PUNCT
bracis-19038	229	151	\	\	NOUN
bracis-19038	229	152	)	)	PUNCT
bracis-19038	229	153	with	with	ADP
bracis-19038	229	154	\(1	\(1	PROPN
bracis-19038	229	155	\le	\le	PROPN
bracis-19038	229	156	i	i	NOUN
bracis-19038	229	157	\le	\le	NOUN
bracis-19038	229	158	m\	m\	NOUN
bracis-19038	229	159	)	)	PUNCT
bracis-19038	229	160	and	and	CCONJ
bracis-19038	229	161	\(1	\(1	PROPN
bracis-19038	229	162	\le	\le	PROPN
bracis-19038	229	163	j	j	PROPN
bracis-19038	229	164	\le	\le	PROPN
bracis-19038	229	165	n\	n\	PROPN
bracis-19038	229	166	)	)	PUNCT
bracis-19038	229	167	(	(	PUNCT
bracis-19038	229	168	negative	negative	ADJ
bracis-19038	229	169	preference	preference	NOUN
bracis-19038	229	170	)	)	PUNCT
bracis-19038	229	171	.	.	PUNCT
bracis-19038	230	1	bipolar	bipolar	ADJ
bracis-19038	230	2	preferences	preference	NOUN
bracis-19038	230	3	as	as	ADP
bracis-19038	230	4	\(\left\	\(\left\	NOUN
bracis-19038	230	5	{	{	PUNCT
bracis-19038	230	6	e_1	e_1	NOUN
bracis-19038	230	7	,	,	PUNCT
bracis-19038	230	8	\ldots	\ldots	INTJ
bracis-19038	230	9	,	,	PUNCT
bracis-19038	230	10	e_m\right\	e_m\right\	VERB
bracis-19038	230	11	}	}	PUNCT
bracis-19038	230	12	\preceq	\preceq	PROPN
bracis-19038	230	13	\left\	\left\	PROPN
bracis-19038	230	14	{	{	PUNCT
bracis-19038	230	15	e_1	e_1	VERB
bracis-19038	230	16	'	'	PROPN
bracis-19038	230	17	,	,	PUNCT
bracis-19038	230	18	\ldots	\ldots	INTJ
bracis-19038	230	19	,	,	PUNCT
bracis-19038	230	20	e_n'\right\	e_n'\right\	ADV
bracis-19038	230	21	}	}	PUNCT
bracis-19038	230	22	\	\	NOUN
bracis-19038	230	23	)	)	PUNCT
bracis-19038	230	24	can	can	AUX
bracis-19038	230	25	be	be	AUX
bracis-19038	230	26	represented	represent	VERB
bracis-19038	230	27	in	in	ADP
bracis-19038	230	28	\((p	\((p	NOUN
bracis-19038	230	29	,	,	PUNCT
bracis-19038	230	30	\varphi	\varphi	PROPN
bracis-19038	230	31	)	)	PUNCT
bracis-19038	230	32	\	\	NOUN
bracis-19038	230	33	)	)	PUNCT
bracis-19038	230	34	by	by	ADP
bracis-19038	230	35	including	include	VERB
bracis-19038	230	36	in	in	ADP
bracis-19038	230	37	\(\varphi	\(\varphi	PROPN
bracis-19038	230	38	\	\	NOUN
bracis-19038	230	39	)	)	PUNCT
bracis-19038	230	40	the	the	DET
bracis-19038	230	41	conjunctive	conjunctive	ADJ
bracis-19038	230	42	preference	preference	NOUN
bracis-19038	230	43	\(\left\	\(\left\	PROPN
bracis-19038	230	44	{	{	PUNCT
bracis-19038	230	45	e_1	e_1	NOUN
bracis-19038	230	46	,	,	PUNCT
bracis-19038	230	47	\ldots	\ldots	INTJ
bracis-19038	230	48	,	,	PUNCT
bracis-19038	230	49	e_m\right\	e_m\right\	VERB
bracis-19038	230	50	}	}	PUNCT
bracis-19038	230	51	\preceq	\preceq	PROPN
bracis-19038	230	52	\left\	\left\	PROPN
bracis-19038	230	53	{	{	PUNCT
bracis-19038	230	54	e_1	e_1	VERB
bracis-19038	230	55	'	'	PROPN
bracis-19038	230	56	,	,	PUNCT
bracis-19038	230	57	\ldots	\ldots	INTJ
bracis-19038	230	58	,	,	PUNCT
bracis-19038	230	59	e_n'\right\	e_n'\right\	ADV
bracis-19038	230	60	}	}	PUNCT
bracis-19038	230	61	\	\	NOUN
bracis-19038	230	62	)	)	PUNCT
bracis-19038	230	63	and	and	CCONJ
bracis-19038	230	64	the	the	DET
bracis-19038	230	65	preferences	preference	NOUN
bracis-19038	230	66	\(\left\	\(\left\	INTJ
bracis-19038	230	67	{	{	PUNCT
bracis-19038	230	68	\mathtt	\mathtt	PROPN
bracis-19038	230	69	{	{	PUNCT
bracis-19038	230	70	not\	not\	PROPN
bracis-19038	230	71	}	}	PUNCT
bracis-19038	230	72	e_j'\right\	e_j'\right\	ADJ
bracis-19038	230	73	}	}	PUNCT
bracis-19038	230	74	\preceq	\preceq	PROPN
bracis-19038	230	75	\left\	\left\	PROPN
bracis-19038	230	76	{	{	PUNCT
bracis-19038	230	77	\mathtt	\mathtt	PROPN
bracis-19038	230	78	{	{	PUNCT
bracis-19038	230	79	not\	not\	PROPN
bracis-19038	230	80	}	}	PUNCT
bracis-19038	230	81	e_i\right\	e_i\right\	ADJ
bracis-19038	230	82	}	}	PUNCT
bracis-19038	230	83	\	\	NOUN
bracis-19038	230	84	)	)	PUNCT
bracis-19038	230	85	with	with	ADP
bracis-19038	230	86	\(1	\(1	PROPN
bracis-19038	230	87	\le	\le	PROPN
bracis-19038	230	88	i	i	NOUN
bracis-19038	230	89	\le	\le	NOUN
bracis-19038	230	90	m\	m\	NOUN
bracis-19038	230	91	)	)	PUNCT
bracis-19038	230	92	and	and	CCONJ
bracis-19038	230	93	\(1	\(1	PROPN
bracis-19038	230	94	\le	\le	PROPN
bracis-19038	230	95	j	j	PROPN
bracis-19038	230	96	\le	\le	PROPN
bracis-19038	230	97	n\	n\	PROPN
bracis-19038	230	98	)	)	PUNCT
bracis-19038	230	99	.	.	PUNCT
bracis-19038	231	1	before	before	ADP
bracis-19038	231	2	moving	move	VERB
bracis-19038	231	3	to	to	ADP
bracis-19038	231	4	the	the	DET
bracis-19038	231	5	next	next	ADJ
bracis-19038	231	6	section	section	NOUN
bracis-19038	231	7	,	,	PUNCT
bracis-19038	231	8	we	we	PRON
bracis-19038	231	9	will	will	AUX
bracis-19038	231	10	emphasise	emphasise	VERB
bracis-19038	231	11	our	our	PRON
bracis-19038	231	12	decision	decision	NOUN
bracis-19038	231	13	of	of	ADP
bracis-19038	231	14	employing	employ	VERB
bracis-19038	231	15	a	a	DET
bracis-19038	231	16	representation	representation	NOUN
bracis-19038	231	17	language	language	NOUN
bracis-19038	231	18	to	to	PART
bracis-19038	231	19	express	express	VERB
bracis-19038	231	20	priorities	priority	NOUN
bracis-19038	231	21	between	between	ADP
bracis-19038	231	22	sets	set	NOUN
bracis-19038	231	23	of	of	ADP
bracis-19038	231	24	literals	literal	NOUN
bracis-19038	231	25	instead	instead	ADV
bracis-19038	231	26	of	of	ADP
bracis-19038	231	27	a	a	DET
bracis-19038	231	28	language	language	NOUN
bracis-19038	231	29	to	to	PART
bracis-19038	231	30	express	express	VERB
bracis-19038	231	31	priorities	priority	NOUN
bracis-19038	231	32	only	only	ADV
bracis-19038	231	33	between	between	ADP
bracis-19038	231	34	literals	literal	NOUN
bracis-19038	231	35	as	as	ADP
bracis-19038	231	36	in	in	ADP
bracis-19038	231	37	[	[	X
bracis-19038	231	38	4	4	NUM
bracis-19038	231	39	]	]	PUNCT
bracis-19038	231	40	.	.	PUNCT
bracis-19038	232	1	although	although	SCONJ
bracis-19038	232	2	the	the	DET
bracis-19038	232	3	approach	approach	NOUN
bracis-19038	232	4	of	of	ADP
bracis-19038	232	5	[	[	X
bracis-19038	232	6	4	4	X
bracis-19038	232	7	]	]	PUNCT
bracis-19038	232	8	suffices	suffice	VERB
bracis-19038	232	9	to	to	PART
bracis-19038	232	10	express	express	VERB
bracis-19038	232	11	in	in	ADP
bracis-19038	232	12	a	a	DET
bracis-19038	232	13	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	232	14	)	)	PUNCT
bracis-19038	232	15	\((p	\((p	NOUN
bracis-19038	232	16	,	,	PUNCT
bracis-19038	232	17	\varphi	\varphi	PROPN
bracis-19038	232	18	)	)	PUNCT
bracis-19038	232	19	\	\	NOUN
bracis-19038	232	20	)	)	PUNCT
bracis-19038	232	21	the	the	DET
bracis-19038	232	22	complex	complex	ADJ
bracis-19038	232	23	forms	form	NOUN
bracis-19038	232	24	of	of	ADP
bracis-19038	232	25	preferences	preference	NOUN
bracis-19038	232	26	showed	show	VERB
bracis-19038	232	27	in	in	ADP
bracis-19038	232	28	this	this	DET
bracis-19038	232	29	section	section	NOUN
bracis-19038	232	30	,	,	PUNCT
bracis-19038	232	31	there	there	PRON
bracis-19038	232	32	is	be	VERB
bracis-19038	232	33	a	a	DET
bracis-19038	232	34	price	price	NOUN
bracis-19038	232	35	to	to	PART
bracis-19038	232	36	pay	pay	VERB
bracis-19038	232	37	:	:	PUNCT
bracis-19038	232	38	the	the	DET
bracis-19038	232	39	program	program	NOUN
bracis-19038	232	40	p	p	NOUN
bracis-19038	232	41	should	should	AUX
bracis-19038	232	42	be	be	AUX
bracis-19038	232	43	changed	change	VERB
bracis-19038	232	44	with	with	ADP
bracis-19038	232	45	the	the	DET
bracis-19038	232	46	introduction	introduction	NOUN
bracis-19038	232	47	of	of	ADP
bracis-19038	232	48	new	new	ADJ
bracis-19038	232	49	atoms	atom	NOUN
bracis-19038	232	50	as	as	ADV
bracis-19038	232	51	well	well	ADV
bracis-19038	232	52	as	as	ADP
bracis-19038	232	53	the	the	DET
bracis-19038	232	54	set	set	NOUN
bracis-19038	232	55	\(\varphi	\(\varphi	NOUN
bracis-19038	232	56	\	\	NOUN
bracis-19038	232	57	)	)	PUNCT
bracis-19038	232	58	of	of	ADP
bracis-19038	232	59	priorities	priority	NOUN
bracis-19038	232	60	.	.	PUNCT
bracis-19038	233	1	in	in	ADP
bracis-19038	233	2	our	our	PRON
bracis-19038	233	3	approach	approach	NOUN
bracis-19038	233	4	,	,	PUNCT
bracis-19038	233	5	as	as	SCONJ
bracis-19038	233	6	the	the	DET
bracis-19038	233	7	priority	priority	NOUN
bracis-19038	233	8	relation	relation	NOUN
bracis-19038	233	9	is	be	AUX
bracis-19038	233	10	given	give	VERB
bracis-19038	233	11	in	in	ADP
bracis-19038	233	12	term	term	NOUN
bracis-19038	233	13	of	of	ADP
bracis-19038	233	14	sets	set	NOUN
bracis-19038	233	15	of	of	ADP
bracis-19038	233	16	literals	literal	NOUN
bracis-19038	233	17	,	,	PUNCT
bracis-19038	233	18	we	we	PRON
bracis-19038	233	19	neither	neither	CCONJ
bracis-19038	233	20	need	need	VERB
bracis-19038	233	21	to	to	PART
bracis-19038	233	22	change	change	VERB
bracis-19038	233	23	the	the	DET
bracis-19038	233	24	program	program	NOUN
bracis-19038	233	25	p	p	NOUN
bracis-19038	233	26	nor	nor	CCONJ
bracis-19038	233	27	to	to	PART
bracis-19038	233	28	add	add	VERB
bracis-19038	233	29	new	new	ADJ
bracis-19038	233	30	artificial	artificial	ADJ
bracis-19038	233	31	atoms	atom	NOUN
bracis-19038	233	32	to	to	PART
bracis-19038	233	33	express	express	VERB
bracis-19038	233	34	priorities	priority	NOUN
bracis-19038	233	35	between	between	ADP
bracis-19038	233	36	conjunctive	conjunctive	ADJ
bracis-19038	233	37	knowledge	knowledge	NOUN
bracis-19038	233	38	,	,	PUNCT
bracis-19038	233	39	priorities	priority	NOUN
bracis-19038	233	40	between	between	ADP
bracis-19038	233	41	disjunctive	disjunctive	ADJ
bracis-19038	233	42	knowledge	knowledge	NOUN
bracis-19038	233	43	,	,	PUNCT
bracis-19038	233	44	conditional	conditional	ADJ
bracis-19038	233	45	priorities	priority	NOUN
bracis-19038	233	46	,	,	PUNCT
bracis-19038	233	47	priorities	priority	NOUN
bracis-19038	233	48	between	between	ADP
bracis-19038	233	49	rules	rule	NOUN
bracis-19038	233	50	and	and	CCONJ
bracis-19038	233	51	bipolar	bipolar	ADJ
bracis-19038	233	52	priorities	priority	NOUN
bracis-19038	233	53	.	.	PUNCT
bracis-19038	234	1	5	5	NUM
bracis-19038	234	2	results	result	NOUN
bracis-19038	234	3	now	now	ADV
bracis-19038	234	4	we	we	PRON
bracis-19038	234	5	will	will	AUX
bracis-19038	234	6	prove	prove	VERB
bracis-19038	234	7	some	some	DET
bracis-19038	234	8	properties	property	NOUN
bracis-19038	234	9	found	find	VERB
bracis-19038	234	10	in	in	ADP
bracis-19038	234	11	our	our	PRON
bracis-19038	234	12	proposal	proposal	NOUN
bracis-19038	234	13	.	.	PUNCT
bracis-19038	235	1	the	the	DET
bracis-19038	235	2	main	main	ADJ
bracis-19038	235	3	results	result	NOUN
bracis-19038	235	4	are	be	AUX
bracis-19038	235	5	both	both	CCONJ
bracis-19038	235	6	the	the	DET
bracis-19038	235	7	preference	preference	NOUN
bracis-19038	235	8	relations	relation	NOUN
bracis-19038	235	9	\(\subseteq	\(\subseteq	PROPN
bracis-19038	235	10	^y_x\	^y_x\	NUM
bracis-19038	235	11	)	)	PUNCT
bracis-19038	235	12	and	and	CCONJ
bracis-19038	235	13	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	235	14	^y_x\	^y_x\	NUM
bracis-19038	235	15	)	)	PUNCT
bracis-19038	235	16	are	be	AUX
bracis-19038	235	17	consistent	consistent	ADJ
bracis-19038	235	18	(	(	PUNCT
bracis-19038	235	19	proposition	proposition	NOUN
bracis-19038	235	20	1	1	NUM
bracis-19038	235	21	)	)	PUNCT
bracis-19038	235	22	and	and	CCONJ
bracis-19038	235	23	have	have	VERB
bracis-19038	235	24	neither	neither	CCONJ
bracis-19038	235	25	a	a	DET
bracis-19038	235	26	monotonic	monotonic	ADJ
bracis-19038	235	27	nor	nor	CCONJ
bracis-19038	235	28	an	an	DET
bracis-19038	235	29	antitonic	antitonic	ADJ
bracis-19038	235	30	behaviour	behaviour	NOUN
bracis-19038	235	31	w.r.t	w.r.t	VERB
bracis-19038	235	32	.	.	PUNCT
bracis-19038	236	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	236	2	\	\	NUM
bracis-19038	236	3	)	)	PUNCT
bracis-19038	236	4	(	(	PUNCT
bracis-19038	236	5	theorem	theorem	NOUN
bracis-19038	236	6	3	3	NUM
bracis-19038	236	7	)	)	PUNCT
bracis-19038	236	8	;	;	PUNCT
bracis-19038	236	9	proposition	proposition	NOUN
bracis-19038	236	10	2	2	NUM
bracis-19038	236	11	and	and	CCONJ
bracis-19038	236	12	theorem	theorem	VERB
bracis-19038	236	13	1	1	NUM
bracis-19038	236	14	establish	establish	VERB
bracis-19038	236	15	conditions	condition	NOUN
bracis-19038	236	16	under	under	ADP
bracis-19038	236	17	which	which	PRON
bracis-19038	236	18	the	the	DET
bracis-19038	236	19	relations	relation	NOUN
bracis-19038	236	20	of	of	ADP
bracis-19038	236	21	preference	preference	NOUN
bracis-19038	236	22	are	be	AUX
bracis-19038	236	23	simplified	simplify	VERB
bracis-19038	236	24	;	;	PUNCT
bracis-19038	236	25	when	when	SCONJ
bracis-19038	236	26	no	no	DET
bracis-19038	236	27	priority	priority	NOUN
bracis-19038	236	28	is	be	AUX
bracis-19038	236	29	available	available	ADJ
bracis-19038	236	30	,	,	PUNCT
bracis-19038	236	31	prioritised	prioritise	VERB
bracis-19038	236	32	logic	logic	NOUN
bracis-19038	236	33	programs	program	NOUN
bracis-19038	236	34	and	and	CCONJ
bracis-19038	236	35	normal	normal	ADJ
bracis-19038	236	36	logic	logic	NOUN
bracis-19038	236	37	programs	program	NOUN
bracis-19038	236	38	have	have	VERB
bracis-19038	236	39	the	the	DET
bracis-19038	236	40	same	same	ADJ
bracis-19038	236	41	semantics	semantic	NOUN
bracis-19038	236	42	(	(	PUNCT
bracis-19038	236	43	theorem	theorem	NOUN
bracis-19038	236	44	2	2	NUM
bracis-19038	236	45	)	)	PUNCT
bracis-19038	236	46	and	and	CCONJ
bracis-19038	236	47	inconsistent	inconsistent	ADJ
bracis-19038	236	48	options	option	NOUN
bracis-19038	236	49	are	be	AUX
bracis-19038	236	50	useless	useless	ADJ
bracis-19038	236	51	(	(	PUNCT
bracis-19038	236	52	theorem	theorem	NOUN
bracis-19038	236	53	4	4	NUM
bracis-19038	236	54	)	)	PUNCT
bracis-19038	236	55	.	.	PUNCT
bracis-19038	237	1	next	next	ADV
bracis-19038	237	2	we	we	PRON
bracis-19038	237	3	define	define	VERB
bracis-19038	237	4	the	the	DET
bracis-19038	237	5	notion	notion	NOUN
bracis-19038	237	6	of	of	ADP
bracis-19038	237	7	cyclic	cyclic	ADJ
bracis-19038	237	8	relation	relation	NOUN
bracis-19038	237	9	:	:	PUNCT
bracis-19038	237	10	definition	definition	NOUN
bracis-19038	237	11	13	13	NUM
bracis-19038	237	12	(	(	PUNCT
bracis-19038	237	13	cyclic	cyclic	NOUN
bracis-19038	237	14	relation	relation	NOUN
bracis-19038	237	15	)	)	PUNCT
bracis-19038	237	16	a	a	DET
bracis-19038	237	17	relation	relation	NOUN
bracis-19038	237	18	\(\sqsubseteq	\(\sqsubseteq	NOUN
bracis-19038	237	19	\	\	NOUN
bracis-19038	237	20	)	)	PUNCT
bracis-19038	237	21	is	be	AUX
bracis-19038	237	22	cyclic	cyclic	ADJ
bracis-19038	237	23	if	if	SCONJ
bracis-19038	237	24	and	and	CCONJ
bracis-19038	237	25	only	only	ADV
bracis-19038	237	26	if	if	SCONJ
bracis-19038	237	27	its	its	PRON
bracis-19038	237	28	induced	induced	ADJ
bracis-19038	237	29	strict	strict	ADJ
bracis-19038	237	30	preference	preference	NOUN
bracis-19038	237	31	relation	relation	NOUN
bracis-19038	237	32	is	be	AUX
bracis-19038	237	33	cyclic	cyclic	ADJ
bracis-19038	237	34	,	,	PUNCT
bracis-19038	237	35	i.e.	i.e.	X
bracis-19038	237	36	,	,	PUNCT
bracis-19038	237	37	there	there	PRON
bracis-19038	237	38	exists	exist	VERB
bracis-19038	237	39	a	a	DET
bracis-19038	237	40	chain	chain	NOUN
bracis-19038	237	41	\(\mathcal	\(\mathcal	ADJ
bracis-19038	237	42	o	o	NOUN
bracis-19038	237	43	\ldots	\ldots	ADP
bracis-19038	237	44	\mathcal	\mathcal	PROPN
bracis-19038	237	45	o'\	o'\	PROPN
bracis-19038	237	46	)	)	PUNCT
bracis-19038	237	47	such	such	ADJ
bracis-19038	237	48	that	that	SCONJ
bracis-19038	237	49	\(\mathcal	\(\mathcal	ADJ
bracis-19038	237	50	o	o	X
bracis-19038	237	51	\sqsubset	\sqsubset	PROPN
bracis-19038	237	52	\mathcal	\mathcal	PROPN
bracis-19038	237	53	o	o	NOUN
bracis-19038	237	54	'	'	PUNCT
bracis-19038	237	55	\sqsubset	\sqsubset	PROPN
bracis-19038	237	56	\cdots	\cdots	PROPN
bracis-19038	237	57	\sqsubset	\sqsubset	PROPN
bracis-19038	237	58	\mathcal	\mathcal	PROPN
bracis-19038	237	59	o\	o\	PROPN
bracis-19038	237	60	)	)	PUNCT
bracis-19038	237	61	.	.	PUNCT
bracis-19038	238	1	otherwise	otherwise	ADV
bracis-19038	238	2	\(\sqsubseteq	\(\sqsubseteq	VERB
bracis-19038	238	3	\	\	NOUN
bracis-19038	238	4	)	)	PUNCT
bracis-19038	238	5	is	be	AUX
bracis-19038	238	6	acyclic	acyclic	ADJ
bracis-19038	238	7	.	.	PUNCT
bracis-19038	239	1	if	if	SCONJ
bracis-19038	239	2	either	either	PRON
bracis-19038	239	3	\(\subseteq	\(\subseteq	PROPN
bracis-19038	239	4	^y_x\	^y_x\	NUM
bracis-19038	239	5	)	)	PUNCT
bracis-19038	239	6	or	or	CCONJ
bracis-19038	239	7	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	239	8	^y_x\	^y_x\	NUM
bracis-19038	239	9	)	)	PUNCT
bracis-19038	239	10	were	be	AUX
bracis-19038	239	11	cyclic	cyclic	ADJ
bracis-19038	239	12	,	,	PUNCT
bracis-19038	239	13	the	the	DET
bracis-19038	239	14	resulting	result	VERB
bracis-19038	239	15	preference	preference	NOUN
bracis-19038	239	16	relation	relation	NOUN
bracis-19038	239	17	would	would	AUX
bracis-19038	239	18	be	be	AUX
bracis-19038	239	19	inconsistent	inconsistent	ADJ
bracis-19038	239	20	.	.	PUNCT
bracis-19038	240	1	in	in	ADP
bracis-19038	240	2	particular	particular	ADJ
bracis-19038	240	3	,	,	PUNCT
bracis-19038	240	4	we	we	PRON
bracis-19038	240	5	would	would	AUX
bracis-19038	240	6	find	find	VERB
bracis-19038	240	7	\(\textit{plp}\)s	\(\textit{plp}\)s	NOUN
bracis-19038	240	8	without	without	ADP
bracis-19038	240	9	preferred	preferred	ADJ
bracis-19038	240	10	partial	partial	ADJ
bracis-19038	240	11	stable	stable	ADJ
bracis-19038	240	12	models	model	NOUN
bracis-19038	240	13	at	at	ADV
bracis-19038	240	14	all	all	ADV
bracis-19038	240	15	.	.	PUNCT
bracis-19038	241	1	for	for	ADP
bracis-19038	241	2	instance	instance	NOUN
bracis-19038	241	3	,	,	PUNCT
bracis-19038	241	4	suppose	suppose	VERB
bracis-19038	241	5	an	an	DET
bracis-19038	241	6	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	241	7	)	)	PUNCT
bracis-19038	241	8	whose	whose	DET
bracis-19038	241	9	partial	partial	ADJ
bracis-19038	241	10	stable	stable	ADJ
bracis-19038	241	11	models	model	NOUN
bracis-19038	241	12	are	be	AUX
bracis-19038	241	13	\(m_1\	\(m_1\	PROPN
bracis-19038	241	14	)	)	PUNCT
bracis-19038	241	15	,	,	PUNCT
bracis-19038	241	16	\(m_2\	\(m_2\	PROPN
bracis-19038	241	17	)	)	PUNCT
bracis-19038	241	18	and	and	CCONJ
bracis-19038	241	19	\(m_3\	\(m_3\	PROPN
bracis-19038	241	20	)	)	PUNCT
bracis-19038	241	21	such	such	ADJ
bracis-19038	241	22	that	that	SCONJ
bracis-19038	241	23	\(m_1	\(m_1	PROPN
bracis-19038	241	24	\subset	\subset	PROPN
bracis-19038	241	25	^y_x	^y_x	NUM
bracis-19038	241	26	m_2\	m_2\	NUM
bracis-19038	241	27	)	)	PUNCT
bracis-19038	241	28	,	,	PUNCT
bracis-19038	241	29	\(m_2	\(m_2	PROPN
bracis-19038	241	30	\subset	\subset	PROPN
bracis-19038	241	31	^y_x	^y_x	NUM
bracis-19038	241	32	m_3\	m_3\	NOUN
bracis-19038	241	33	)	)	PUNCT
bracis-19038	241	34	and	and	CCONJ
bracis-19038	241	35	\(m_3	\(m_3	PROPN
bracis-19038	241	36	\subset	\subset	PROPN
bracis-19038	241	37	^y_x	^y_x	PRON
bracis-19038	241	38	m_1\	m_1\	PROPN
bracis-19038	241	39	)	)	PUNCT
bracis-19038	241	40	.	.	PUNCT
bracis-19038	242	1	clearly	clearly	ADV
bracis-19038	242	2	the	the	DET
bracis-19038	242	3	resulting	result	VERB
bracis-19038	242	4	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	242	5	)	)	PUNCT
bracis-19038	242	6	would	would	AUX
bracis-19038	242	7	not	not	PART
bracis-19038	242	8	have	have	VERB
bracis-19038	242	9	any	any	DET
bracis-19038	242	10	preferred	prefer	VERB
bracis-19038	242	11	partial	partial	ADJ
bracis-19038	242	12	stable	stable	ADJ
bracis-19038	242	13	model	model	NOUN
bracis-19038	242	14	.	.	PUNCT
bracis-19038	243	1	fortunately	fortunately	ADV
bracis-19038	243	2	,	,	PUNCT
bracis-19038	243	3	both	both	PRON
bracis-19038	243	4	\(\subseteq	\(\subseteq	PROPN
bracis-19038	243	5	^y_x\	^y_x\	NUM
bracis-19038	243	6	)	)	PUNCT
bracis-19038	243	7	and	and	CCONJ
bracis-19038	243	8	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	243	9	^y_x\	^y_x\	NUM
bracis-19038	243	10	)	)	PUNCT
bracis-19038	243	11	are	be	AUX
bracis-19038	243	12	acyclic	acyclic	ADJ
bracis-19038	243	13	:	:	PUNCT
bracis-19038	243	14	proposition	proposition	NOUN
bracis-19038	243	15	1	1	NUM
bracis-19038	243	16	for	for	ADP
bracis-19038	243	17	any	any	DET
bracis-19038	243	18	\(x	\(x	ADJ
bracis-19038	243	19	\in	\in	PROPN
bracis-19038	243	20	\left\	\left\	PROPN
bracis-19038	243	21	{	{	PUNCT
bracis-19038	243	22	st	st	PROPN
bracis-19038	243	23	,	,	PUNCT
bracis-19038	243	24	opt	opt	NOUN
bracis-19038	243	25	,	,	PUNCT
bracis-19038	243	26	pes	pe	NOUN
bracis-19038	243	27	,	,	PUNCT
bracis-19038	243	28	opp	opp	PROPN
bracis-19038	243	29	\right\	\right\	ADV
bracis-19038	243	30	}	}	PUNCT
bracis-19038	243	31	\	\	NOUN
bracis-19038	243	32	)	)	PUNCT
bracis-19038	243	33	and	and	CCONJ
bracis-19038	243	34	any	any	DET
bracis-19038	243	35	\(y	\(y	PROPN
bracis-19038	243	36	\in	\in	PROPN
bracis-19038	243	37	\left\	\left\	PROPN
bracis-19038	243	38	{	{	PUNCT
bracis-19038	243	39	\forall	\forall	INTJ
bracis-19038	243	40	\forall	\forall	INTJ
bracis-19038	243	41	,	,	PUNCT
bracis-19038	243	42	\forall	\forall	DET
bracis-19038	243	43	\exists	\exist	NOUN
bracis-19038	243	44	,	,	PUNCT
bracis-19038	243	45	\exists	\exist	NOUN
bracis-19038	243	46	\forall	\forall	ADV
bracis-19038	243	47	,	,	PUNCT
bracis-19038	243	48	\exists	\exist	NOUN
bracis-19038	243	49	\exists	\exist	NOUN
bracis-19038	243	50	\right\	\right\	ADV
bracis-19038	243	51	}	}	PUNCT
bracis-19038	243	52	\	\	NOUN
bracis-19038	243	53	)	)	PUNCT
bracis-19038	243	54	,	,	PUNCT
bracis-19038	243	55	both	both	CCONJ
bracis-19038	243	56	the	the	DET
bracis-19038	243	57	preference	preference	NOUN
bracis-19038	243	58	relations	relation	NOUN
bracis-19038	243	59	\(\subseteq	\(\subseteq	PROPN
bracis-19038	243	60	^y_x\	^y_x\	NUM
bracis-19038	243	61	)	)	PUNCT
bracis-19038	243	62	and	and	CCONJ
bracis-19038	243	63	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	243	64	^y_x\	^y_x\	NUM
bracis-19038	243	65	)	)	PUNCT
bracis-19038	244	1	are	be	AUX
bracis-19038	244	2	acyclic	acyclic	ADJ
bracis-19038	244	3	.	.	PUNCT
bracis-19038	245	1	proof	proof	NOUN
bracis-19038	245	2	by	by	ADP
bracis-19038	245	3	absurd	absurd	ADJ
bracis-19038	245	4	,	,	PUNCT
bracis-19038	245	5	suppose	suppose	VERB
bracis-19038	245	6	\(\subseteq	\(\subseteq	PROPN
bracis-19038	245	7	^y_x\	^y_x\	NUM
bracis-19038	245	8	)	)	PUNCT
bracis-19038	245	9	is	be	AUX
bracis-19038	245	10	cyclic	cyclic	ADJ
bracis-19038	245	11	.	.	PUNCT
bracis-19038	246	1	this	this	PRON
bracis-19038	246	2	means	mean	VERB
bracis-19038	246	3	there	there	PRON
bracis-19038	246	4	exists	exist	VERB
bracis-19038	246	5	a	a	DET
bracis-19038	246	6	chain	chain	NOUN
bracis-19038	247	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	247	2	o	o	NOUN
bracis-19038	247	3	\ldots	\ldots	ADP
bracis-19038	247	4	\mathcal	\mathcal	PROPN
bracis-19038	247	5	o'\	o'\	PROPN
bracis-19038	247	6	)	)	PUNCT
bracis-19038	247	7	such	such	ADJ
bracis-19038	247	8	that	that	SCONJ
bracis-19038	247	9	\(\mathcal	\(\mathcal	ADJ
bracis-19038	247	10	o	o	X
bracis-19038	247	11	\subset	\subset	PROPN
bracis-19038	247	12	^y_x	^y_x	VERB
bracis-19038	247	13	\mathcal	\mathcal	PROPN
bracis-19038	247	14	o	o	NOUN
bracis-19038	247	15	'	'	PUNCT
bracis-19038	247	16	\subset	\subset	PROPN
bracis-19038	247	17	^y_x	^y_x	NUM
bracis-19038	247	18	\cdots	\cdots	PROPN
bracis-19038	247	19	\subset	\subset	PROPN
bracis-19038	247	20	^y_x	^y_x	NUM
bracis-19038	247	21	\mathcal	\mathcal	PROPN
bracis-19038	247	22	o\	o\	PROPN
bracis-19038	247	23	)	)	PUNCT
bracis-19038	247	24	.	.	PUNCT
bracis-19038	248	1	as	as	ADP
bracis-19038	248	2	\(\subseteq	\(\subseteq	PROPN
bracis-19038	248	3	^y_x\	^y_x\	NUM
bracis-19038	248	4	)	)	PUNCT
bracis-19038	248	5	is	be	AUX
bracis-19038	248	6	reflexive	reflexive	ADJ
bracis-19038	248	7	(	(	PUNCT
bracis-19038	248	8	definition	definition	NOUN
bracis-19038	248	9	10	10	NUM
bracis-19038	248	10	)	)	PUNCT
bracis-19038	248	11	,	,	PUNCT
bracis-19038	248	12	it	it	PRON
bracis-19038	248	13	holds	hold	VERB
bracis-19038	248	14	\(\mathcal	\(\mathcal	ADJ
bracis-19038	248	15	o	o	NOUN
bracis-19038	248	16	\not	\not	ADV
bracis-19038	248	17	\subset	\subset	PROPN
bracis-19038	248	18	^y_x	^y_x	PRON
bracis-19038	248	19	\mathcal	\mathcal	PROPN
bracis-19038	248	20	o\	o\	PROPN
bracis-19038	248	21	)	)	PUNCT
bracis-19038	248	22	.	.	PUNCT
bracis-19038	249	1	besides	besides	SCONJ
bracis-19038	249	2	,	,	PUNCT
bracis-19038	249	3	by	by	ADP
bracis-19038	249	4	transitivity	transitivity	NOUN
bracis-19038	249	5	,	,	PUNCT
bracis-19038	249	6	we	we	PRON
bracis-19038	249	7	obtain	obtain	VERB
bracis-19038	249	8	\(\mathcal	\(\mathcal	ADJ
bracis-19038	249	9	o	o	NOUN
bracis-19038	249	10	'	'	PUNCT
bracis-19038	249	11	\subseteq	\subseteq	PROPN
bracis-19038	249	12	^y_x	^y_x	NOUN
bracis-19038	249	13	\mathcal	\mathcal	PROPN
bracis-19038	249	14	o\	o\	PROPN
bracis-19038	249	15	)	)	PUNCT
bracis-19038	249	16	.	.	PUNCT
bracis-19038	250	1	it	it	PRON
bracis-19038	250	2	is	be	AUX
bracis-19038	250	3	an	an	DET
bracis-19038	250	4	absurd	absurd	ADJ
bracis-19038	250	5	as	as	ADP
bracis-19038	250	6	\(\mathcal	\(\mathcal	ADJ
bracis-19038	250	7	o	o	X
bracis-19038	250	8	\subset	\subset	PROPN
bracis-19038	250	9	^y_x	^y_x	PRON
bracis-19038	250	10	\mathcal	\mathcal	PROPN
bracis-19038	250	11	o'\	o'\	PROPN
bracis-19038	250	12	)	)	PUNCT
bracis-19038	250	13	.	.	PUNCT
bracis-19038	251	1	the	the	DET
bracis-19038	251	2	proof	proof	NOUN
bracis-19038	251	3	for	for	ADP
bracis-19038	251	4	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	251	5	^y_x\	^y_x\	NUM
bracis-19038	251	6	)	)	PUNCT
bracis-19038	251	7	is	be	AUX
bracis-19038	251	8	similar	similar	ADJ
bracis-19038	251	9	.	.	PUNCT
bracis-19038	252	1	notice	notice	NOUN
bracis-19038	252	2	in	in	ADP
bracis-19038	252	3	this	this	DET
bracis-19038	252	4	last	last	ADJ
bracis-19038	252	5	result	result	NOUN
bracis-19038	252	6	the	the	DET
bracis-19038	252	7	importance	importance	NOUN
bracis-19038	252	8	of	of	ADP
bracis-19038	252	9	imposing	impose	VERB
bracis-19038	252	10	reflexivity	reflexivity	NOUN
bracis-19038	252	11	and	and	CCONJ
bracis-19038	252	12	transitivity	transitivity	NOUN
bracis-19038	252	13	in	in	ADP
bracis-19038	252	14	definition	definition	NOUN
bracis-19038	252	15	10	10	NUM
bracis-19038	252	16	to	to	PART
bracis-19038	252	17	ensure	ensure	VERB
bracis-19038	252	18	every	every	DET
bracis-19038	252	19	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	252	20	)	)	PUNCT
bracis-19038	252	21	will	will	AUX
bracis-19038	252	22	have	have	VERB
bracis-19038	252	23	at	at	ADV
bracis-19038	252	24	least	least	ADJ
bracis-19038	252	25	one	one	NUM
bracis-19038	252	26	preferable	preferable	ADJ
bracis-19038	252	27	\	\	NOUN
bracis-19038	252	28	(	(	PUNCT
bracis-19038	252	29	ps	ps	NOUN
bracis-19038	252	30	\	\	ADJ
bracis-19038	252	31	)	)	PUNCT
bracis-19038	252	32	model	model	NOUN
bracis-19038	252	33	.	.	PUNCT
bracis-19038	253	1	now	now	ADV
bracis-19038	253	2	we	we	PRON
bracis-19038	253	3	will	will	AUX
bracis-19038	253	4	show	show	VERB
bracis-19038	253	5	when	when	SCONJ
bracis-19038	253	6	the	the	DET
bracis-19038	253	7	best	well	ADV
bracis-19038	253	8	-	-	PUNCT
bracis-19038	253	9	ranked	rank	VERB
bracis-19038	253	10	options	option	NOUN
bracis-19038	253	11	of	of	ADP
bracis-19038	253	12	the	the	DET
bracis-19038	253	13	\	\	PROPN
bracis-19038	253	14	(	(	PUNCT
bracis-19038	253	15	ps	ps	PROPN
bracis-19038	253	16	\	\	ADJ
bracis-19038	253	17	)	)	PUNCT
bracis-19038	253	18	models	model	NOUN
bracis-19038	253	19	have	have	VERB
bracis-19038	253	20	the	the	DET
bracis-19038	253	21	same	same	ADJ
bracis-19038	253	22	priority	priority	NOUN
bracis-19038	253	23	and	and	CCONJ
bracis-19038	253	24	the	the	DET
bracis-19038	253	25	worst	worst	ADV
bracis-19038	253	26	-	-	PUNCT
bracis-19038	253	27	ranked	rank	VERB
bracis-19038	253	28	options	option	NOUN
bracis-19038	253	29	of	of	ADP
bracis-19038	253	30	the	the	DET
bracis-19038	253	31	\	\	PROPN
bracis-19038	253	32	(	(	PUNCT
bracis-19038	253	33	ps	ps	PROPN
bracis-19038	253	34	\	\	ADJ
bracis-19038	253	35	)	)	PUNCT
bracis-19038	253	36	models	model	NOUN
bracis-19038	253	37	have	have	VERB
bracis-19038	253	38	the	the	DET
bracis-19038	253	39	same	same	ADJ
bracis-19038	253	40	priority	priority	NOUN
bracis-19038	253	41	,	,	PUNCT
bracis-19038	253	42	the	the	DET
bracis-19038	253	43	relations	relation	NOUN
bracis-19038	253	44	of	of	ADP
bracis-19038	253	45	preference	preference	NOUN
bracis-19038	253	46	are	be	AUX
bracis-19038	253	47	simplified	simplify	VERB
bracis-19038	253	48	:	:	PUNCT
bracis-19038	253	49	proposition	proposition	NOUN
bracis-19038	253	50	2	2	NUM
bracis-19038	253	51	let	let	VERB
bracis-19038	253	52	\((p	\((p	NOUN
bracis-19038	253	53	,	,	PUNCT
bracis-19038	253	54	\varphi	\varphi	PROPN
bracis-19038	253	55	)	)	PUNCT
bracis-19038	253	56	\	\	NOUN
bracis-19038	253	57	)	)	PUNCT
bracis-19038	253	58	be	be	AUX
bracis-19038	253	59	a	a	DET
bracis-19038	253	60	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	253	61	)	)	PUNCT
bracis-19038	253	62	,	,	PUNCT
bracis-19038	253	63	\(i_1\	\(i_1\	PROPN
bracis-19038	253	64	)	)	PUNCT
bracis-19038	253	65	and	and	CCONJ
bracis-19038	253	66	\(i_2\	\(i_2\	PROPN
bracis-19038	253	67	)	)	PUNCT
bracis-19038	253	68	be	be	VERB
bracis-19038	253	69	subsets	subset	NOUN
bracis-19038	253	70	of	of	ADP
bracis-19038	253	71	\	\	NOUN
bracis-19038	253	72	(	(	PUNCT
bracis-19038	253	73	lit	light	VERB
bracis-19038	253	74	_	_	PROPN
bracis-19038	253	75	p\	p\	NOUN
bracis-19038	253	76	)	)	PUNCT
bracis-19038	253	77	,	,	PUNCT
bracis-19038	253	78	\(\mathcal	\(\mathcal	ADJ
bracis-19038	253	79	b_1\	b_1\	NOUN
bracis-19038	253	80	)	)	PUNCT
bracis-19038	253	81	and	and	CCONJ
bracis-19038	253	82	\(\mathcal	\(\mathcal	ADJ
bracis-19038	253	83	b_2\	b_2\	PROPN
bracis-19038	253	84	)	)	PUNCT
bracis-19038	253	85	be	be	VERB
bracis-19038	253	86	respectively	respectively	ADV
bracis-19038	253	87	the	the	DET
bracis-19038	253	88	set	set	NOUN
bracis-19038	253	89	of	of	ADP
bracis-19038	253	90	best	well	ADV
bracis-19038	253	91	-	-	PUNCT
bracis-19038	253	92	ranked	rank	VERB
bracis-19038	253	93	options	option	NOUN
bracis-19038	253	94	in	in	ADP
bracis-19038	253	95	\(i_1\	\(i_1\	NOUN
bracis-19038	253	96	)	)	PUNCT
bracis-19038	253	97	and	and	CCONJ
bracis-19038	253	98	\(i_2\	\(i_2\	PROPN
bracis-19038	253	99	)	)	PUNCT
bracis-19038	253	100	w.r.t	w.r.t	NOUN
bracis-19038	253	101	.	.	PUNCT
bracis-19038	254	1	\(\varphi	\(\varphi	ADJ
bracis-19038	254	2	\	\	NOUN
bracis-19038	254	3	)	)	PUNCT
bracis-19038	254	4	,	,	PUNCT
bracis-19038	254	5	and	and	CCONJ
bracis-19038	254	6	\(\mathcal	\(\mathcal	ADJ
bracis-19038	254	7	w_1\	w_1\	PROPN
bracis-19038	254	8	)	)	PUNCT
bracis-19038	254	9	and	and	CCONJ
bracis-19038	254	10	\(\mathcal	\(\mathcal	ADJ
bracis-19038	254	11	w_2\	w_2\	PROPN
bracis-19038	254	12	)	)	PUNCT
bracis-19038	254	13	be	be	VERB
bracis-19038	254	14	respectively	respectively	ADV
bracis-19038	254	15	the	the	DET
bracis-19038	254	16	set	set	NOUN
bracis-19038	254	17	of	of	ADP
bracis-19038	254	18	worst	worst	ADV
bracis-19038	254	19	-	-	PUNCT
bracis-19038	254	20	ranked	rank	VERB
bracis-19038	254	21	options	option	NOUN
bracis-19038	254	22	in	in	ADP
bracis-19038	254	23	\(i_1\	\(i_1\	NOUN
bracis-19038	254	24	)	)	PUNCT
bracis-19038	254	25	and	and	CCONJ
bracis-19038	254	26	\(i_2\	\(i_2\	PROPN
bracis-19038	254	27	)	)	PUNCT
bracis-19038	254	28	w.r.t	w.r.t	NOUN
bracis-19038	254	29	.	.	PUNCT
bracis-19038	255	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	255	2	\	\	NOUN
bracis-19038	255	3	)	)	PUNCT
bracis-19038	255	4	.	.	PUNCT
bracis-19038	256	1	assume	assume	VERB
bracis-19038	256	2	for	for	ADP
bracis-19038	256	3	each	each	DET
bracis-19038	256	4	\(o_1\	\(o_1\	NOUN
bracis-19038	256	5	)	)	PUNCT
bracis-19038	256	6	and	and	CCONJ
bracis-19038	256	7	\(o_2\	\(o_2\	VERB
bracis-19038	256	8	)	)	PUNCT
bracis-19038	256	9	in	in	ADP
bracis-19038	256	10	\(\mathcal	\(\mathcal	ADJ
bracis-19038	256	11	b_i\	b_i\	NOUN
bracis-19038	256	12	)	)	PUNCT
bracis-19038	256	13	and	and	CCONJ
bracis-19038	256	14	for	for	ADP
bracis-19038	256	15	each	each	DET
bracis-19038	256	16	\(o_1'\	\(o_1'\	NOUN
bracis-19038	256	17	)	)	PUNCT
bracis-19038	256	18	and	and	CCONJ
bracis-19038	256	19	\(o_2'\	\(o_2'\	NOUN
bracis-19038	256	20	)	)	PUNCT
bracis-19038	256	21	in	in	ADP
bracis-19038	256	22	\(\mathcal	\(\mathcal	ADJ
bracis-19038	256	23	w_i\	w_i\	NOUN
bracis-19038	256	24	)	)	PUNCT
bracis-19038	256	25	with	with	ADP
bracis-19038	256	26	\(i	\(i	PROPN
bracis-19038	256	27	\in	\in	PROPN
bracis-19038	256	28	\left\	\left\	PROPN
bracis-19038	256	29	{	{	PUNCT
bracis-19038	256	30	1,2\right\	1,2\right\	NUM
bracis-19038	256	31	}	}	PUNCT
bracis-19038	256	32	\	\	NOUN
bracis-19038	256	33	)	)	PUNCT
bracis-19038	256	34	,	,	PUNCT
bracis-19038	256	35	it	it	PRON
bracis-19038	256	36	holds	hold	VERB
bracis-19038	256	37	\(o_1	\(o_1	PROPN
bracis-19038	256	38	\approx	\approx	PROPN
bracis-19038	256	39	o_2\	o_2\	PROPN
bracis-19038	256	40	)	)	PUNCT
bracis-19038	256	41	and	and	CCONJ
bracis-19038	256	42	\(o_1	\(o_1	PROPN
bracis-19038	256	43	'	'	PART
bracis-19038	256	44	\approx	\approx	PROPN
bracis-19038	256	45	o_2'\	o_2'\	NOUN
bracis-19038	256	46	)	)	PUNCT
bracis-19038	256	47	.	.	PUNCT
bracis-19038	257	1	consider	consider	VERB
bracis-19038	257	2	\(\mathcal	\(\mathcal	ADJ
bracis-19038	257	3	x	x	X
bracis-19038	257	4	=	=	PUNCT
bracis-19038	257	5	\mathcal	\mathcal	ADJ
bracis-19038	257	6	b_1\	b_1\	PROPN
bracis-19038	257	7	)	)	PUNCT
bracis-19038	257	8	if	if	SCONJ
bracis-19038	257	9	\(x	\(x	ADJ
bracis-19038	257	10	\in	\in	PROPN
bracis-19038	257	11	\	\	PROPN
bracis-19038	257	12	{	{	PUNCT
bracis-19038	257	13	st	st	PROPN
bracis-19038	257	14	,	,	PUNCT
bracis-19038	257	15	opt	opt	VERB
bracis-19038	257	16	\}\	\}\	NOUN
bracis-19038	257	17	)	)	PUNCT
bracis-19038	257	18	and	and	CCONJ
bracis-19038	257	19	\(\mathcal	\(\mathcal	ADJ
bracis-19038	257	20	x	x	X
bracis-19038	257	21	=	=	PUNCT
bracis-19038	257	22	\mathcal	\mathcal	PROPN
bracis-19038	257	23	w_1\	w_1\	PROPN
bracis-19038	257	24	)	)	PUNCT
bracis-19038	258	1	if	if	SCONJ
bracis-19038	258	2	\(x	\(x	ADJ
bracis-19038	258	3	\in	\in	PROPN
bracis-19038	258	4	\	\	PROPN
bracis-19038	258	5	{	{	PUNCT
bracis-19038	258	6	pes	pe	NOUN
bracis-19038	258	7	,	,	PUNCT
bracis-19038	258	8	opp	opp	PROPN
bracis-19038	258	9	\}\	\}\	NOUN
bracis-19038	258	10	)	)	PUNCT
bracis-19038	258	11	,	,	PUNCT
bracis-19038	258	12	and	and	CCONJ
bracis-19038	258	13	\(\mathcal	\(\mathcal	ADJ
bracis-19038	258	14	y	y	PROPN
bracis-19038	258	15	=	=	PROPN
bracis-19038	258	16	\mathcal	\mathcal	PROPN
bracis-19038	258	17	b_2\	b_2\	PROPN
bracis-19038	258	18	)	)	PUNCT
bracis-19038	258	19	if	if	SCONJ
bracis-19038	258	20	\(x	\(x	ADJ
bracis-19038	258	21	\in	\in	PROPN
bracis-19038	258	22	\	\	PROPN
bracis-19038	258	23	{	{	PUNCT
bracis-19038	258	24	opt	opt	NOUN
bracis-19038	258	25	,	,	PUNCT
bracis-19038	258	26	opp	opp	PROPN
bracis-19038	258	27	\}\	\}\	NOUN
bracis-19038	258	28	)	)	PUNCT
bracis-19038	258	29	and	and	CCONJ
bracis-19038	258	30	\(\mathcal	\(\mathcal	ADJ
bracis-19038	258	31	y	y	PROPN
bracis-19038	258	32	=	=	PROPN
bracis-19038	258	33	\mathcal	\mathcal	PROPN
bracis-19038	258	34	w_2\	w_2\	PROPN
bracis-19038	258	35	)	)	PUNCT
bracis-19038	258	36	if	if	SCONJ
bracis-19038	258	37	\(x	\(x	ADJ
bracis-19038	258	38	\in	\in	PROPN
bracis-19038	258	39	\	\	PROPN
bracis-19038	258	40	{	{	PUNCT
bracis-19038	258	41	st	st	PROPN
bracis-19038	258	42	,	,	PUNCT
bracis-19038	258	43	pes	pe	NOUN
bracis-19038	258	44	\}\	\}\	NOUN
bracis-19038	258	45	)	)	PUNCT
bracis-19038	258	46	.	.	PUNCT
bracis-19038	259	1	then	then	ADV
bracis-19038	259	2	for	for	ADP
bracis-19038	259	3	any	any	DET
bracis-19038	259	4	\(x	\(x	ADJ
bracis-19038	259	5	\in	\in	PROPN
bracis-19038	259	6	\	\	PROPN
bracis-19038	259	7	{	{	PUNCT
bracis-19038	259	8	st	st	PROPN
bracis-19038	259	9	,	,	PUNCT
bracis-19038	259	10	opt	opt	NOUN
bracis-19038	259	11	,	,	PUNCT
bracis-19038	259	12	\	\	ADJ
bracis-19038	259	13	)	)	PUNCT
bracis-19038	259	14	\	\	PROPN
bracis-19038	259	15	(	(	PUNCT
bracis-19038	259	16	pes	pe	NOUN
bracis-19038	259	17	,	,	PUNCT
bracis-19038	259	18	opp	opp	PROPN
bracis-19038	259	19	\}\	\}\	NOUN
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bracis-19038	259	21	,	,	PUNCT
bracis-19038	259	22	\(\forall	\(\forall	ADV
bracis-19038	259	23	o	o	X
bracis-19038	259	24	\in	\in	PROPN
bracis-19038	259	25	\mathcal	\mathcal	PROPN
bracis-19038	259	26	x\	x\	NOUN
bracis-19038	259	27	)	)	PUNCT
bracis-19038	259	28	and	and	CCONJ
bracis-19038	259	29	\(\forall	\(\forall	ADV
bracis-19038	259	30	o	o	NOUN
bracis-19038	259	31	'	'	PUNCT
bracis-19038	259	32	\in	\in	PROPN
bracis-19038	259	33	\mathcal	\mathcal	PROPN
bracis-19038	259	34	y\	y\	NOUN
bracis-19038	259	35	)	)	PUNCT
bracis-19038	259	36	,	,	PUNCT
bracis-19038	259	37	it	it	PRON
bracis-19038	259	38	holds	hold	VERB
bracis-19038	259	39	\(o	\(o	NOUN
bracis-19038	259	40	'	'	PUNCT
bracis-19038	259	41	\not	\not	ADV
bracis-19038	259	42	\prec	\prec	ADP
bracis-19038	259	43	o	o	X
bracis-19038	259	44	\in	\in	PROPN
bracis-19038	259	45	\varphi	\varphi	PROPN
bracis-19038	259	46	\	\	NOUN
bracis-19038	259	47	)	)	PUNCT
bracis-19038	259	48	iff	iff	VERB
bracis-19038	259	49	\(\forall	\(\forall	ADV
bracis-19038	259	50	o	o	X
bracis-19038	259	51	\in	\in	PROPN
bracis-19038	259	52	\mathcal	\mathcal	PROPN
bracis-19038	259	53	x\	x\	NOUN
bracis-19038	259	54	)	)	PUNCT
bracis-19038	259	55	,	,	PUNCT
bracis-19038	259	56	it	it	PRON
bracis-19038	259	57	holds	hold	VERB
bracis-19038	259	58	\(\exists	\(\exist	NOUN
bracis-19038	259	59	o	o	NOUN
bracis-19038	259	60	'	'	PUNCT
bracis-19038	259	61	\in	\in	PROPN
bracis-19038	259	62	\mathcal	\mathcal	PROPN
bracis-19038	259	63	y\	y\	NOUN
bracis-19038	259	64	)	)	PUNCT
bracis-19038	259	65	such	such	ADJ
bracis-19038	259	66	that	that	SCONJ
bracis-19038	259	67	\(o	\(o	NOUN
bracis-19038	259	68	'	'	PUNCT
bracis-19038	259	69	\not	\not	ADV
bracis-19038	259	70	\prec	\prec	ADP
bracis-19038	259	71	o	o	X
bracis-19038	259	72	\in	\in	PROPN
bracis-19038	259	73	\varphi	\varphi	PROPN
bracis-19038	259	74	\	\	NOUN
bracis-19038	259	75	)	)	PUNCT
bracis-19038	259	76	iff	iff	VERB
bracis-19038	259	77	\(o_2	\(o_2	PROPN
bracis-19038	259	78	\not	\not	ADV
bracis-19038	259	79	\prec	\prec	PROPN
bracis-19038	259	80	o_1	o_1	ADP
bracis-19038	259	81	\in	\in	PROPN
bracis-19038	259	82	\varphi	\varphi	PROPN
bracis-19038	259	83	\	\	NOUN
bracis-19038	259	84	)	)	PUNCT
bracis-19038	260	1	iff	iff	VERB
bracis-19038	260	2	\(\exists	\(\exist	NOUN
bracis-19038	260	3	o	o	PROPN
bracis-19038	260	4	\in	\in	PROPN
bracis-19038	260	5	\mathcal	\mathcal	PROPN
bracis-19038	260	6	x\	x\	NOUN
bracis-19038	260	7	)	)	PUNCT
bracis-19038	260	8	such	such	ADJ
bracis-19038	260	9	that	that	SCONJ
bracis-19038	260	10	\(\forall	\(\forall	ADV
bracis-19038	260	11	o	o	NOUN
bracis-19038	260	12	'	'	PUNCT
bracis-19038	260	13	\in	\in	PROPN
bracis-19038	260	14	\mathcal	\mathcal	PROPN
bracis-19038	260	15	y\	y\	NOUN
bracis-19038	260	16	)	)	PUNCT
bracis-19038	260	17	,	,	PUNCT
bracis-19038	260	18	it	it	PRON
bracis-19038	260	19	holds	hold	VERB
bracis-19038	260	20	\(o	\(o	NOUN
bracis-19038	260	21	'	'	PUNCT
bracis-19038	260	22	\not	\not	ADV
bracis-19038	260	23	\prec	\prec	ADP
bracis-19038	260	24	o	o	X
bracis-19038	260	25	\in	\in	PROPN
bracis-19038	260	26	\varphi	\varphi	PROPN
bracis-19038	260	27	\	\	NOUN
bracis-19038	260	28	)	)	PUNCT
bracis-19038	260	29	iff	iff	VERB
bracis-19038	260	30	\(o_2	\(o_2	PROPN
bracis-19038	260	31	\not	\not	ADV
bracis-19038	260	32	\prec	\prec	PROPN
bracis-19038	260	33	o_1	o_1	ADP
bracis-19038	260	34	\in	\in	PROPN
bracis-19038	260	35	\varphi	\varphi	PROPN
bracis-19038	260	36	\	\	NOUN
bracis-19038	260	37	)	)	PUNCT
bracis-19038	261	1	iff	iff	VERB
bracis-19038	261	2	\(\exists	\(\exist	NOUN
bracis-19038	261	3	o	o	PROPN
bracis-19038	261	4	\in	\in	PROPN
bracis-19038	261	5	\mathcal	\mathcal	PROPN
bracis-19038	261	6	x\	x\	NOUN
bracis-19038	261	7	)	)	PUNCT
bracis-19038	261	8	and	and	CCONJ
bracis-19038	261	9	\(\exists	\(\exist	NOUN
bracis-19038	261	10	o	o	NOUN
bracis-19038	261	11	'	'	PUNCT
bracis-19038	261	12	\in	\in	PROPN
bracis-19038	261	13	\mathcal	\mathcal	PROPN
bracis-19038	261	14	y\	y\	NOUN
bracis-19038	261	15	)	)	PUNCT
bracis-19038	261	16	such	such	ADJ
bracis-19038	261	17	that	that	SCONJ
bracis-19038	261	18	\(o	\(o	NOUN
bracis-19038	261	19	'	'	PUNCT
bracis-19038	261	20	\not	\not	ADV
bracis-19038	261	21	\prec	\prec	ADP
bracis-19038	261	22	o	o	X
bracis-19038	261	23	\in	\in	PROPN
bracis-19038	261	24	\varphi	\varphi	PROPN
bracis-19038	261	25	\	\	NOUN
bracis-19038	261	26	)	)	PUNCT
bracis-19038	261	27	.	.	PUNCT
bracis-19038	262	1	proof	proof	NOUN
bracis-19038	262	2	for	for	ADP
bracis-19038	262	3	any	any	DET
bracis-19038	262	4	\(x	\(x	ADJ
bracis-19038	262	5	\in	\in	PROPN
bracis-19038	262	6	\	\	PROPN
bracis-19038	262	7	{	{	PUNCT
bracis-19038	262	8	st	st	PROPN
bracis-19038	262	9	,	,	PUNCT
bracis-19038	262	10	opt	opt	NOUN
bracis-19038	262	11	,	,	PUNCT
bracis-19038	262	12	pes	pe	NOUN
bracis-19038	262	13	,	,	PUNCT
bracis-19038	262	14	opp	opp	PROPN
bracis-19038	262	15	\}\	\}\	NOUN
bracis-19038	262	16	)	)	PUNCT
bracis-19038	262	17	,	,	PUNCT
bracis-19038	262	18	let	let	VERB
bracis-19038	262	19	\(o_1\	\(o_1\	NOUN
bracis-19038	262	20	)	)	PUNCT
bracis-19038	262	21	be	be	AUX
bracis-19038	262	22	an	an	DET
bracis-19038	262	23	element	element	NOUN
bracis-19038	262	24	of	of	ADP
bracis-19038	262	25	\(\mathcal	\(\mathcal	ADJ
bracis-19038	262	26	x\	x\	NOUN
bracis-19038	262	27	)	)	PUNCT
bracis-19038	262	28	and	and	CCONJ
bracis-19038	262	29	\(o_2\	\(o_2\	VERB
bracis-19038	262	30	)	)	PUNCT
bracis-19038	262	31	be	be	VERB
bracis-19038	262	32	an	an	DET
bracis-19038	262	33	element	element	NOUN
bracis-19038	262	34	of	of	ADP
bracis-19038	262	35	\(\mathcal	\(\mathcal	ADJ
bracis-19038	262	36	y\	y\	NOUN
bracis-19038	262	37	)	)	PUNCT
bracis-19038	262	38	.	.	PUNCT
bracis-19038	263	1	given	give	VERB
bracis-19038	263	2	the	the	DET
bracis-19038	263	3	elements	element	NOUN
bracis-19038	263	4	of	of	ADP
bracis-19038	263	5	\(\mathcal	\(\mathcal	ADJ
bracis-19038	263	6	x\	x\	NOUN
bracis-19038	263	7	)	)	PUNCT
bracis-19038	263	8	are	be	AUX
bracis-19038	263	9	indifferent	indifferent	ADJ
bracis-19038	263	10	to	to	ADP
bracis-19038	263	11	each	each	DET
bracis-19038	263	12	other	other	ADJ
bracis-19038	263	13	and	and	CCONJ
bracis-19038	263	14	the	the	DET
bracis-19038	263	15	elements	element	NOUN
bracis-19038	263	16	of	of	ADP
bracis-19038	263	17	\(\mathcal	\(\mathcal	ADJ
bracis-19038	263	18	y\	y\	NOUN
bracis-19038	263	19	)	)	PUNCT
bracis-19038	263	20	are	be	AUX
bracis-19038	263	21	also	also	ADV
bracis-19038	263	22	indifferent	indifferent	ADJ
bracis-19038	263	23	to	to	ADP
bracis-19038	263	24	each	each	DET
bracis-19038	263	25	other	other	ADJ
bracis-19038	263	26	,	,	PUNCT
bracis-19038	263	27	we	we	PRON
bracis-19038	263	28	obtain	obtain	VERB
bracis-19038	263	29	\(o_2	\(o_2	PROPN
bracis-19038	263	30	\not	\not	ADV
bracis-19038	263	31	\prec	\prec	PROPN
bracis-19038	263	32	o_1	o_1	ADP
bracis-19038	263	33	\in	\in	PROPN
bracis-19038	263	34	\varphi	\varphi	PROPN
bracis-19038	263	35	\	\	NOUN
bracis-19038	263	36	)	)	PUNCT
bracis-19038	263	37	iff	iff	VERB
bracis-19038	263	38	\(\forall	\(\forall	ADV
bracis-19038	263	39	o	o	X
bracis-19038	263	40	\in	\in	PROPN
bracis-19038	263	41	\mathcal	\mathcal	PROPN
bracis-19038	263	42	x\	x\	NOUN
bracis-19038	263	43	)	)	PUNCT
bracis-19038	263	44	and	and	CCONJ
bracis-19038	263	45	\(\forall	\(\forall	ADV
bracis-19038	263	46	o	o	NOUN
bracis-19038	263	47	'	'	PUNCT
bracis-19038	263	48	\in	\in	PROPN
bracis-19038	263	49	\mathcal	\mathcal	PROPN
bracis-19038	263	50	y\	y\	NOUN
bracis-19038	263	51	)	)	PUNCT
bracis-19038	263	52	,	,	PUNCT
bracis-19038	263	53	it	it	PRON
bracis-19038	263	54	holds	hold	VERB
bracis-19038	263	55	\(o	\(o	NOUN
bracis-19038	263	56	'	'	PUNCT
bracis-19038	263	57	\not	\not	ADV
bracis-19038	263	58	\prec	\prec	ADP
bracis-19038	263	59	o	o	X
bracis-19038	263	60	\in	\in	PROPN
bracis-19038	263	61	\varphi	\varphi	PROPN
bracis-19038	263	62	\	\	NOUN
bracis-19038	263	63	)	)	PUNCT
bracis-19038	263	64	;	;	PUNCT
bracis-19038	263	65	\(o_2	\(o_2	PROPN
bracis-19038	263	66	\not	\not	ADV
bracis-19038	263	67	\prec	\prec	PROPN
bracis-19038	263	68	o_1	o_1	ADP
bracis-19038	263	69	\in	\in	PROPN
bracis-19038	263	70	\varphi	\varphi	PROPN
bracis-19038	263	71	\	\	NOUN
bracis-19038	263	72	)	)	PUNCT
bracis-19038	263	73	iff	iff	VERB
bracis-19038	263	74	\(\forall	\(\forall	ADV
bracis-19038	263	75	o	o	X
bracis-19038	263	76	\in	\in	PROPN
bracis-19038	263	77	\mathcal	\mathcal	PROPN
bracis-19038	263	78	x\	x\	NOUN
bracis-19038	263	79	)	)	PUNCT
bracis-19038	263	80	,	,	PUNCT
bracis-19038	263	81	it	it	PRON
bracis-19038	263	82	holds	hold	VERB
bracis-19038	263	83	\(\exists	\(\exist	NOUN
bracis-19038	263	84	o	o	NOUN
bracis-19038	263	85	'	'	PUNCT
bracis-19038	263	86	\in	\in	PROPN
bracis-19038	263	87	\mathcal	\mathcal	PROPN
bracis-19038	263	88	y\	y\	NOUN
bracis-19038	263	89	)	)	PUNCT
bracis-19038	263	90	such	such	ADJ
bracis-19038	263	91	that	that	SCONJ
bracis-19038	263	92	\(o	\(o	NOUN
bracis-19038	263	93	'	'	PUNCT
bracis-19038	263	94	\not	\not	ADV
bracis-19038	263	95	\prec	\prec	ADP
bracis-19038	263	96	o	o	X
bracis-19038	263	97	\in	\in	PROPN
bracis-19038	263	98	\varphi	\varphi	PROPN
bracis-19038	263	99	\	\	NOUN
bracis-19038	263	100	)	)	PUNCT
bracis-19038	263	101	;	;	PUNCT
bracis-19038	263	102	\(o_2	\(o_2	PROPN
bracis-19038	263	103	\not	\not	ADV
bracis-19038	263	104	\prec	\prec	PROPN
bracis-19038	263	105	o_1	o_1	ADP
bracis-19038	263	106	\in	\in	PROPN
bracis-19038	263	107	\varphi	\varphi	PROPN
bracis-19038	263	108	\	\	NOUN
bracis-19038	263	109	)	)	PUNCT
bracis-19038	263	110	iff	iff	VERB
bracis-19038	263	111	\(\exists	\(\exist	NOUN
bracis-19038	263	112	o	o	PROPN
bracis-19038	263	113	\in	\in	PROPN
bracis-19038	263	114	\mathcal	\mathcal	PROPN
bracis-19038	263	115	x\	x\	NOUN
bracis-19038	263	116	)	)	PUNCT
bracis-19038	263	117	such	such	ADJ
bracis-19038	263	118	that	that	SCONJ
bracis-19038	263	119	\(\forall	\(\forall	ADV
bracis-19038	263	120	o	o	NOUN
bracis-19038	263	121	'	'	PUNCT
bracis-19038	263	122	\in	\in	PROPN
bracis-19038	263	123	\mathcal	\mathcal	PROPN
bracis-19038	263	124	y\	y\	NOUN
bracis-19038	263	125	)	)	PUNCT
bracis-19038	263	126	,	,	PUNCT
bracis-19038	263	127	it	it	PRON
bracis-19038	263	128	holds	hold	VERB
bracis-19038	263	129	\(o	\(o	NOUN
bracis-19038	263	130	'	'	PUNCT
bracis-19038	263	131	\not	\not	ADV
bracis-19038	263	132	\prec	\prec	ADP
bracis-19038	263	133	o	o	X
bracis-19038	263	134	\in	\in	PROPN
bracis-19038	263	135	\varphi	\varphi	PROPN
bracis-19038	263	136	\	\	NOUN
bracis-19038	263	137	)	)	PUNCT
bracis-19038	263	138	;	;	PUNCT
bracis-19038	263	139	\(o_2	\(o_2	PROPN
bracis-19038	263	140	\not	\not	ADV
bracis-19038	263	141	\prec	\prec	PROPN
bracis-19038	263	142	o_1	o_1	ADP
bracis-19038	263	143	\in	\in	PROPN
bracis-19038	263	144	\varphi	\varphi	PROPN
bracis-19038	263	145	\	\	NOUN
bracis-19038	263	146	)	)	PUNCT
bracis-19038	264	1	iff	iff	VERB
bracis-19038	264	2	\(\exists	\(\exist	NOUN
bracis-19038	264	3	o	o	PROPN
bracis-19038	264	4	\in	\in	PROPN
bracis-19038	264	5	\mathcal	\mathcal	PROPN
bracis-19038	264	6	x\	x\	NOUN
bracis-19038	264	7	)	)	PUNCT
bracis-19038	264	8	and	and	CCONJ
bracis-19038	264	9	\(\exists	\(\exist	NOUN
bracis-19038	264	10	o	o	NOUN
bracis-19038	264	11	'	'	PUNCT
bracis-19038	264	12	\in	\in	PROPN
bracis-19038	264	13	\mathcal	\mathcal	PROPN
bracis-19038	264	14	y\	y\	NOUN
bracis-19038	264	15	)	)	PUNCT
bracis-19038	264	16	such	such	ADJ
bracis-19038	264	17	that	that	SCONJ
bracis-19038	264	18	\(o	\(o	NOUN
bracis-19038	264	19	'	'	PUNCT
bracis-19038	264	20	\not	\not	ADV
bracis-19038	264	21	\prec	\prec	ADP
bracis-19038	264	22	o	o	X
bracis-19038	264	23	\in	\in	PROPN
bracis-19038	264	24	\varphi	\varphi	PROPN
bracis-19038	264	25	\	\	NOUN
bracis-19038	264	26	)	)	PUNCT
bracis-19038	264	27	.	.	PUNCT
bracis-19038	265	1	i.e.	i.e.	X
bracis-19038	265	2	,	,	PUNCT
bracis-19038	265	3	\(\forall	\(\forall	ADV
bracis-19038	265	4	o	o	X
bracis-19038	265	5	\in	\in	PROPN
bracis-19038	265	6	\mathcal	\mathcal	PROPN
bracis-19038	265	7	x\	x\	NOUN
bracis-19038	265	8	)	)	PUNCT
bracis-19038	265	9	and	and	CCONJ
bracis-19038	265	10	\(\forall	\(\forall	ADV
bracis-19038	265	11	o	o	NOUN
bracis-19038	265	12	'	'	PUNCT
bracis-19038	265	13	\in	\in	PROPN
bracis-19038	265	14	\mathcal	\mathcal	PROPN
bracis-19038	265	15	y\	y\	NOUN
bracis-19038	265	16	)	)	PUNCT
bracis-19038	265	17	,	,	PUNCT
bracis-19038	265	18	it	it	PRON
bracis-19038	265	19	holds	hold	VERB
bracis-19038	265	20	\(o	\(o	NOUN
bracis-19038	265	21	'	'	PUNCT
bracis-19038	265	22	\not	\not	ADV
bracis-19038	265	23	\prec	\prec	ADP
bracis-19038	265	24	o	o	X
bracis-19038	265	25	\in	\in	PROPN
bracis-19038	265	26	\varphi	\varphi	PROPN
bracis-19038	265	27	\	\	NOUN
bracis-19038	265	28	)	)	PUNCT
bracis-19038	265	29	iff	iff	VERB
bracis-19038	265	30	\(\forall	\(\forall	ADV
bracis-19038	265	31	o	o	X
bracis-19038	265	32	\in	\in	PROPN
bracis-19038	265	33	\mathcal	\mathcal	PROPN
bracis-19038	265	34	x\	x\	NOUN
bracis-19038	265	35	)	)	PUNCT
bracis-19038	265	36	,	,	PUNCT
bracis-19038	265	37	it	it	PRON
bracis-19038	265	38	holds	hold	VERB
bracis-19038	265	39	\(\exists	\(\exist	NOUN
bracis-19038	265	40	o	o	NOUN
bracis-19038	265	41	'	'	PUNCT
bracis-19038	265	42	\in	\in	PROPN
bracis-19038	265	43	\mathcal	\mathcal	PROPN
bracis-19038	265	44	y\	y\	NOUN
bracis-19038	265	45	)	)	PUNCT
bracis-19038	265	46	such	such	ADJ
bracis-19038	265	47	that	that	SCONJ
bracis-19038	265	48	\(o	\(o	NOUN
bracis-19038	265	49	'	'	PUNCT
bracis-19038	265	50	\not	\not	ADV
bracis-19038	265	51	\prec	\prec	ADP
bracis-19038	265	52	o	o	X
bracis-19038	265	53	\in	\in	PROPN
bracis-19038	265	54	\varphi	\varphi	PROPN
bracis-19038	265	55	\	\	NOUN
bracis-19038	265	56	)	)	PUNCT
bracis-19038	265	57	iff	iff	VERB
bracis-19038	265	58	\(o_2	\(o_2	PROPN
bracis-19038	265	59	\not	\not	ADV
bracis-19038	265	60	\prec	\prec	PROPN
bracis-19038	265	61	o_1	o_1	ADP
bracis-19038	265	62	\in	\in	PROPN
bracis-19038	265	63	\varphi	\varphi	PROPN
bracis-19038	265	64	\	\	NOUN
bracis-19038	265	65	)	)	PUNCT
bracis-19038	266	1	iff	iff	VERB
bracis-19038	266	2	\(\exists	\(\exist	NOUN
bracis-19038	266	3	o	o	PROPN
bracis-19038	266	4	\in	\in	PROPN
bracis-19038	266	5	\mathcal	\mathcal	PROPN
bracis-19038	266	6	x\	x\	NOUN
bracis-19038	266	7	)	)	PUNCT
bracis-19038	266	8	such	such	ADJ
bracis-19038	266	9	that	that	SCONJ
bracis-19038	266	10	\(\forall	\(\forall	ADV
bracis-19038	266	11	o	o	NOUN
bracis-19038	266	12	'	'	PUNCT
bracis-19038	266	13	\in	\in	PROPN
bracis-19038	266	14	\mathcal	\mathcal	PROPN
bracis-19038	266	15	y\	y\	NOUN
bracis-19038	266	16	)	)	PUNCT
bracis-19038	266	17	,	,	PUNCT
bracis-19038	266	18	it	it	PRON
bracis-19038	266	19	holds	hold	VERB
bracis-19038	266	20	\(o	\(o	NOUN
bracis-19038	266	21	'	'	PUNCT
bracis-19038	266	22	\not	\not	ADV
bracis-19038	266	23	\prec	\prec	ADP
bracis-19038	266	24	o	o	X
bracis-19038	266	25	\in	\in	PROPN
bracis-19038	266	26	\varphi	\varphi	PROPN
bracis-19038	266	27	\	\	NOUN
bracis-19038	266	28	)	)	PUNCT
bracis-19038	266	29	iff	iff	VERB
bracis-19038	266	30	\(o_2	\(o_2	PROPN
bracis-19038	266	31	\not	\not	ADV
bracis-19038	266	32	\prec	\prec	PROPN
bracis-19038	266	33	o_1	o_1	ADP
bracis-19038	266	34	\in	\in	PROPN
bracis-19038	266	35	\varphi	\varphi	PROPN
bracis-19038	266	36	\	\	NOUN
bracis-19038	266	37	)	)	PUNCT
bracis-19038	267	1	iff	iff	VERB
bracis-19038	267	2	\(\exists	\(\exist	NOUN
bracis-19038	267	3	o	o	PROPN
bracis-19038	267	4	\in	\in	PROPN
bracis-19038	267	5	\mathcal	\mathcal	PROPN
bracis-19038	267	6	x\	x\	NOUN
bracis-19038	267	7	)	)	PUNCT
bracis-19038	267	8	and	and	CCONJ
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bracis-19038	267	10	o	o	NOUN
bracis-19038	267	11	'	'	PUNCT
bracis-19038	267	12	\in	\in	PROPN
bracis-19038	267	13	\mathcal	\mathcal	PROPN
bracis-19038	267	14	y\	y\	NOUN
bracis-19038	267	15	)	)	PUNCT
bracis-19038	267	16	such	such	ADJ
bracis-19038	267	17	that	that	SCONJ
bracis-19038	267	18	\(o	\(o	NOUN
bracis-19038	267	19	'	'	PUNCT
bracis-19038	267	20	\not	\not	ADV
bracis-19038	267	21	\prec	\prec	ADP
bracis-19038	267	22	o	o	X
bracis-19038	267	23	\in	\in	PROPN
bracis-19038	267	24	\varphi	\varphi	PROPN
bracis-19038	267	25	\	\	NOUN
bracis-19038	267	26	)	)	PUNCT
bracis-19038	267	27	.	.	PUNCT
bracis-19038	268	1	   	   	SPACE
bracis-19038	268	2	\(\square	\(\square	VERB
bracis-19038	268	3	\	\	NOUN
bracis-19038	268	4	)	)	PUNCT
bracis-19038	268	5	a	a	DET
bracis-19038	268	6	binary	binary	ADJ
bracis-19038	268	7	relation	relation	NOUN
bracis-19038	268	8	\(\sqsubset	\(\sqsubset	VERB
bracis-19038	268	9	\	\	PROPN
bracis-19038	268	10	)	)	PUNCT
bracis-19038	268	11	on	on	ADP
bracis-19038	268	12	a	a	DET
bracis-19038	268	13	set	set	NOUN
bracis-19038	268	14	\(\mathcal	\(\mathcal	ADJ
bracis-19038	268	15	o\	o\	NOUN
bracis-19038	268	16	)	)	PUNCT
bracis-19038	268	17	is	be	AUX
bracis-19038	268	18	a	a	DET
bracis-19038	268	19	total	total	ADJ
bracis-19038	268	20	preorder	preorder	NOUN
bracis-19038	268	21	if	if	SCONJ
bracis-19038	268	22	it	it	PRON
bracis-19038	268	23	is	be	AUX
bracis-19038	268	24	reflexive	reflexive	ADJ
bracis-19038	268	25	,	,	PUNCT
bracis-19038	268	26	transitive	transitive	ADJ
bracis-19038	268	27	and	and	CCONJ
bracis-19038	268	28	for	for	ADP
bracis-19038	268	29	each	each	DET
bracis-19038	268	30	\(o_1\	\(o_1\	NOUN
bracis-19038	268	31	)	)	PUNCT
bracis-19038	268	32	and	and	CCONJ
bracis-19038	268	33	\(o_2\	\(o_2\	VERB
bracis-19038	268	34	)	)	PUNCT
bracis-19038	268	35	in	in	ADP
bracis-19038	268	36	\(\mathcal	\(\mathcal	ADJ
bracis-19038	268	37	o\	o\	NOUN
bracis-19038	268	38	)	)	PUNCT
bracis-19038	268	39	,	,	PUNCT
bracis-19038	268	40	it	it	PRON
bracis-19038	268	41	holds	hold	VERB
bracis-19038	268	42	\(o_1	\(o_1	PROPN
bracis-19038	268	43	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	268	44	o_2\	o_2\	NUM
bracis-19038	268	45	)	)	PUNCT
bracis-19038	268	46	or	or	CCONJ
bracis-19038	268	47	\(o_2	\(o_2	PROPN
bracis-19038	268	48	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	268	49	o_1\	o_1\	PROPN
bracis-19038	268	50	)	)	PUNCT
bracis-19038	268	51	.	.	PUNCT
bracis-19038	269	1	for	for	ADP
bracis-19038	269	2	all	all	DET
bracis-19038	269	3	\(x	\(x	ADJ
bracis-19038	269	4	\in	\in	PROPN
bracis-19038	269	5	\left\	\left\	PROPN
bracis-19038	269	6	{	{	PUNCT
bracis-19038	269	7	st	st	PROPN
bracis-19038	269	8	,	,	PUNCT
bracis-19038	269	9	opt	opt	NOUN
bracis-19038	269	10	,	,	PUNCT
bracis-19038	269	11	pes	pe	NOUN
bracis-19038	269	12	,	,	PUNCT
bracis-19038	269	13	opp	opp	PROPN
bracis-19038	269	14	\right\	\right\	ADV
bracis-19038	269	15	}	}	PUNCT
bracis-19038	269	16	\	\	NOUN
bracis-19038	269	17	)	)	PUNCT
bracis-19038	269	18	,	,	PUNCT
bracis-19038	269	19	if	if	SCONJ
bracis-19038	269	20	the	the	DET
bracis-19038	269	21	relation	relation	NOUN
bracis-19038	269	22	\(\preceq	\(\preceq	X
bracis-19038	269	23	\	\	PROPN
bracis-19038	269	24	)	)	PUNCT
bracis-19038	269	25	is	be	AUX
bracis-19038	269	26	a	a	DET
bracis-19038	269	27	total	total	ADJ
bracis-19038	269	28	preorder	preorder	NOUN
bracis-19038	269	29	,	,	PUNCT
bracis-19038	269	30	\(\subseteq	\(\subseteq	ADV
bracis-19038	269	31	^{\forall	^{\forall	NOUN
bracis-19038	270	1	\forall	\forall	DET
bracis-19038	270	2	}	}	PUNCT
bracis-19038	270	3	_	_	PUNCT
bracis-19038	270	4	x\	x\	NOUN
bracis-19038	270	5	)	)	PUNCT
bracis-19038	270	6	,	,	PUNCT
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bracis-19038	270	8	^{\forall	^{\forall	DET
bracis-19038	270	9	\exists	\exist	NOUN
bracis-19038	270	10	}	}	PUNCT
bracis-19038	270	11	_	_	PUNCT
bracis-19038	270	12	x\	x\	NOUN
bracis-19038	270	13	)	)	PUNCT
bracis-19038	270	14	,	,	PUNCT
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bracis-19038	270	16	^{\exists	^{\exist	NOUN
bracis-19038	270	17	\forall	\forall	PRON
bracis-19038	270	18	}	}	PUNCT
bracis-19038	270	19	_	_	PUNCT
bracis-19038	270	20	x\	x\	NOUN
bracis-19038	270	21	)	)	PUNCT
bracis-19038	270	22	and	and	CCONJ
bracis-19038	270	23	\(\subseteq	\(\subseteq	PROPN
bracis-19038	270	24	^{\exists	^{\exist	VERB
bracis-19038	270	25	\exists	\exist	NOUN
bracis-19038	270	26	}	}	PUNCT
bracis-19038	270	27	_	_	PUNCT
bracis-19038	270	28	x\	x\	NOUN
bracis-19038	270	29	)	)	PUNCT
bracis-19038	270	30	(	(	PUNCT
bracis-19038	270	31	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	270	32	^{\forall	^{\forall	NOUN
bracis-19038	271	1	\forall	\forall	PRON
bracis-19038	271	2	}	}	PUNCT
bracis-19038	271	3	_	_	PUNCT
bracis-19038	271	4	x\	x\	NOUN
bracis-19038	271	5	)	)	PUNCT
bracis-19038	271	6	,	,	PUNCT
bracis-19038	271	7	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	271	8	^{\forall	^{\forall	DET
bracis-19038	271	9	\exists	\exist	NOUN
bracis-19038	271	10	}	}	PUNCT
bracis-19038	271	11	_	_	PUNCT
bracis-19038	271	12	x\	x\	NOUN
bracis-19038	271	13	)	)	PUNCT
bracis-19038	271	14	,	,	PUNCT
bracis-19038	271	15	\(\sqsubseteq	\(\sqsubseteq	VERB
bracis-19038	271	16	^{\exists	^{\exist	NOUN
bracis-19038	271	17	\forall	\forall	PRON
bracis-19038	271	18	}	}	PUNCT
bracis-19038	271	19	_	_	PUNCT
bracis-19038	271	20	x\	x\	NOUN
bracis-19038	271	21	)	)	PUNCT
bracis-19038	271	22	and	and	CCONJ
bracis-19038	271	23	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	271	24	^{\exists	^{\exist	NOUN
bracis-19038	271	25	\exists	\exist	NOUN
bracis-19038	271	26	}	}	PUNCT
bracis-19038	271	27	_	_	PUNCT
bracis-19038	271	28	x\	x\	NOUN
bracis-19038	271	29	)	)	PUNCT
bracis-19038	271	30	)	)	PUNCT
bracis-19038	271	31	will	will	AUX
bracis-19038	271	32	collapse	collapse	VERB
bracis-19038	271	33	into	into	ADP
bracis-19038	271	34	each	each	DET
bracis-19038	271	35	other	other	ADJ
bracis-19038	271	36	.	.	PUNCT
bracis-19038	272	1	theorem	theorem	ADJ
bracis-19038	272	2	1	1	NUM
bracis-19038	272	3	let	let	VERB
bracis-19038	272	4	\((p	\((p	NOUN
bracis-19038	272	5	,	,	PUNCT
bracis-19038	272	6	\varphi	\varphi	PROPN
bracis-19038	272	7	)	)	PUNCT
bracis-19038	272	8	\	\	NOUN
bracis-19038	272	9	)	)	PUNCT
bracis-19038	272	10	be	be	AUX
bracis-19038	272	11	a	a	DET
bracis-19038	272	12	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	272	13	)	)	PUNCT
bracis-19038	272	14	such	such	ADJ
bracis-19038	272	15	that	that	SCONJ
bracis-19038	272	16	the	the	DET
bracis-19038	272	17	preference	preference	NOUN
bracis-19038	272	18	relation	relation	NOUN
bracis-19038	272	19	\(\preceq	\(\preceq	X
bracis-19038	272	20	\	\	PROPN
bracis-19038	272	21	)	)	PUNCT
bracis-19038	272	22	in	in	ADP
bracis-19038	272	23	\(\varphi	\(\varphi	ADJ
bracis-19038	272	24	\	\	NOUN
bracis-19038	272	25	)	)	PUNCT
bracis-19038	272	26	is	be	AUX
bracis-19038	272	27	a	a	DET
bracis-19038	272	28	total	total	ADJ
bracis-19038	272	29	preorder	preorder	NOUN
bracis-19038	272	30	on	on	ADP
bracis-19038	272	31	\(\mathcal	\(\mathcal	ADJ
bracis-19038	272	32	{	{	PUNCT
bracis-19038	272	33	o}_p\	o}_p\	NOUN
bracis-19038	272	34	)	)	PUNCT
bracis-19038	272	35	.	.	PUNCT
bracis-19038	273	1	then	then	ADV
bracis-19038	273	2	for	for	ADP
bracis-19038	273	3	any	any	DET
bracis-19038	273	4	\(x	\(x	ADJ
bracis-19038	273	5	\in	\in	PROPN
bracis-19038	273	6	\left\	\left\	PROPN
bracis-19038	273	7	{	{	PUNCT
bracis-19038	273	8	st	st	PROPN
bracis-19038	273	9	,	,	PUNCT
bracis-19038	273	10	opt	opt	NOUN
bracis-19038	273	11	,	,	PUNCT
bracis-19038	273	12	pes	pe	NOUN
bracis-19038	273	13	,	,	PUNCT
bracis-19038	273	14	opp	opp	PROPN
bracis-19038	273	15	\right\	\right\	ADV
bracis-19038	273	16	}	}	PUNCT
bracis-19038	273	17	\	\	NOUN
bracis-19038	273	18	)	)	PUNCT
bracis-19038	273	19	,	,	PUNCT
bracis-19038	273	20	i	i	PRON
bracis-19038	273	21	is	be	AUX
bracis-19038	273	22	a	a	DET
bracis-19038	273	23	\	\	PROPN
bracis-19038	273	24	(	(	PUNCT
bracis-19038	273	25	pps	pps	PROPN
bracis-19038	273	26	\	\	ADJ
bracis-19038	273	27	)	)	PUNCT
bracis-19038	273	28	model	model	NOUN
bracis-19038	273	29	of	of	ADP
bracis-19038	273	30	\((p	\((p	NOUN
bracis-19038	273	31	,	,	PUNCT
bracis-19038	273	32	\varphi	\varphi	PROPN
bracis-19038	273	33	)	)	PUNCT
bracis-19038	273	34	\	\	NOUN
bracis-19038	273	35	)	)	PUNCT
bracis-19038	273	36	w.r.t	w.r.t	NOUN
bracis-19038	273	37	.	.	PUNCT
bracis-19038	274	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	274	2	^{\forall	^{\forall	NOUN
bracis-19038	275	1	\forall	\forall	DET
bracis-19038	275	2	}	}	PUNCT
bracis-19038	275	3	_	_	PUNCT
bracis-19038	275	4	x\	x\	NOUN
bracis-19038	275	5	)	)	PUNCT
bracis-19038	275	6	(	(	PUNCT
bracis-19038	275	7	resp	resp	NOUN
bracis-19038	275	8	.	.	PUNCT
bracis-19038	276	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	276	2	^{\forall	^{\forall	NOUN
bracis-19038	277	1	\forall	\forall	PRON
bracis-19038	277	2	}	}	PUNCT
bracis-19038	277	3	_	_	PUNCT
bracis-19038	277	4	x\	x\	NOUN
bracis-19038	277	5	)	)	PUNCT
bracis-19038	277	6	)	)	PUNCT
bracis-19038	278	1	iff	iff	PROPN
bracis-19038	278	2	i	i	PRON
bracis-19038	278	3	is	be	AUX
bracis-19038	278	4	a	a	DET
bracis-19038	278	5	\	\	PROPN
bracis-19038	278	6	(	(	PUNCT
bracis-19038	278	7	pps	pps	PROPN
bracis-19038	278	8	\	\	ADJ
bracis-19038	278	9	)	)	PUNCT
bracis-19038	278	10	model	model	NOUN
bracis-19038	278	11	of	of	ADP
bracis-19038	278	12	\((p	\((p	NOUN
bracis-19038	278	13	,	,	PUNCT
bracis-19038	278	14	\varphi	\varphi	PROPN
bracis-19038	278	15	)	)	PUNCT
bracis-19038	278	16	\	\	NOUN
bracis-19038	278	17	)	)	PUNCT
bracis-19038	278	18	w.r.t	w.r.t	NOUN
bracis-19038	278	19	.	.	PUNCT
bracis-19038	279	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	279	2	^{\forall	^{\forall	DET
bracis-19038	279	3	\exists	\exist	NOUN
bracis-19038	279	4	}	}	PUNCT
bracis-19038	279	5	_	_	PUNCT
bracis-19038	279	6	x\	x\	NOUN
bracis-19038	279	7	)	)	PUNCT
bracis-19038	279	8	(	(	PUNCT
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bracis-19038	279	10	.	.	PUNCT
bracis-19038	280	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	280	2	^{\forall	^{\forall	PRON
bracis-19038	280	3	\exists	\exist	NOUN
bracis-19038	280	4	}	}	PUNCT
bracis-19038	280	5	_	_	PUNCT
bracis-19038	280	6	x\	x\	NOUN
bracis-19038	280	7	)	)	PUNCT
bracis-19038	280	8	)	)	PUNCT
bracis-19038	281	1	iff	iff	PROPN
bracis-19038	281	2	i	i	PRON
bracis-19038	281	3	is	be	AUX
bracis-19038	281	4	a	a	DET
bracis-19038	281	5	\	\	PROPN
bracis-19038	281	6	(	(	PUNCT
bracis-19038	281	7	pps	pps	PROPN
bracis-19038	281	8	\	\	ADJ
bracis-19038	281	9	)	)	PUNCT
bracis-19038	281	10	model	model	NOUN
bracis-19038	281	11	of	of	ADP
bracis-19038	281	12	\((p	\((p	NOUN
bracis-19038	281	13	,	,	PUNCT
bracis-19038	281	14	\varphi	\varphi	PROPN
bracis-19038	281	15	)	)	PUNCT
bracis-19038	281	16	\	\	NOUN
bracis-19038	281	17	)	)	PUNCT
bracis-19038	281	18	w.r.t	w.r.t	NOUN
bracis-19038	281	19	.	.	PUNCT
bracis-19038	282	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	282	2	^{\exists	^{\exist	NOUN
bracis-19038	283	1	\forall	\forall	DET
bracis-19038	283	2	}	}	PUNCT
bracis-19038	283	3	_	_	PUNCT
bracis-19038	283	4	x\	x\	NOUN
bracis-19038	283	5	)	)	PUNCT
bracis-19038	283	6	(	(	PUNCT
bracis-19038	283	7	resp	resp	NOUN
bracis-19038	283	8	.	.	PUNCT
bracis-19038	284	1	\(\sqsubseteq	\(\sqsubseteq	NOUN
bracis-19038	284	2	^{\exists	^{\exist	NOUN
bracis-19038	285	1	\forall	\forall	DET
bracis-19038	285	2	}	}	PUNCT
bracis-19038	285	3	_	_	PUNCT
bracis-19038	285	4	x\	x\	NOUN
bracis-19038	285	5	)	)	PUNCT
bracis-19038	285	6	)	)	PUNCT
bracis-19038	286	1	iff	iff	PROPN
bracis-19038	286	2	i	i	PRON
bracis-19038	286	3	is	be	AUX
bracis-19038	286	4	a	a	DET
bracis-19038	286	5	\	\	PROPN
bracis-19038	286	6	(	(	PUNCT
bracis-19038	286	7	pps	pps	PROPN
bracis-19038	286	8	\	\	ADJ
bracis-19038	286	9	)	)	PUNCT
bracis-19038	286	10	model	model	NOUN
bracis-19038	286	11	of	of	ADP
bracis-19038	286	12	\((p	\((p	NOUN
bracis-19038	286	13	,	,	PUNCT
bracis-19038	286	14	\varphi	\varphi	PROPN
bracis-19038	286	15	)	)	PUNCT
bracis-19038	286	16	\	\	NOUN
bracis-19038	286	17	)	)	PUNCT
bracis-19038	286	18	w.r.t	w.r.t	NOUN
bracis-19038	286	19	.	.	PUNCT
bracis-19038	287	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	287	2	^{\exists	^{\exist	VERB
bracis-19038	287	3	\exists	\exist	NOUN
bracis-19038	287	4	}	}	PUNCT
bracis-19038	287	5	_	_	PUNCT
bracis-19038	287	6	x\	x\	NOUN
bracis-19038	287	7	)	)	PUNCT
bracis-19038	287	8	(	(	PUNCT
bracis-19038	287	9	resp	resp	NOUN
bracis-19038	287	10	.	.	PUNCT
bracis-19038	288	1	\(\sqsubseteq	\(\sqsubseteq	VERB
bracis-19038	288	2	^{\exists	^{\exist	NOUN
bracis-19038	288	3	\exists	\exist	NOUN
bracis-19038	288	4	}	}	PUNCT
bracis-19038	288	5	_	_	PUNCT
bracis-19038	288	6	x\	x\	NOUN
bracis-19038	288	7	)	)	PUNCT
bracis-19038	288	8	)	)	PUNCT
bracis-19038	288	9	.	.	PUNCT
bracis-19038	289	1	proof	proof	NOUN
bracis-19038	289	2	let	let	VERB
bracis-19038	289	3	\(i_1\	\(i_1\	PROPN
bracis-19038	289	4	)	)	PUNCT
bracis-19038	289	5	and	and	CCONJ
bracis-19038	289	6	\(i_2\	\(i_2\	PROPN
bracis-19038	289	7	)	)	PUNCT
bracis-19038	289	8	be	be	VERB
bracis-19038	289	9	\	\	PROPN
bracis-19038	289	10	(	(	PUNCT
bracis-19038	289	11	ps	ps	NOUN
bracis-19038	289	12	\	\	ADJ
bracis-19038	289	13	)	)	PUNCT
bracis-19038	289	14	models	model	NOUN
bracis-19038	289	15	of	of	ADP
bracis-19038	289	16	p	p	X
bracis-19038	289	17	,	,	PUNCT
bracis-19038	289	18	\(\mathcal	\(\mathcal	ADJ
bracis-19038	289	19	b_1\	b_1\	NOUN
bracis-19038	289	20	)	)	PUNCT
bracis-19038	289	21	and	and	CCONJ
bracis-19038	289	22	\(\mathcal	\(\mathcal	ADJ
bracis-19038	289	23	b_2\	b_2\	PROPN
bracis-19038	289	24	)	)	PUNCT
bracis-19038	289	25	be	be	VERB
bracis-19038	289	26	respectively	respectively	ADV
bracis-19038	289	27	the	the	DET
bracis-19038	289	28	set	set	NOUN
bracis-19038	289	29	of	of	ADP
bracis-19038	289	30	best	well	ADV
bracis-19038	289	31	-	-	PUNCT
bracis-19038	289	32	ranked	rank	VERB
bracis-19038	289	33	options	option	NOUN
bracis-19038	289	34	in	in	ADP
bracis-19038	289	35	\(i_1\	\(i_1\	NOUN
bracis-19038	289	36	)	)	PUNCT
bracis-19038	289	37	and	and	CCONJ
bracis-19038	289	38	\(i_2\	\(i_2\	PROPN
bracis-19038	289	39	)	)	PUNCT
bracis-19038	289	40	w.r.t	w.r.t	NOUN
bracis-19038	289	41	.	.	PUNCT
bracis-19038	290	1	\(\varphi	\(\varphi	ADJ
bracis-19038	290	2	\	\	NOUN
bracis-19038	290	3	)	)	PUNCT
bracis-19038	290	4	,	,	PUNCT
bracis-19038	290	5	and	and	CCONJ
bracis-19038	290	6	\(\mathcal	\(\mathcal	ADJ
bracis-19038	290	7	w_1\	w_1\	PROPN
bracis-19038	290	8	)	)	PUNCT
bracis-19038	290	9	and	and	CCONJ
bracis-19038	290	10	\(\mathcal	\(\mathcal	ADJ
bracis-19038	290	11	w_2\	w_2\	PROPN
bracis-19038	290	12	)	)	PUNCT
bracis-19038	290	13	be	be	VERB
bracis-19038	290	14	respectively	respectively	ADV
bracis-19038	290	15	the	the	DET
bracis-19038	290	16	set	set	NOUN
bracis-19038	290	17	of	of	ADP
bracis-19038	290	18	worst	worst	ADV
bracis-19038	290	19	-	-	PUNCT
bracis-19038	290	20	ranked	rank	VERB
bracis-19038	290	21	options	option	NOUN
bracis-19038	290	22	in	in	ADP
bracis-19038	290	23	\(i_1\	\(i_1\	NOUN
bracis-19038	290	24	)	)	PUNCT
bracis-19038	290	25	and	and	CCONJ
bracis-19038	290	26	\(i_2\	\(i_2\	PROPN
bracis-19038	290	27	)	)	PUNCT
bracis-19038	290	28	w.r.t	w.r.t	NOUN
bracis-19038	290	29	.	.	PUNCT
bracis-19038	291	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	291	2	\	\	NOUN
bracis-19038	291	3	)	)	PUNCT
bracis-19038	291	4	.	.	PUNCT
bracis-19038	292	1	consider	consider	VERB
bracis-19038	292	2	\(\mathcal	\(\mathcal	ADJ
bracis-19038	292	3	x	x	X
bracis-19038	292	4	=	=	PUNCT
bracis-19038	292	5	\mathcal	\mathcal	ADJ
bracis-19038	292	6	b_1\	b_1\	PROPN
bracis-19038	292	7	)	)	PUNCT
bracis-19038	292	8	if	if	SCONJ
bracis-19038	292	9	\(x	\(x	ADJ
bracis-19038	292	10	\in	\in	PROPN
bracis-19038	292	11	\	\	PROPN
bracis-19038	292	12	{	{	PUNCT
bracis-19038	292	13	st	st	PROPN
bracis-19038	292	14	,	,	PUNCT
bracis-19038	292	15	opt	opt	VERB
bracis-19038	292	16	\}\	\}\	NOUN
bracis-19038	292	17	)	)	PUNCT
bracis-19038	292	18	and	and	CCONJ
bracis-19038	292	19	\(\mathcal	\(\mathcal	ADJ
bracis-19038	292	20	x	x	X
bracis-19038	292	21	=	=	PUNCT
bracis-19038	292	22	\mathcal	\mathcal	PROPN
bracis-19038	292	23	w_1\	w_1\	PROPN
bracis-19038	292	24	)	)	PUNCT
bracis-19038	293	1	if	if	SCONJ
bracis-19038	293	2	\(x	\(x	ADJ
bracis-19038	293	3	\in	\in	PROPN
bracis-19038	293	4	\	\	PROPN
bracis-19038	293	5	{	{	PUNCT
bracis-19038	293	6	pes	pe	NOUN
bracis-19038	293	7	,	,	PUNCT
bracis-19038	293	8	opp	opp	PROPN
bracis-19038	293	9	\}\	\}\	NOUN
bracis-19038	293	10	)	)	PUNCT
bracis-19038	293	11	,	,	PUNCT
bracis-19038	293	12	and	and	CCONJ
bracis-19038	293	13	\(\mathcal	\(\mathcal	ADJ
bracis-19038	293	14	y	y	PROPN
bracis-19038	293	15	=	=	PROPN
bracis-19038	293	16	\mathcal	\mathcal	PROPN
bracis-19038	293	17	b_2\	b_2\	PROPN
bracis-19038	293	18	)	)	PUNCT
bracis-19038	293	19	if	if	SCONJ
bracis-19038	293	20	\(x	\(x	ADJ
bracis-19038	293	21	\in	\in	PROPN
bracis-19038	293	22	\	\	PROPN
bracis-19038	293	23	{	{	PUNCT
bracis-19038	293	24	opt	opt	NOUN
bracis-19038	293	25	,	,	PUNCT
bracis-19038	293	26	opp	opp	PROPN
bracis-19038	293	27	\}\	\}\	NOUN
bracis-19038	293	28	)	)	PUNCT
bracis-19038	293	29	and	and	CCONJ
bracis-19038	293	30	\(\mathcal	\(\mathcal	ADJ
bracis-19038	293	31	y	y	PROPN
bracis-19038	293	32	=	=	PROPN
bracis-19038	293	33	\mathcal	\mathcal	PROPN
bracis-19038	293	34	w_2\	w_2\	PROPN
bracis-19038	293	35	)	)	PUNCT
bracis-19038	293	36	if	if	SCONJ
bracis-19038	293	37	\(x	\(x	ADJ
bracis-19038	293	38	\in	\in	PROPN
bracis-19038	293	39	\	\	PROPN
bracis-19038	293	40	{	{	PUNCT
bracis-19038	293	41	st	st	PROPN
bracis-19038	293	42	,	,	PUNCT
bracis-19038	293	43	pes	pe	NOUN
bracis-19038	293	44	\}\	\}\	NOUN
bracis-19038	293	45	)	)	PUNCT
bracis-19038	293	46	.	.	PUNCT
bracis-19038	294	1	it	it	PRON
bracis-19038	294	2	suffices	suffice	VERB
bracis-19038	294	3	to	to	PART
bracis-19038	294	4	show	show	VERB
bracis-19038	294	5	for	for	ADP
bracis-19038	294	6	any	any	DET
bracis-19038	294	7	\(x	\(x	ADJ
bracis-19038	294	8	\in	\in	PROPN
bracis-19038	294	9	\	\	PROPN
bracis-19038	294	10	{	{	PUNCT
bracis-19038	294	11	st	st	PROPN
bracis-19038	294	12	,	,	PUNCT
bracis-19038	294	13	opt	opt	NOUN
bracis-19038	294	14	,	,	PUNCT
bracis-19038	294	15	pes	pe	NOUN
bracis-19038	294	16	,	,	PUNCT
bracis-19038	294	17	opp	opp	PROPN
bracis-19038	294	18	\}\	\}\	NOUN
bracis-19038	294	19	)	)	PUNCT
bracis-19038	294	20	,	,	PUNCT
bracis-19038	294	21	\(i_1	\(i_1	PROPN
bracis-19038	294	22	\subseteq	\subseteq	PROPN
bracis-19038	294	23	^{\forall	^{\forall	NOUN
bracis-19038	294	24	\forall	\forall	PRON
bracis-19038	294	25	}	}	PUNCT
bracis-19038	294	26	_	_	PUNCT
bracis-19038	294	27	x	x	SYM
bracis-19038	294	28	i_2\	i_2\	PRON
bracis-19038	294	29	)	)	PUNCT
bracis-19038	294	30	iff	iff	VERB
bracis-19038	294	31	\(i_1	\(i_1	PROPN
bracis-19038	294	32	\subseteq	\subseteq	PROPN
bracis-19038	294	33	^{\forall	^{\forall	PRON
bracis-19038	294	34	\exists	\exist	NOUN
bracis-19038	294	35	}	}	PUNCT
bracis-19038	294	36	_	_	PUNCT
bracis-19038	294	37	x	x	SYM
bracis-19038	294	38	i_2\	i_2\	PRON
bracis-19038	294	39	)	)	PUNCT
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bracis-19038	294	41	\(i_1	\(i_1	PROPN
bracis-19038	294	42	\subseteq	\subseteq	PROPN
bracis-19038	294	43	^{\exists	^{\exist	NOUN
bracis-19038	295	1	\forall	\forall	PRON
bracis-19038	295	2	}	}	PUNCT
bracis-19038	295	3	_	_	PUNCT
bracis-19038	295	4	x	x	SYM
bracis-19038	295	5	i_2\	i_2\	PRON
bracis-19038	295	6	)	)	PUNCT
bracis-19038	295	7	iff	iff	VERB
bracis-19038	295	8	\(i_1	\(i_1	PROPN
bracis-19038	295	9	\subseteq	\subseteq	PROPN
bracis-19038	295	10	^{\exists	^{\exist	VERB
bracis-19038	295	11	\exists	\exist	NOUN
bracis-19038	295	12	}	}	PUNCT
bracis-19038	295	13	_	_	PUNCT
bracis-19038	295	14	x	x	X
bracis-19038	295	15	i_2\	i_2\	PRON
bracis-19038	295	16	)	)	PUNCT
bracis-19038	295	17	and	and	CCONJ
bracis-19038	295	18	\(i_1	\(i_1	PROPN
bracis-19038	295	19	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	295	20	^{\forall	^{\forall	NOUN
bracis-19038	296	1	\forall	\forall	PRON
bracis-19038	296	2	}	}	PUNCT
bracis-19038	296	3	_	_	PUNCT
bracis-19038	296	4	x	x	SYM
bracis-19038	296	5	i_2\	i_2\	PRON
bracis-19038	296	6	)	)	PUNCT
bracis-19038	296	7	iff	iff	VERB
bracis-19038	296	8	\(i_1	\(i_1	PROPN
bracis-19038	296	9	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	296	10	^{\forall	^{\forall	DET
bracis-19038	296	11	\exists	\exist	NOUN
bracis-19038	296	12	}	}	PUNCT
bracis-19038	296	13	_	_	PUNCT
bracis-19038	296	14	x	x	SYM
bracis-19038	296	15	i_2\	i_2\	PRON
bracis-19038	296	16	)	)	PUNCT
bracis-19038	297	1	iff	iff	VERB
bracis-19038	297	2	\(i_1	\(i_1	PROPN
bracis-19038	297	3	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	297	4	^{\exists	^{\exist	VERB
bracis-19038	298	1	\forall	\forall	PRON
bracis-19038	298	2	}	}	PUNCT
bracis-19038	298	3	_	_	PUNCT
bracis-19038	298	4	x	x	SYM
bracis-19038	298	5	i_2\	i_2\	PRON
bracis-19038	298	6	)	)	PUNCT
bracis-19038	298	7	iff	iff	VERB
bracis-19038	298	8	\(i_1	\(i_1	PROPN
bracis-19038	298	9	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	298	10	^{\exists	^{\exist	VERB
bracis-19038	298	11	\exists	\exist	NOUN
bracis-19038	298	12	}	}	PUNCT
bracis-19038	298	13	_	_	PUNCT
bracis-19038	298	14	x	x	PUNCT
bracis-19038	298	15	i_2\	i_2\	PROPN
bracis-19038	298	16	):	):	PUNCT
bracis-19038	298	17	as	as	ADP
bracis-19038	298	18	\(\preceq	\(\preceq	X
bracis-19038	298	19	\	\	NOUN
bracis-19038	298	20	)	)	PUNCT
bracis-19038	298	21	in	in	ADP
bracis-19038	298	22	\(\varphi	\(\varphi	ADJ
bracis-19038	298	23	\	\	NOUN
bracis-19038	298	24	)	)	PUNCT
bracis-19038	298	25	is	be	AUX
bracis-19038	298	26	a	a	DET
bracis-19038	298	27	total	total	ADJ
bracis-19038	298	28	preorder	preorder	NOUN
bracis-19038	298	29	on	on	ADP
bracis-19038	298	30	\(\mathcal	\(\mathcal	ADJ
bracis-19038	298	31	{	{	PUNCT
bracis-19038	298	32	o}_p\	o}_p\	NOUN
bracis-19038	298	33	)	)	PUNCT
bracis-19038	298	34	,	,	PUNCT
bracis-19038	298	35	for	for	ADP
bracis-19038	298	36	each	each	DET
bracis-19038	298	37	\(o_1\	\(o_1\	NOUN
bracis-19038	298	38	)	)	PUNCT
bracis-19038	298	39	and	and	CCONJ
bracis-19038	298	40	\(o_2\	\(o_2\	VERB
bracis-19038	298	41	)	)	PUNCT
bracis-19038	298	42	in	in	ADP
bracis-19038	298	43	\(\mathcal	\(\mathcal	ADJ
bracis-19038	298	44	b_i\	b_i\	NOUN
bracis-19038	298	45	)	)	PUNCT
bracis-19038	298	46	and	and	CCONJ
bracis-19038	298	47	for	for	ADP
bracis-19038	298	48	each	each	DET
bracis-19038	298	49	\(o_1'\	\(o_1'\	NOUN
bracis-19038	298	50	)	)	PUNCT
bracis-19038	298	51	and	and	CCONJ
bracis-19038	298	52	\(o_2'\	\(o_2'\	NOUN
bracis-19038	298	53	)	)	PUNCT
bracis-19038	298	54	in	in	ADP
bracis-19038	298	55	\(\mathcal	\(\mathcal	ADJ
bracis-19038	298	56	w_i\	w_i\	NOUN
bracis-19038	298	57	)	)	PUNCT
bracis-19038	298	58	with	with	ADP
bracis-19038	298	59	\(i	\(i	PROPN
bracis-19038	298	60	\in	\in	PROPN
bracis-19038	298	61	\left\	\left\	PROPN
bracis-19038	298	62	{	{	PUNCT
bracis-19038	298	63	1,2\right\	1,2\right\	NUM
bracis-19038	298	64	}	}	PUNCT
bracis-19038	298	65	\	\	NOUN
bracis-19038	298	66	)	)	PUNCT
bracis-19038	298	67	,	,	PUNCT
bracis-19038	298	68	it	it	PRON
bracis-19038	298	69	holds	hold	VERB
bracis-19038	298	70	\(o_1	\(o_1	PROPN
bracis-19038	298	71	\approx	\approx	PROPN
bracis-19038	298	72	o_2\	o_2\	PROPN
bracis-19038	298	73	)	)	PUNCT
bracis-19038	298	74	and	and	CCONJ
bracis-19038	298	75	\(o_1	\(o_1	PROPN
bracis-19038	298	76	'	'	PART
bracis-19038	298	77	\approx	\approx	PROPN
bracis-19038	298	78	o_2'\	o_2'\	NUM
bracis-19038	298	79	)	)	PUNCT
bracis-19038	298	80	.	.	PUNCT
bracis-19038	299	1	let	let	VERB
bracis-19038	299	2	\(i	\(i	PRON
bracis-19038	299	3	\subseteq	\subseteq	PROPN
bracis-19038	299	4	^{\forall	^{\forall	NOUN
bracis-19038	300	1	\forall	\forall	DET
bracis-19038	300	2	}	}	PUNCT
bracis-19038	300	3	_	_	PUNCT
bracis-19038	300	4	x	x	SYM
bracis-19038	300	5	i'\	i'\	PROPN
bracis-19038	300	6	)	)	PUNCT
bracis-19038	300	7	;	;	PUNCT
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bracis-19038	300	9	are	be	VERB
bracis-19038	300	10	three	three	NUM
bracis-19038	300	11	possibilities	possibility	NOUN
bracis-19038	300	12	:	:	PUNCT
bracis-19038	300	13	1	1	X
bracis-19038	300	14	.	.	X
bracis-19038	301	1	\(i_2	\(i_2	NOUN
bracis-19038	301	2	=	=	SYM
bracis-19038	301	3	i_1\	i_1\	PROPN
bracis-19038	301	4	)	)	PUNCT
bracis-19038	301	5	.	.	PUNCT
bracis-19038	302	1	then	then	ADV
bracis-19038	302	2	\(i_1	\(i_1	PROPN
bracis-19038	302	3	\subseteq	\subseteq	PROPN
bracis-19038	302	4	^{\forall	^{\forall	PRON
bracis-19038	302	5	\exists	\exist	NOUN
bracis-19038	302	6	}	}	PUNCT
bracis-19038	302	7	_	_	PUNCT
bracis-19038	302	8	x	x	X
bracis-19038	302	9	i_2\	i_2\	PROPN
bracis-19038	302	10	)	)	PUNCT
bracis-19038	302	11	,	,	PUNCT
bracis-19038	302	12	\(i_1	\(i_1	PROPN
bracis-19038	302	13	\subseteq	\subseteq	PROPN
bracis-19038	302	14	^{\exists	^{\exist	NOUN
bracis-19038	302	15	\forall	\forall	PRON
bracis-19038	302	16	}	}	PUNCT
bracis-19038	302	17	_	_	PUNCT
bracis-19038	302	18	x	x	X
bracis-19038	302	19	i_2\	i_2\	PRON
bracis-19038	302	20	)	)	PUNCT
bracis-19038	302	21	and	and	CCONJ
bracis-19038	302	22	\(i_1	\(i_1	PROPN
bracis-19038	302	23	\subseteq	\subseteq	PROPN
bracis-19038	302	24	^{\exists	^{\exist	VERB
bracis-19038	302	25	\exists	\exist	NOUN
bracis-19038	302	26	}	}	PUNCT
bracis-19038	302	27	_	_	PUNCT
bracis-19038	302	28	x	x	X
bracis-19038	302	29	i_2\	i_2\	PROPN
bracis-19038	302	30	)	)	PUNCT
bracis-19038	302	31	.	.	PUNCT
bracis-19038	303	1	2	2	X
bracis-19038	303	2	.	.	X
bracis-19038	303	3	\(\forall	\(\forall	ADV
bracis-19038	303	4	o	o	X
bracis-19038	303	5	\in	\in	PROPN
bracis-19038	303	6	\mathcal	\mathcal	PROPN
bracis-19038	303	7	x\	x\	NOUN
bracis-19038	303	8	)	)	PUNCT
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bracis-19038	303	12	'	'	PUNCT
bracis-19038	303	13	\in	\in	PROPN
bracis-19038	303	14	\mathcal	\mathcal	PROPN
bracis-19038	303	15	y\	y\	NOUN
bracis-19038	303	16	)	)	PUNCT
bracis-19038	303	17	,	,	PUNCT
bracis-19038	303	18	it	it	PRON
bracis-19038	303	19	holds	hold	VERB
bracis-19038	303	20	\(o	\(o	NOUN
bracis-19038	303	21	'	'	PUNCT
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bracis-19038	303	23	\prec	\prec	ADP
bracis-19038	303	24	o	o	X
bracis-19038	303	25	\in	\in	PROPN
bracis-19038	303	26	\varphi	\varphi	PROPN
bracis-19038	303	27	\	\	NOUN
bracis-19038	303	28	)	)	PUNCT
bracis-19038	303	29	.	.	PUNCT
bracis-19038	304	1	then	then	ADV
bracis-19038	304	2	by	by	ADP
bracis-19038	304	3	proposition	proposition	NOUN
bracis-19038	304	4	2	2	NUM
bracis-19038	304	5	,	,	PUNCT
bracis-19038	304	6	a	a	PRON
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bracis-19038	304	8	\(\forall	\(\forall	ADV
bracis-19038	304	9	o	o	X
bracis-19038	304	10	\in	\in	PROPN
bracis-19038	304	11	\mathcal	\mathcal	PROPN
bracis-19038	304	12	x\	x\	NOUN
bracis-19038	304	13	)	)	PUNCT
bracis-19038	304	14	,	,	PUNCT
bracis-19038	304	15	it	it	PRON
bracis-19038	304	16	holds	hold	VERB
bracis-19038	304	17	\(\exists	\(\exist	NOUN
bracis-19038	304	18	o	o	NOUN
bracis-19038	304	19	'	'	PUNCT
bracis-19038	304	20	\in	\in	PROPN
bracis-19038	304	21	\mathcal	\mathcal	PROPN
bracis-19038	304	22	y\	y\	NOUN
bracis-19038	304	23	)	)	PUNCT
bracis-19038	304	24	such	such	ADJ
bracis-19038	304	25	that	that	SCONJ
bracis-19038	304	26	\(o	\(o	NOUN
bracis-19038	304	27	'	'	PUNCT
bracis-19038	304	28	\not	\not	ADV
bracis-19038	304	29	\prec	\prec	ADP
bracis-19038	304	30	o	o	X
bracis-19038	304	31	\in	\in	PROPN
bracis-19038	304	32	\varphi	\varphi	PROPN
bracis-19038	304	33	\	\	NOUN
bracis-19038	304	34	)	)	PUNCT
bracis-19038	304	35	and	and	CCONJ
bracis-19038	304	36	b	b	X
bracis-19038	304	37	)	)	PUNCT
bracis-19038	304	38	\(\exists	\(\exist	NOUN
bracis-19038	304	39	o	o	PROPN
bracis-19038	304	40	\in	\in	PROPN
bracis-19038	304	41	\mathcal	\mathcal	PROPN
bracis-19038	304	42	x\	x\	NOUN
bracis-19038	304	43	)	)	PUNCT
bracis-19038	304	44	such	such	ADJ
bracis-19038	304	45	that	that	SCONJ
bracis-19038	304	46	\(\forall	\(\forall	ADV
bracis-19038	304	47	o	o	NOUN
bracis-19038	304	48	'	'	PUNCT
bracis-19038	304	49	\in	\in	PROPN
bracis-19038	304	50	\mathcal	\mathcal	PROPN
bracis-19038	304	51	y\	y\	NOUN
bracis-19038	304	52	)	)	PUNCT
bracis-19038	304	53	,	,	PUNCT
bracis-19038	304	54	it	it	PRON
bracis-19038	304	55	holds	hold	VERB
bracis-19038	304	56	\(o	\(o	NOUN
bracis-19038	304	57	'	'	PUNCT
bracis-19038	304	58	\not	\not	ADV
bracis-19038	304	59	\prec	\prec	ADP
bracis-19038	304	60	o	o	X
bracis-19038	304	61	\in	\in	PROPN
bracis-19038	304	62	\varphi	\varphi	PROPN
bracis-19038	304	63	\	\	NOUN
bracis-19038	304	64	)	)	PUNCT
bracis-19038	304	65	and	and	CCONJ
bracis-19038	304	66	c	c	X
bracis-19038	304	67	)	)	PUNCT
bracis-19038	304	68	\(\exists	\(\exist	NOUN
bracis-19038	304	69	o	o	PROPN
bracis-19038	304	70	\in	\in	PROPN
bracis-19038	304	71	\mathcal	\mathcal	PROPN
bracis-19038	304	72	x\	x\	NOUN
bracis-19038	304	73	)	)	PUNCT
bracis-19038	304	74	and	and	CCONJ
bracis-19038	304	75	\(\exists	\(\exist	NOUN
bracis-19038	304	76	o	o	NOUN
bracis-19038	304	77	'	'	PUNCT
bracis-19038	304	78	\in	\in	PROPN
bracis-19038	304	79	\mathcal	\mathcal	PROPN
bracis-19038	304	80	y\	y\	NOUN
bracis-19038	304	81	)	)	PUNCT
bracis-19038	304	82	such	such	ADJ
bracis-19038	304	83	that	that	SCONJ
bracis-19038	304	84	\(o	\(o	NOUN
bracis-19038	304	85	'	'	PUNCT
bracis-19038	304	86	\not	\not	ADV
bracis-19038	304	87	\prec	\prec	ADP
bracis-19038	304	88	o	o	X
bracis-19038	304	89	\in	\in	PROPN
bracis-19038	304	90	\varphi	\varphi	PROPN
bracis-19038	304	91	\	\	NOUN
bracis-19038	304	92	)	)	PUNCT
bracis-19038	304	93	.	.	PUNCT
bracis-19038	305	1	hence	hence	ADV
bracis-19038	305	2	,	,	PUNCT
bracis-19038	305	3	\(i_1	\(i_1	PROPN
bracis-19038	305	4	\subseteq	\subseteq	PROPN
bracis-19038	305	5	^{\forall	^{\forall	PRON
bracis-19038	305	6	\exists	\exist	NOUN
bracis-19038	305	7	}	}	PUNCT
bracis-19038	305	8	_	_	PUNCT
bracis-19038	305	9	x	x	X
bracis-19038	305	10	i_2\	i_2\	PRON
bracis-19038	305	11	)	)	PUNCT
bracis-19038	305	12	and	and	CCONJ
bracis-19038	305	13	\(i_1	\(i_1	PROPN
bracis-19038	305	14	\subseteq	\subseteq	PROPN
bracis-19038	305	15	^{\exists	^{\exist	NOUN
bracis-19038	305	16	\forall	\forall	DET
bracis-19038	305	17	}	}	PUNCT
bracis-19038	305	18	_	_	PUNCT
bracis-19038	305	19	x	x	X
bracis-19038	305	20	i_2\	i_2\	PRON
bracis-19038	305	21	)	)	PUNCT
bracis-19038	305	22	and	and	CCONJ
bracis-19038	305	23	\(i_1	\(i_1	PROPN
bracis-19038	305	24	\subseteq	\subseteq	PROPN
bracis-19038	305	25	^{\exists	^{\exist	VERB
bracis-19038	305	26	\exists	\exist	NOUN
bracis-19038	305	27	}	}	PUNCT
bracis-19038	305	28	_	_	PUNCT
bracis-19038	305	29	x	x	X
bracis-19038	305	30	i_2\	i_2\	PROPN
bracis-19038	305	31	)	)	PUNCT
bracis-19038	305	32	.	.	PUNCT
bracis-19038	306	1	3	3	X
bracis-19038	306	2	.	.	X
bracis-19038	307	1	\(i_1	\(i_1	NUM
bracis-19038	307	2	\subseteq	\subseteq	PROPN
bracis-19038	307	3	^{\forall	^{\forall	NOUN
bracis-19038	308	1	\forall	\forall	PRON
bracis-19038	308	2	}	}	PUNCT
bracis-19038	309	1	_	_	PUNCT
bracis-19038	309	2	x	x	X
bracis-19038	309	3	i\	i\	NOUN
bracis-19038	309	4	)	)	PUNCT
bracis-19038	309	5	and	and	CCONJ
bracis-19038	309	6	\(i	\(i	NOUN
bracis-19038	309	7	\subseteq	\subseteq	PROPN
bracis-19038	309	8	^{\forall	^{\forall	NOUN
bracis-19038	310	1	\forall	\forall	PRON
bracis-19038	310	2	}	}	PUNCT
bracis-19038	310	3	_	_	PUNCT
bracis-19038	310	4	x	x	SYM
bracis-19038	311	1	i_2\).this	i_2\).this	NOUN
bracis-19038	311	2	means	mean	VERB
bracis-19038	311	3	there	there	PRON
bracis-19038	311	4	exists	exist	VERB
bracis-19038	311	5	a	a	DET
bracis-19038	311	6	sequence	sequence	NOUN
bracis-19038	312	1	$	$	SYM
bracis-19038	312	2	$	$	SYM
bracis-19038	312	3	\begin{aligned	\begin{aligne	VERB
bracis-19038	312	4	}	}	PUNCT
bracis-19038	312	5	i_1	i_1	NOUN
bracis-19038	312	6	=	=	SYM
bracis-19038	312	7	j_1	j_1	NOUN
bracis-19038	312	8	\subseteq	\subseteq	INTJ
bracis-19038	312	9	^{\forall	^{\forall	NOUN
bracis-19038	313	1	\forall	\forall	PRON
bracis-19038	314	1	}	}	PUNCT
bracis-19038	314	2	_	_	PUNCT
bracis-19038	314	3	x	x	PUNCT
bracis-19038	314	4	j_2	j_2	PROPN
bracis-19038	314	5	\subseteq	\subseteq	INTJ
bracis-19038	314	6	^{\forall	^{\forall	NOUN
bracis-19038	315	1	\forall	\forall	PRON
bracis-19038	315	2	}	}	PUNCT
bracis-19038	315	3	_	_	PUNCT
bracis-19038	315	4	x	x	SYM
bracis-19038	315	5	\cdots	\cdot	NOUN
bracis-19038	315	6	\subseteq	\subseteq	PROPN
bracis-19038	315	7	^{\forall	^{\forall	NOUN
bracis-19038	316	1	\forall	\forall	PRON
bracis-19038	316	2	}	}	PUNCT
bracis-19038	316	3	_	_	PUNCT
bracis-19038	316	4	x	x	X
bracis-19038	316	5	j_m	j_m	PUNCT
bracis-19038	317	1	=	=	PUNCT
bracis-19038	317	2	i	i	PRON
bracis-19038	317	3	\subseteq	\subseteq	VERB
bracis-19038	317	4	^{\forall	^{\forall	NOUN
bracis-19038	317	5	\forall	\forall	PRON
bracis-19038	317	6	}	}	PUNCT
bracis-19038	317	7	_	_	PUNCT
bracis-19038	317	8	x	x	X
bracis-19038	317	9	j_{m+1	j_{m+1	PROPN
bracis-19038	317	10	}	}	PUNCT
bracis-19038	317	11	\subseteq	\subseteq	PROPN
bracis-19038	317	12	^{\forall	^{\forall	NOUN
bracis-19038	318	1	\forall	\forall	PRON
bracis-19038	318	2	}	}	PUNCT
bracis-19038	318	3	_	_	PUNCT
bracis-19038	318	4	x	x	SYM
bracis-19038	318	5	\cdots	\cdot	NOUN
bracis-19038	318	6	\subseteq	\subseteq	PROPN
bracis-19038	318	7	^{\forall	^{\forall	NOUN
bracis-19038	319	1	\forall	\forall	PRON
bracis-19038	319	2	}	}	PUNCT
bracis-19038	319	3	_	_	PUNCT
bracis-19038	319	4	x	x	X
bracis-19038	319	5	j_n	j_n	PUNCT
bracis-19038	320	1	=	=	NOUN
bracis-19038	320	2	i_2	i_2	VERB
bracis-19038	320	3	\end{aligned}$$	\end{aligned}$$	PRON
bracis-19038	321	1	such	such	ADJ
bracis-19038	321	2	that	that	SCONJ
bracis-19038	321	3	\(\forall	\(\forall	ADV
bracis-19038	321	4	i	i	PRON
bracis-19038	321	5	\in	\in	PROPN
bracis-19038	321	6	\left\	\left\	PROPN
bracis-19038	321	7	{	{	PUNCT
bracis-19038	321	8	1	1	NUM
bracis-19038	321	9	,	,	PUNCT
bracis-19038	321	10	\ldots	\ldots	INTJ
bracis-19038	321	11	,	,	PUNCT
bracis-19038	321	12	n	n	PRON
bracis-19038	321	13	1\right\	1\right\	ADJ
bracis-19038	321	14	}	}	PUNCT
bracis-19038	321	15	\	\	NOUN
bracis-19038	321	16	)	)	PUNCT
bracis-19038	321	17	,	,	PUNCT
bracis-19038	321	18	we	we	PRON
bracis-19038	321	19	have	have	VERB
bracis-19038	321	20	\(j_1	\(j_1	PROPN
bracis-19038	321	21	\subseteq	\subseteq	PROPN
bracis-19038	321	22	^{\forall	^{\forall	NOUN
bracis-19038	322	1	\forall	\forall	PRON
bracis-19038	322	2	}	}	PUNCT
bracis-19038	322	3	_	_	PUNCT
bracis-19038	322	4	x	x	X
bracis-19038	322	5	j_2\	j_2\	PROPN
bracis-19038	322	6	)	)	PUNCT
bracis-19038	323	1	iff	iff	VERB
bracis-19038	323	2	the	the	DET
bracis-19038	323	3	condition	condition	NOUN
bracis-19038	323	4	2	2	NUM
bracis-19038	323	5	of	of	ADP
bracis-19038	323	6	definition	definition	NOUN
bracis-19038	323	7	10	10	NUM
bracis-19038	323	8	holds	hold	NOUN
bracis-19038	323	9	.	.	PUNCT
bracis-19038	324	1	again	again	ADV
bracis-19038	324	2	by	by	ADP
bracis-19038	324	3	proposition	proposition	NOUN
bracis-19038	324	4	2	2	NUM
bracis-19038	324	5	,	,	PUNCT
bracis-19038	324	6	condition	condition	NOUN
bracis-19038	324	7	2	2	NUM
bracis-19038	324	8	of	of	ADP
bracis-19038	324	9	definition	definition	NOUN
bracis-19038	324	10	10	10	NUM
bracis-19038	324	11	also	also	ADV
bracis-19038	324	12	holds	hold	VERB
bracis-19038	324	13	for	for	ADP
bracis-19038	324	14	\(j_1	\(j_1	PROPN
bracis-19038	324	15	\subseteq	\subseteq	PROPN
bracis-19038	324	16	^{\forall	^{\forall	DET
bracis-19038	324	17	\exists	\exist	NOUN
bracis-19038	324	18	}	}	PUNCT
bracis-19038	324	19	_	_	PUNCT
bracis-19038	324	20	x	x	X
bracis-19038	324	21	j_2\	j_2\	PROPN
bracis-19038	324	22	)	)	PUNCT
bracis-19038	324	23	,	,	PUNCT
bracis-19038	324	24	\(j_1	\(j_1	PROPN
bracis-19038	324	25	\subseteq	\subseteq	PROPN
bracis-19038	324	26	^{\exists	^{\exist	NOUN
bracis-19038	324	27	\forall	\forall	PRON
bracis-19038	324	28	}	}	PUNCT
bracis-19038	324	29	_	_	PUNCT
bracis-19038	324	30	x	x	X
bracis-19038	324	31	j_2\	j_2\	PROPN
bracis-19038	324	32	)	)	PUNCT
bracis-19038	324	33	and	and	CCONJ
bracis-19038	324	34	\(j_1	\(j_1	NUM
bracis-19038	324	35	\subseteq	\subseteq	PROPN
bracis-19038	324	36	^{\exists	^{\exist	VERB
bracis-19038	324	37	\exists	\exist	NOUN
bracis-19038	324	38	}	}	PUNCT
bracis-19038	324	39	_	_	PUNCT
bracis-19038	324	40	x	x	X
bracis-19038	324	41	j_2\	j_2\	PROPN
bracis-19038	324	42	)	)	PUNCT
bracis-19038	324	43	for	for	ADP
bracis-19038	324	44	each	each	DET
bracis-19038	324	45	\(i	\(i	NOUN
bracis-19038	324	46	\in	\in	PROPN
bracis-19038	324	47	\left\	\left\	PROPN
bracis-19038	324	48	{	{	PUNCT
bracis-19038	324	49	1	1	NUM
bracis-19038	324	50	,	,	PUNCT
bracis-19038	324	51	\ldots	\ldots	INTJ
bracis-19038	324	52	,	,	PUNCT
bracis-19038	324	53	n	n	PRON
bracis-19038	324	54	1\right\	1\right\	ADJ
bracis-19038	324	55	}	}	PUNCT
bracis-19038	324	56	\	\	NOUN
bracis-19038	324	57	)	)	PUNCT
bracis-19038	324	58	.	.	PUNCT
bracis-19038	325	1	hence	hence	ADV
bracis-19038	325	2	,	,	PUNCT
bracis-19038	325	3	by	by	ADP
bracis-19038	325	4	condition	condition	NOUN
bracis-19038	325	5	3	3	NUM
bracis-19038	325	6	of	of	ADP
bracis-19038	325	7	definition	definition	NOUN
bracis-19038	325	8	10	10	NUM
bracis-19038	325	9	,	,	PUNCT
bracis-19038	325	10	we	we	PRON
bracis-19038	325	11	obtain	obtain	VERB
bracis-19038	325	12	\(i_1	\(i_1	PROPN
bracis-19038	325	13	\subseteq	\subseteq	PROPN
bracis-19038	325	14	^{\forall	^{\forall	DET
bracis-19038	325	15	\exists	\exist	NOUN
bracis-19038	325	16	}	}	PUNCT
bracis-19038	325	17	_	_	PUNCT
bracis-19038	325	18	x	x	X
bracis-19038	325	19	i_2\	i_2\	PRON
bracis-19038	325	20	)	)	PUNCT
bracis-19038	325	21	and	and	CCONJ
bracis-19038	325	22	\(i_1	\(i_1	PROPN
bracis-19038	325	23	\subseteq	\subseteq	PROPN
bracis-19038	325	24	^{\exists	^{\exist	NOUN
bracis-19038	325	25	\forall	\forall	PRON
bracis-19038	325	26	}	}	PUNCT
bracis-19038	325	27	_	_	PUNCT
bracis-19038	325	28	x	x	X
bracis-19038	325	29	i_2\	i_2\	PRON
bracis-19038	325	30	)	)	PUNCT
bracis-19038	325	31	and	and	CCONJ
bracis-19038	325	32	\(i_1	\(i_1	PROPN
bracis-19038	325	33	\subseteq	\subseteq	PROPN
bracis-19038	325	34	^{\exists	^{\exist	VERB
bracis-19038	325	35	\exists	\exist	NOUN
bracis-19038	325	36	}	}	PUNCT
bracis-19038	325	37	_	_	PUNCT
bracis-19038	325	38	x	x	X
bracis-19038	325	39	i_2\	i_2\	PROPN
bracis-19038	325	40	)	)	PUNCT
bracis-19038	325	41	.	.	PUNCT
bracis-19038	326	1	similarly	similarly	ADV
bracis-19038	326	2	for	for	ADP
bracis-19038	326	3	\(i_1	\(i_1	PROPN
bracis-19038	326	4	\subseteq	\subseteq	PROPN
bracis-19038	326	5	^{\forall	^{\forall	PRON
bracis-19038	326	6	\exists	\exist	NOUN
bracis-19038	326	7	}	}	PUNCT
bracis-19038	326	8	_	_	PUNCT
bracis-19038	326	9	x	x	X
bracis-19038	326	10	i_2\	i_2\	PROPN
bracis-19038	326	11	)	)	PUNCT
bracis-19038	326	12	,	,	PUNCT
bracis-19038	326	13	\(i_1	\(i_1	PROPN
bracis-19038	326	14	\subseteq	\subseteq	PROPN
bracis-19038	326	15	^{\exists	^{\exist	NOUN
bracis-19038	326	16	\forall	\forall	PRON
bracis-19038	326	17	}	}	PUNCT
bracis-19038	326	18	_	_	PUNCT
bracis-19038	326	19	x	x	X
bracis-19038	326	20	i_2\	i_2\	PRON
bracis-19038	326	21	)	)	PUNCT
bracis-19038	326	22	and	and	CCONJ
bracis-19038	326	23	\(i_1	\(i_1	PROPN
bracis-19038	326	24	\subseteq	\subseteq	PROPN
bracis-19038	326	25	^{\exists	^{\exist	VERB
bracis-19038	326	26	\exists	\exist	NOUN
bracis-19038	326	27	}	}	PUNCT
bracis-19038	326	28	_	_	PUNCT
bracis-19038	326	29	x	x	X
bracis-19038	326	30	i_2\	i_2\	PROPN
bracis-19038	326	31	)	)	PUNCT
bracis-19038	326	32	.	.	PUNCT
bracis-19038	327	1	the	the	DET
bracis-19038	327	2	proof	proof	NOUN
bracis-19038	327	3	of	of	ADP
bracis-19038	327	4	\(i_1	\(i_1	PROPN
bracis-19038	327	5	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	327	6	^{\forall	^{\forall	NOUN
bracis-19038	328	1	\forall	\forall	PRON
bracis-19038	328	2	}	}	PUNCT
bracis-19038	328	3	_	_	PUNCT
bracis-19038	328	4	x	x	SYM
bracis-19038	328	5	i_2\	i_2\	PRON
bracis-19038	328	6	)	)	PUNCT
bracis-19038	328	7	iff	iff	VERB
bracis-19038	328	8	\(i_1	\(i_1	PROPN
bracis-19038	328	9	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	328	10	^{\forall	^{\forall	DET
bracis-19038	328	11	\exists	\exist	NOUN
bracis-19038	328	12	}	}	PUNCT
bracis-19038	328	13	_	_	PUNCT
bracis-19038	328	14	x	x	SYM
bracis-19038	328	15	i_2\	i_2\	PRON
bracis-19038	328	16	)	)	PUNCT
bracis-19038	329	1	iff	iff	VERB
bracis-19038	329	2	\(i_1	\(i_1	PROPN
bracis-19038	329	3	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	329	4	^{\exists	^{\exist	VERB
bracis-19038	330	1	\forall	\forall	PRON
bracis-19038	330	2	}	}	PUNCT
bracis-19038	330	3	_	_	PUNCT
bracis-19038	330	4	x	x	SYM
bracis-19038	330	5	i_2\	i_2\	PRON
bracis-19038	330	6	)	)	PUNCT
bracis-19038	330	7	iff	iff	VERB
bracis-19038	330	8	\(i_1	\(i_1	PROPN
bracis-19038	330	9	\sqsubseteq	\sqsubseteq	PROPN
bracis-19038	330	10	^{\exists	^{\exist	VERB
bracis-19038	330	11	\exists	\exist	NOUN
bracis-19038	330	12	}	}	PUNCT
bracis-19038	330	13	_	_	PUNCT
bracis-19038	330	14	x	x	X
bracis-19038	330	15	i_2\	i_2\	PROPN
bracis-19038	330	16	)	)	PUNCT
bracis-19038	330	17	is	be	AUX
bracis-19038	330	18	similar	similar	ADJ
bracis-19038	330	19	.	.	PUNCT
bracis-19038	330	20	   	   	SPACE
bracis-19038	330	21	\(\square	\(\square	VERB
bracis-19038	330	22	\	\	NOUN
bracis-19038	330	23	)	)	PUNCT
bracis-19038	330	24	corollary	corollary	ADJ
bracis-19038	330	25	1	1	NUM
bracis-19038	330	26	let	let	VERB
bracis-19038	330	27	\((p	\((p	NOUN
bracis-19038	330	28	,	,	PUNCT
bracis-19038	330	29	\varphi	\varphi	PROPN
bracis-19038	330	30	)	)	PUNCT
bracis-19038	330	31	\	\	NOUN
bracis-19038	330	32	)	)	PUNCT
bracis-19038	330	33	be	be	AUX
bracis-19038	330	34	a	a	DET
bracis-19038	330	35	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	330	36	)	)	PUNCT
bracis-19038	330	37	such	such	ADJ
bracis-19038	330	38	that	that	SCONJ
bracis-19038	330	39	the	the	DET
bracis-19038	330	40	preference	preference	NOUN
bracis-19038	330	41	relation	relation	NOUN
bracis-19038	330	42	\(\preceq	\(\preceq	X
bracis-19038	330	43	\	\	PROPN
bracis-19038	330	44	)	)	PUNCT
bracis-19038	330	45	in	in	ADP
bracis-19038	330	46	\(\varphi	\(\varphi	ADJ
bracis-19038	330	47	\	\	NOUN
bracis-19038	330	48	)	)	PUNCT
bracis-19038	330	49	is	be	AUX
bracis-19038	330	50	a	a	DET
bracis-19038	330	51	total	total	ADJ
bracis-19038	330	52	preorder	preorder	NOUN
bracis-19038	330	53	on	on	ADP
bracis-19038	330	54	\(\mathcal	\(\mathcal	ADJ
bracis-19038	330	55	{	{	PUNCT
bracis-19038	330	56	o}_p\	o}_p\	NOUN
bracis-19038	330	57	)	)	PUNCT
bracis-19038	330	58	.	.	PUNCT
bracis-19038	331	1	then	then	ADV
bracis-19038	331	2	\(\forall	\(\forall	ADV
bracis-19038	331	3	x	x	X
bracis-19038	331	4	\in	\in	PROPN
bracis-19038	331	5	\left\	\left\	PROPN
bracis-19038	331	6	{	{	PUNCT
bracis-19038	331	7	st	st	PROPN
bracis-19038	331	8	,	,	PUNCT
bracis-19038	331	9	opt	opt	NOUN
bracis-19038	331	10	,	,	PUNCT
bracis-19038	331	11	pes	pe	NOUN
bracis-19038	331	12	,	,	PUNCT
bracis-19038	331	13	opp	opp	PROPN
bracis-19038	331	14	\right\	\right\	ADV
bracis-19038	331	15	}	}	PUNCT
bracis-19038	331	16	\	\	NOUN
bracis-19038	331	17	)	)	PUNCT
bracis-19038	331	18	,	,	PUNCT
bracis-19038	331	19	and	and	CCONJ
bracis-19038	331	20	\(\forall	\(\forall	ADV
bracis-19038	331	21	y	y	PROPN
bracis-19038	331	22	,	,	PUNCT
bracis-19038	331	23	\forall	\forall	DET
bracis-19038	331	24	z	z	PROPN
bracis-19038	331	25	\in	\in	PROPN
bracis-19038	331	26	\left\	\left\	PROPN
bracis-19038	331	27	{	{	PUNCT
bracis-19038	331	28	\forall	\forall	INTJ
bracis-19038	331	29	\forall	\forall	INTJ
bracis-19038	331	30	,	,	PUNCT
bracis-19038	331	31	\forall	\forall	DET
bracis-19038	331	32	\exists	\exist	NOUN
bracis-19038	331	33	,	,	PUNCT
bracis-19038	331	34	\exists	\exist	NOUN
bracis-19038	331	35	\forall	\forall	ADV
bracis-19038	331	36	,	,	PUNCT
bracis-19038	331	37	\exists	\exist	VERB
bracis-19038	331	38	\exists	\exist	NOUN
bracis-19038	331	39	\right\	\right\	ADV
bracis-19038	331	40	}	}	PUNCT
bracis-19038	331	41	\	\	NOUN
bracis-19038	331	42	)	)	PUNCT
bracis-19038	332	1	i	i	PRON
bracis-19038	332	2	is	be	AUX
bracis-19038	332	3	a	a	DET
bracis-19038	332	4	preferential	preferential	ADJ
bracis-19038	332	5	well	well	ADV
bracis-19038	332	6	-	-	PUNCT
bracis-19038	332	7	founded	found	VERB
bracis-19038	332	8	model	model	NOUN
bracis-19038	332	9	of	of	ADP
bracis-19038	332	10	\((p	\((p	NOUN
bracis-19038	332	11	,	,	PUNCT
bracis-19038	332	12	\varphi	\varphi	PROPN
bracis-19038	332	13	)	)	PUNCT
bracis-19038	332	14	\	\	NOUN
bracis-19038	332	15	)	)	PUNCT
bracis-19038	332	16	w.r.t	w.r.t	NOUN
bracis-19038	332	17	.	.	PUNCT
bracis-19038	332	18	\(\subseteq	\(\subseteq	PROPN
bracis-19038	332	19	^y_x\	^y_x\	NUM
bracis-19038	332	20	)	)	PUNCT
bracis-19038	332	21	(	(	PUNCT
bracis-19038	332	22	resp	resp	NOUN
bracis-19038	332	23	.	.	PUNCT
bracis-19038	332	24	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	332	25	^y_x\	^y_x\	NUM
bracis-19038	332	26	)	)	PUNCT
bracis-19038	332	27	)	)	PUNCT
bracis-19038	333	1	iff	iff	PROPN
bracis-19038	333	2	i	i	PRON
bracis-19038	333	3	is	be	AUX
bracis-19038	333	4	a	a	DET
bracis-19038	333	5	preferential	preferential	ADJ
bracis-19038	333	6	well	well	ADV
bracis-19038	333	7	-	-	PUNCT
bracis-19038	333	8	founded	found	VERB
bracis-19038	333	9	model	model	NOUN
bracis-19038	333	10	of	of	ADP
bracis-19038	333	11	\((p	\((p	NOUN
bracis-19038	333	12	,	,	PUNCT
bracis-19038	333	13	\varphi	\varphi	PROPN
bracis-19038	333	14	)	)	PUNCT
bracis-19038	333	15	\	\	NOUN
bracis-19038	333	16	)	)	PUNCT
bracis-19038	333	17	w.r.t	w.r.t	NOUN
bracis-19038	333	18	.	.	PUNCT
bracis-19038	334	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	334	2	^z_x\	^z_x\	NUM
bracis-19038	334	3	)	)	PUNCT
bracis-19038	334	4	(	(	PUNCT
bracis-19038	334	5	resp	resp	NOUN
bracis-19038	334	6	.	.	PUNCT
bracis-19038	335	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	335	2	^z_x\	^z_x\	NUM
bracis-19038	335	3	)	)	PUNCT
bracis-19038	335	4	)	)	PUNCT
bracis-19038	336	1	;	;	PUNCT
bracis-19038	336	2	i	i	PRON
bracis-19038	336	3	is	be	AUX
bracis-19038	336	4	a	a	DET
bracis-19038	336	5	preferential	preferential	ADJ
bracis-19038	336	6	regular	regular	ADJ
bracis-19038	336	7	model	model	NOUN
bracis-19038	336	8	of	of	ADP
bracis-19038	336	9	\((p	\((p	NOUN
bracis-19038	336	10	,	,	PUNCT
bracis-19038	336	11	\varphi	\varphi	PROPN
bracis-19038	336	12	)	)	PUNCT
bracis-19038	336	13	\	\	NOUN
bracis-19038	336	14	)	)	PUNCT
bracis-19038	336	15	w.r.t	w.r.t	NOUN
bracis-19038	336	16	.	.	PUNCT
bracis-19038	337	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	337	2	^y_x\	^y_x\	NUM
bracis-19038	337	3	)	)	PUNCT
bracis-19038	337	4	(	(	PUNCT
bracis-19038	337	5	resp	resp	NOUN
bracis-19038	337	6	.	.	PUNCT
bracis-19038	338	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	338	2	^y_x\	^y_x\	NUM
bracis-19038	338	3	)	)	PUNCT
bracis-19038	338	4	)	)	PUNCT
bracis-19038	339	1	iff	iff	PROPN
bracis-19038	339	2	i	i	PRON
bracis-19038	339	3	is	be	AUX
bracis-19038	339	4	a	a	DET
bracis-19038	339	5	preferential	preferential	ADJ
bracis-19038	339	6	regular	regular	ADJ
bracis-19038	339	7	model	model	NOUN
bracis-19038	339	8	of	of	ADP
bracis-19038	339	9	\((p	\((p	NOUN
bracis-19038	339	10	,	,	PUNCT
bracis-19038	339	11	\varphi	\varphi	PROPN
bracis-19038	339	12	)	)	PUNCT
bracis-19038	339	13	\	\	NOUN
bracis-19038	339	14	)	)	PUNCT
bracis-19038	339	15	w.r.t	w.r.t	NOUN
bracis-19038	339	16	.	.	PUNCT
bracis-19038	340	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	340	2	^z_x\	^z_x\	NUM
bracis-19038	340	3	)	)	PUNCT
bracis-19038	340	4	(	(	PUNCT
bracis-19038	340	5	resp	resp	NOUN
bracis-19038	340	6	.	.	PUNCT
bracis-19038	341	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	341	2	^z_x\	^z_x\	NUM
bracis-19038	341	3	)	)	PUNCT
bracis-19038	341	4	)	)	PUNCT
bracis-19038	342	1	;	;	PUNCT
bracis-19038	342	2	i	i	PRON
bracis-19038	342	3	is	be	AUX
bracis-19038	342	4	a	a	DET
bracis-19038	342	5	preferential	preferential	ADJ
bracis-19038	342	6	stable	stable	ADJ
bracis-19038	342	7	model	model	NOUN
bracis-19038	342	8	of	of	ADP
bracis-19038	342	9	\((p	\((p	NOUN
bracis-19038	342	10	,	,	PUNCT
bracis-19038	342	11	\varphi	\varphi	PROPN
bracis-19038	342	12	)	)	PUNCT
bracis-19038	342	13	\	\	NOUN
bracis-19038	342	14	)	)	PUNCT
bracis-19038	342	15	w.r.t	w.r.t	NOUN
bracis-19038	342	16	.	.	PUNCT
bracis-19038	343	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	343	2	^y_x\	^y_x\	NUM
bracis-19038	343	3	)	)	PUNCT
bracis-19038	343	4	(	(	PUNCT
bracis-19038	343	5	resp	resp	NOUN
bracis-19038	343	6	.	.	PUNCT
bracis-19038	344	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	344	2	^y_x\	^y_x\	NUM
bracis-19038	344	3	)	)	PUNCT
bracis-19038	344	4	)	)	PUNCT
bracis-19038	345	1	iff	iff	PROPN
bracis-19038	345	2	i	i	PRON
bracis-19038	345	3	is	be	AUX
bracis-19038	345	4	a	a	DET
bracis-19038	345	5	preferential	preferential	ADJ
bracis-19038	345	6	stable	stable	ADJ
bracis-19038	345	7	model	model	NOUN
bracis-19038	345	8	of	of	ADP
bracis-19038	345	9	\((p	\((p	NOUN
bracis-19038	345	10	,	,	PUNCT
bracis-19038	345	11	\varphi	\varphi	PROPN
bracis-19038	345	12	)	)	PUNCT
bracis-19038	345	13	\	\	NOUN
bracis-19038	345	14	)	)	PUNCT
bracis-19038	345	15	w.r.t	w.r.t	NOUN
bracis-19038	345	16	.	.	PUNCT
bracis-19038	346	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	346	2	^z_x\	^z_x\	NUM
bracis-19038	346	3	)	)	PUNCT
bracis-19038	346	4	(	(	PUNCT
bracis-19038	346	5	resp	resp	NOUN
bracis-19038	346	6	.	.	PUNCT
bracis-19038	347	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	347	2	^z_x\	^z_x\	NUM
bracis-19038	347	3	)	)	PUNCT
bracis-19038	347	4	)	)	PUNCT
bracis-19038	348	1	;	;	PUNCT
bracis-19038	348	2	i	i	PRON
bracis-19038	348	3	is	be	AUX
bracis-19038	348	4	a	a	DET
bracis-19038	348	5	preferential	preferential	ADJ
bracis-19038	348	6	l	l	ADJ
bracis-19038	348	7	-	-	ADJ
bracis-19038	348	8	stable	stable	ADJ
bracis-19038	348	9	model	model	NOUN
bracis-19038	348	10	of	of	ADP
bracis-19038	348	11	\((p	\((p	NOUN
bracis-19038	348	12	,	,	PUNCT
bracis-19038	348	13	\varphi	\varphi	PROPN
bracis-19038	348	14	)	)	PUNCT
bracis-19038	348	15	\	\	NOUN
bracis-19038	348	16	)	)	PUNCT
bracis-19038	348	17	w.r.t	w.r.t	NOUN
bracis-19038	348	18	.	.	PUNCT
bracis-19038	349	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	349	2	^y_x\	^y_x\	NUM
bracis-19038	349	3	)	)	PUNCT
bracis-19038	349	4	(	(	PUNCT
bracis-19038	349	5	resp	resp	NOUN
bracis-19038	349	6	.	.	PUNCT
bracis-19038	350	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	350	2	^y_x\	^y_x\	NUM
bracis-19038	350	3	)	)	PUNCT
bracis-19038	350	4	)	)	PUNCT
bracis-19038	351	1	iff	iff	PROPN
bracis-19038	351	2	i	i	PRON
bracis-19038	351	3	is	be	AUX
bracis-19038	351	4	a	a	DET
bracis-19038	351	5	preferential	preferential	ADJ
bracis-19038	351	6	l	l	ADJ
bracis-19038	351	7	-	-	ADJ
bracis-19038	351	8	stable	stable	ADJ
bracis-19038	351	9	model	model	NOUN
bracis-19038	351	10	of	of	ADP
bracis-19038	351	11	\((p	\((p	NOUN
bracis-19038	351	12	,	,	PUNCT
bracis-19038	351	13	\varphi	\varphi	PROPN
bracis-19038	351	14	)	)	PUNCT
bracis-19038	351	15	\	\	NOUN
bracis-19038	351	16	)	)	PUNCT
bracis-19038	351	17	w.r.t	w.r.t	NOUN
bracis-19038	351	18	.	.	PUNCT
bracis-19038	352	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	352	2	^z_x\	^z_x\	NUM
bracis-19038	352	3	)	)	PUNCT
bracis-19038	352	4	(	(	PUNCT
bracis-19038	352	5	resp	resp	NOUN
bracis-19038	352	6	.	.	PUNCT
bracis-19038	353	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	353	2	^z_x\	^z_x\	NUM
bracis-19038	353	3	)	)	PUNCT
bracis-19038	353	4	)	)	PUNCT
bracis-19038	353	5	.	.	PUNCT
bracis-19038	354	1	proof	proof	NOUN
bracis-19038	354	2	it	it	PRON
bracis-19038	354	3	follows	follow	VERB
bracis-19038	354	4	from	from	ADP
bracis-19038	354	5	theorem	theorem	ADJ
bracis-19038	354	6	1	1	NUM
bracis-19038	354	7	and	and	CCONJ
bracis-19038	354	8	definition	definition	NOUN
bracis-19038	354	9	12	12	NUM
bracis-19038	354	10	.	.	PUNCT
bracis-19038	354	11	   	   	SPACE
bracis-19038	354	12	\(\square	\(\square	VERB
bracis-19038	354	13	\	\	NOUN
bracis-19038	354	14	)	)	PUNCT
bracis-19038	354	15	when	when	SCONJ
bracis-19038	354	16	no	no	DET
bracis-19038	354	17	priority	priority	NOUN
bracis-19038	354	18	is	be	AUX
bracis-19038	354	19	available	available	ADJ
bracis-19038	354	20	(	(	PUNCT
bracis-19038	354	21	\(\varphi	\(\varphi	NOUN
bracis-19038	354	22	=	=	SYM
bracis-19038	354	23	\emptyset	\emptyset	VERB
bracis-19038	354	24	\	\	NOUN
bracis-19038	354	25	)	)	PUNCT
bracis-19038	354	26	)	)	PUNCT
bracis-19038	354	27	,	,	PUNCT
bracis-19038	354	28	the	the	DET
bracis-19038	354	29	semantics	semantic	NOUN
bracis-19038	354	30	for	for	ADP
bracis-19038	354	31	\((p	\((p	NOUN
bracis-19038	354	32	,	,	PUNCT
bracis-19038	354	33	\varphi	\varphi	PROPN
bracis-19038	354	34	)	)	PUNCT
bracis-19038	354	35	\	\	NOUN
bracis-19038	354	36	)	)	PUNCT
bracis-19038	354	37	collapse	collapse	NOUN
bracis-19038	354	38	into	into	ADP
bracis-19038	354	39	the	the	DET
bracis-19038	354	40	semantics	semantic	NOUN
bracis-19038	354	41	for	for	ADP
bracis-19038	354	42	p	p	NOUN
bracis-19038	354	43	(	(	PUNCT
bracis-19038	354	44	and	and	CCONJ
bracis-19038	354	45	vice	vice	ADV
bracis-19038	354	46	versa	versa	ADV
bracis-19038	354	47	):	):	PUNCT
bracis-19038	354	48	theorem	theorem	ADJ
bracis-19038	354	49	2	2	NUM
bracis-19038	354	50	let	let	VERB
bracis-19038	354	51	\((p	\((p	NOUN
bracis-19038	354	52	,	,	PUNCT
bracis-19038	354	53	\varphi	\varphi	PROPN
bracis-19038	354	54	)	)	PUNCT
bracis-19038	354	55	\	\	NOUN
bracis-19038	354	56	)	)	PUNCT
bracis-19038	354	57	be	be	AUX
bracis-19038	354	58	a	a	DET
bracis-19038	354	59	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	354	60	)	)	PUNCT
bracis-19038	355	1	such	such	ADJ
bracis-19038	355	2	that	that	SCONJ
bracis-19038	355	3	\(\varphi	\(\varphi	ADV
bracis-19038	355	4	=	=	SYM
bracis-19038	355	5	\emptyset	\emptyset	VERB
bracis-19038	355	6	\	\	NOUN
bracis-19038	355	7	)	)	PUNCT
bracis-19038	355	8	,	,	PUNCT
bracis-19038	355	9	i.e.	i.e.	X
bracis-19038	355	10	,	,	PUNCT
bracis-19038	355	11	\((p	\((p	NOUN
bracis-19038	355	12	,	,	PUNCT
bracis-19038	355	13	\varphi	\varphi	PROPN
bracis-19038	355	14	)	)	PUNCT
bracis-19038	355	15	\	\	NOUN
bracis-19038	355	16	)	)	PUNCT
bracis-19038	355	17	corresponds	correspond	VERB
bracis-19038	355	18	to	to	ADP
bracis-19038	355	19	the	the	DET
bracis-19038	355	20	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	355	21	)	)	PUNCT
bracis-19038	356	1	p.	p.	NOUN
bracis-19038	356	2	then	then	ADV
bracis-19038	356	3	\(\forall	\(\forall	ADV
bracis-19038	356	4	x	x	X
bracis-19038	356	5	\in	\in	PROPN
bracis-19038	356	6	\left\	\left\	PROPN
bracis-19038	356	7	{	{	PUNCT
bracis-19038	356	8	st	st	PROPN
bracis-19038	356	9	,	,	PUNCT
bracis-19038	356	10	opt	opt	NOUN
bracis-19038	356	11	,	,	PUNCT
bracis-19038	356	12	pes	pe	NOUN
bracis-19038	356	13	,	,	PUNCT
bracis-19038	356	14	opp	opp	PROPN
bracis-19038	356	15	\right\	\right\	ADV
bracis-19038	356	16	}	}	PUNCT
bracis-19038	356	17	\	\	NOUN
bracis-19038	356	18	)	)	PUNCT
bracis-19038	356	19	and	and	CCONJ
bracis-19038	356	20	\(\forall	\(\forall	ADV
bracis-19038	356	21	y	y	PROPN
bracis-19038	356	22	\in	\in	PROPN
bracis-19038	356	23	\left\	\left\	PROPN
bracis-19038	356	24	{	{	PUNCT
bracis-19038	356	25	\forall	\forall	INTJ
bracis-19038	357	1	\forall	\forall	INTJ
bracis-19038	357	2	,	,	PUNCT
bracis-19038	357	3	\forall	\forall	DET
bracis-19038	357	4	\exists	\exist	NOUN
bracis-19038	357	5	,	,	PUNCT
bracis-19038	357	6	\exists	\exist	NOUN
bracis-19038	357	7	\forall	\forall	ADV
bracis-19038	357	8	,	,	PUNCT
bracis-19038	357	9	\exists	\exist	NOUN
bracis-19038	357	10	\exists	\exist	NOUN
bracis-19038	357	11	\right\	\right\	ADV
bracis-19038	357	12	}	}	PUNCT
bracis-19038	357	13	\	\	NOUN
bracis-19038	357	14	)	)	PUNCT
bracis-19038	357	15	,	,	PUNCT
bracis-19038	357	16	it	it	PRON
bracis-19038	357	17	holds	hold	VERB
bracis-19038	357	18	i	i	PRON
bracis-19038	357	19	is	be	AUX
bracis-19038	357	20	a	a	DET
bracis-19038	357	21	\	\	PROPN
bracis-19038	357	22	(	(	PUNCT
bracis-19038	357	23	ps	ps	PROPN
bracis-19038	357	24	\	\	ADJ
bracis-19038	357	25	)	)	PUNCT
bracis-19038	357	26	model	model	NOUN
bracis-19038	357	27	of	of	ADP
bracis-19038	357	28	p	p	PROPN
bracis-19038	357	29	iff	iff	PROPN
bracis-19038	357	30	i	i	PRON
bracis-19038	357	31	is	be	AUX
bracis-19038	357	32	a	a	DET
bracis-19038	357	33	\	\	PROPN
bracis-19038	357	34	(	(	PUNCT
bracis-19038	357	35	pps	pps	PROPN
bracis-19038	357	36	\	\	ADJ
bracis-19038	357	37	)	)	PUNCT
bracis-19038	357	38	model	model	NOUN
bracis-19038	357	39	of	of	ADP
bracis-19038	357	40	\((p	\((p	NOUN
bracis-19038	357	41	,	,	PUNCT
bracis-19038	357	42	\varphi	\varphi	PROPN
bracis-19038	357	43	)	)	PUNCT
bracis-19038	357	44	\	\	NOUN
bracis-19038	357	45	)	)	PUNCT
bracis-19038	357	46	w.r.t	w.r.t	NOUN
bracis-19038	357	47	.	.	PUNCT
bracis-19038	358	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	358	2	^y_x\	^y_x\	NUM
bracis-19038	358	3	)	)	PUNCT
bracis-19038	359	1	iff	iff	PROPN
bracis-19038	359	2	i	i	PRON
bracis-19038	359	3	is	be	AUX
bracis-19038	359	4	a	a	DET
bracis-19038	359	5	\	\	PROPN
bracis-19038	359	6	(	(	PUNCT
bracis-19038	359	7	pps	pps	PROPN
bracis-19038	359	8	\	\	ADJ
bracis-19038	359	9	)	)	PUNCT
bracis-19038	359	10	model	model	NOUN
bracis-19038	359	11	of	of	ADP
bracis-19038	359	12	\((p	\((p	NOUN
bracis-19038	359	13	,	,	PUNCT
bracis-19038	359	14	\varphi	\varphi	PROPN
bracis-19038	359	15	)	)	PUNCT
bracis-19038	360	1	\	\	NOUN
bracis-19038	360	2	)	)	PUNCT
bracis-19038	360	3	w.r.t	w.r.t	NOUN
bracis-19038	360	4	.	.	PUNCT
bracis-19038	361	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	361	2	^y_x\	^y_x\	NUM
bracis-19038	361	3	)	)	PUNCT
bracis-19038	361	4	.	.	PUNCT
bracis-19038	362	1	i	i	PRON
bracis-19038	362	2	is	be	AUX
bracis-19038	362	3	a	a	DET
bracis-19038	362	4	well	well	ADV
bracis-19038	362	5	-	-	PUNCT
bracis-19038	362	6	founded	found	VERB
bracis-19038	362	7	model	model	NOUN
bracis-19038	362	8	of	of	ADP
bracis-19038	362	9	p	p	PROPN
bracis-19038	362	10	iff	iff	PROPN
bracis-19038	362	11	i	i	PRON
bracis-19038	362	12	is	be	AUX
bracis-19038	362	13	a	a	DET
bracis-19038	362	14	preferential	preferential	ADJ
bracis-19038	362	15	well	well	ADV
bracis-19038	362	16	-	-	PUNCT
bracis-19038	362	17	founded	found	VERB
bracis-19038	362	18	model	model	NOUN
bracis-19038	362	19	of	of	ADP
bracis-19038	362	20	\((p	\((p	NOUN
bracis-19038	362	21	,	,	PUNCT
bracis-19038	362	22	\varphi	\varphi	PROPN
bracis-19038	362	23	)	)	PUNCT
bracis-19038	362	24	\	\	NOUN
bracis-19038	362	25	)	)	PUNCT
bracis-19038	362	26	w.r.t	w.r.t	NOUN
bracis-19038	362	27	.	.	PUNCT
bracis-19038	363	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	363	2	^y_x\	^y_x\	NUM
bracis-19038	363	3	)	)	PUNCT
bracis-19038	364	1	iff	iff	PROPN
bracis-19038	364	2	i	i	PRON
bracis-19038	364	3	is	be	AUX
bracis-19038	364	4	a	a	DET
bracis-19038	364	5	preferential	preferential	ADJ
bracis-19038	364	6	well	well	ADV
bracis-19038	364	7	-	-	PUNCT
bracis-19038	364	8	founded	found	VERB
bracis-19038	364	9	model	model	NOUN
bracis-19038	364	10	of	of	ADP
bracis-19038	364	11	\((p	\((p	NOUN
bracis-19038	364	12	,	,	PUNCT
bracis-19038	364	13	\varphi	\varphi	PROPN
bracis-19038	364	14	)	)	PUNCT
bracis-19038	365	1	\	\	NOUN
bracis-19038	365	2	)	)	PUNCT
bracis-19038	365	3	w.r.t	w.r.t	NOUN
bracis-19038	365	4	.	.	PUNCT
bracis-19038	366	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	366	2	^y_x\	^y_x\	NUM
bracis-19038	366	3	)	)	PUNCT
bracis-19038	366	4	.	.	PUNCT
bracis-19038	367	1	i	i	PRON
bracis-19038	367	2	is	be	AUX
bracis-19038	367	3	a	a	DET
bracis-19038	367	4	regular	regular	ADJ
bracis-19038	367	5	model	model	NOUN
bracis-19038	367	6	of	of	ADP
bracis-19038	367	7	p	p	PROPN
bracis-19038	367	8	iff	iff	PROPN
bracis-19038	367	9	i	i	PRON
bracis-19038	367	10	is	be	AUX
bracis-19038	367	11	a	a	DET
bracis-19038	367	12	preferential	preferential	ADJ
bracis-19038	367	13	regular	regular	ADJ
bracis-19038	367	14	model	model	NOUN
bracis-19038	367	15	of	of	ADP
bracis-19038	367	16	\((p	\((p	NOUN
bracis-19038	367	17	,	,	PUNCT
bracis-19038	367	18	\varphi	\varphi	PROPN
bracis-19038	367	19	)	)	PUNCT
bracis-19038	367	20	\	\	NOUN
bracis-19038	367	21	)	)	PUNCT
bracis-19038	367	22	w.r.t	w.r.t	NOUN
bracis-19038	367	23	.	.	PUNCT
bracis-19038	368	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	368	2	^y_x\	^y_x\	NUM
bracis-19038	368	3	)	)	PUNCT
bracis-19038	369	1	iff	iff	PROPN
bracis-19038	369	2	i	i	PRON
bracis-19038	369	3	is	be	AUX
bracis-19038	369	4	a	a	DET
bracis-19038	369	5	preferential	preferential	ADJ
bracis-19038	369	6	regular	regular	ADJ
bracis-19038	369	7	model	model	NOUN
bracis-19038	369	8	of	of	ADP
bracis-19038	369	9	\((p	\((p	NOUN
bracis-19038	369	10	,	,	PUNCT
bracis-19038	369	11	\varphi	\varphi	PROPN
bracis-19038	369	12	)	)	PUNCT
bracis-19038	370	1	\	\	NOUN
bracis-19038	370	2	)	)	PUNCT
bracis-19038	370	3	w.r.t	w.r.t	NOUN
bracis-19038	370	4	.	.	PUNCT
bracis-19038	371	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	371	2	^y_x\	^y_x\	NUM
bracis-19038	371	3	)	)	PUNCT
bracis-19038	371	4	.	.	PUNCT
bracis-19038	372	1	i	i	PRON
bracis-19038	372	2	is	be	AUX
bracis-19038	372	3	a	a	DET
bracis-19038	372	4	stable	stable	ADJ
bracis-19038	372	5	model	model	NOUN
bracis-19038	372	6	of	of	ADP
bracis-19038	372	7	p	p	PROPN
bracis-19038	372	8	iff	iff	PROPN
bracis-19038	372	9	i	i	PRON
bracis-19038	372	10	is	be	AUX
bracis-19038	372	11	a	a	DET
bracis-19038	372	12	preferential	preferential	ADJ
bracis-19038	372	13	stable	stable	ADJ
bracis-19038	372	14	model	model	NOUN
bracis-19038	372	15	of	of	ADP
bracis-19038	372	16	\((p	\((p	NOUN
bracis-19038	372	17	,	,	PUNCT
bracis-19038	372	18	\varphi	\varphi	PROPN
bracis-19038	372	19	)	)	PUNCT
bracis-19038	372	20	\	\	NOUN
bracis-19038	372	21	)	)	PUNCT
bracis-19038	372	22	w.r.t	w.r.t	NOUN
bracis-19038	372	23	.	.	PUNCT
bracis-19038	373	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	373	2	^y_x\	^y_x\	NUM
bracis-19038	373	3	)	)	PUNCT
bracis-19038	374	1	iff	iff	PROPN
bracis-19038	374	2	i	i	PRON
bracis-19038	374	3	is	be	AUX
bracis-19038	374	4	a	a	DET
bracis-19038	374	5	preferential	preferential	ADJ
bracis-19038	374	6	stable	stable	ADJ
bracis-19038	374	7	model	model	NOUN
bracis-19038	374	8	of	of	ADP
bracis-19038	374	9	\((p	\((p	NOUN
bracis-19038	374	10	,	,	PUNCT
bracis-19038	374	11	\varphi	\varphi	PROPN
bracis-19038	374	12	)	)	PUNCT
bracis-19038	375	1	\	\	NOUN
bracis-19038	375	2	)	)	PUNCT
bracis-19038	375	3	w.r.t	w.r.t	NOUN
bracis-19038	375	4	.	.	PUNCT
bracis-19038	376	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	376	2	^y_x\	^y_x\	NUM
bracis-19038	376	3	)	)	PUNCT
bracis-19038	376	4	.	.	PUNCT
bracis-19038	377	1	i	i	PRON
bracis-19038	377	2	is	be	AUX
bracis-19038	377	3	an	an	DET
bracis-19038	377	4	l	l	ADJ
bracis-19038	377	5	-	-	ADJ
bracis-19038	377	6	stable	stable	ADJ
bracis-19038	377	7	model	model	NOUN
bracis-19038	377	8	of	of	ADP
bracis-19038	377	9	p	p	PROPN
bracis-19038	377	10	iff	iff	PROPN
bracis-19038	377	11	i	i	PRON
bracis-19038	377	12	is	be	AUX
bracis-19038	377	13	a	a	DET
bracis-19038	377	14	preferential	preferential	ADJ
bracis-19038	377	15	l	l	ADJ
bracis-19038	377	16	-	-	ADJ
bracis-19038	377	17	stable	stable	ADJ
bracis-19038	377	18	model	model	NOUN
bracis-19038	377	19	of	of	ADP
bracis-19038	377	20	\((p	\((p	NOUN
bracis-19038	377	21	,	,	PUNCT
bracis-19038	377	22	\varphi	\varphi	PROPN
bracis-19038	377	23	)	)	PUNCT
bracis-19038	377	24	\	\	NOUN
bracis-19038	377	25	)	)	PUNCT
bracis-19038	377	26	w.r.t	w.r.t	NOUN
bracis-19038	377	27	.	.	PUNCT
bracis-19038	378	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	378	2	^y_x\	^y_x\	NUM
bracis-19038	378	3	)	)	PUNCT
bracis-19038	379	1	iff	iff	PROPN
bracis-19038	379	2	i	i	PRON
bracis-19038	379	3	is	be	AUX
bracis-19038	379	4	a	a	DET
bracis-19038	379	5	preferential	preferential	ADJ
bracis-19038	379	6	l	l	ADJ
bracis-19038	379	7	-	-	ADJ
bracis-19038	379	8	stable	stable	ADJ
bracis-19038	379	9	model	model	NOUN
bracis-19038	379	10	of	of	ADP
bracis-19038	379	11	\((p	\((p	NOUN
bracis-19038	379	12	,	,	PUNCT
bracis-19038	379	13	\varphi	\varphi	PROPN
bracis-19038	379	14	)	)	PUNCT
bracis-19038	380	1	\	\	NOUN
bracis-19038	380	2	)	)	PUNCT
bracis-19038	380	3	w.r.t	w.r.t	NOUN
bracis-19038	380	4	.	.	PUNCT
bracis-19038	381	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	381	2	^y_x\	^y_x\	NUM
bracis-19038	381	3	)	)	PUNCT
bracis-19038	381	4	.	.	PUNCT
bracis-19038	382	1	proof	proof	NOUN
bracis-19038	382	2	since	since	SCONJ
bracis-19038	382	3	\(\varphi	\(\varphi	NOUN
bracis-19038	382	4	=	=	SYM
bracis-19038	382	5	\emptyset	\emptyset	VERB
bracis-19038	382	6	\	\	NOUN
bracis-19038	382	7	)	)	PUNCT
bracis-19038	382	8	,	,	PUNCT
bracis-19038	382	9	\(\varphi	\(\varphi	PROPN
bracis-19038	382	10	^	^	SYM
bracis-19038	382	11	*	*	PUNCT
bracis-19038	382	12	=	=	SYM
bracis-19038	382	13	\left\	\left\	PROPN
bracis-19038	382	14	{	{	PUNCT
bracis-19038	382	15	o	o	NOUN
bracis-19038	382	16	\preceq	\preceq	PROPN
bracis-19038	382	17	o	o	NOUN
bracis-19038	382	18	\mid	\mid	ADP
bracis-19038	382	19	o	o	PROPN
bracis-19038	382	20	\in	\in	PROPN
bracis-19038	382	21	\mathcal	\mathcal	PROPN
bracis-19038	382	22	{	{	PUNCT
bracis-19038	382	23	o}_p\right\	o}_p\right\	NOUN
bracis-19038	382	24	}	}	PUNCT
bracis-19038	382	25	\	\	NOUN
bracis-19038	382	26	)	)	PUNCT
bracis-19038	382	27	according	accord	VERB
bracis-19038	382	28	to	to	ADP
bracis-19038	382	29	\(\varphi	\(\varphi	PROPN
bracis-19038	382	30	^*\	^*\	NUM
bracis-19038	382	31	)	)	PUNCT
bracis-19038	382	32	.	.	PUNCT
bracis-19038	383	1	this	this	PRON
bracis-19038	383	2	means	mean	VERB
bracis-19038	383	3	for	for	ADP
bracis-19038	383	4	every	every	DET
bracis-19038	383	5	\(o	\(o	ADJ
bracis-19038	383	6	,	,	PUNCT
bracis-19038	383	7	o	o	NOUN
bracis-19038	383	8	'	'	PUNCT
bracis-19038	383	9	\in	\in	PROPN
bracis-19038	383	10	\mathcal	\mathcal	PROPN
bracis-19038	383	11	{	{	PUNCT
bracis-19038	383	12	o}_p\	o}_p\	NOUN
bracis-19038	383	13	)	)	PUNCT
bracis-19038	383	14	,	,	PUNCT
bracis-19038	383	15	it	it	PRON
bracis-19038	383	16	holds	hold	VERB
bracis-19038	383	17	\(o	\(o	PRON
bracis-19038	383	18	\not	\not	ADV
bracis-19038	383	19	\prec	\prec	PROPN
bracis-19038	383	20	o'\	o'\	NOUN
bracis-19038	383	21	)	)	PUNCT
bracis-19038	383	22	.	.	PUNCT
bracis-19038	384	1	thus	thus	ADV
bracis-19038	384	2	for	for	ADP
bracis-19038	384	3	any	any	DET
bracis-19038	384	4	\(i	\(i	NOUN
bracis-19038	384	5	\subseteq	\subseteq	AUX
bracis-19038	384	6	lit	light	VERB
bracis-19038	384	7	_	_	PUNCT
bracis-19038	384	8	p\	p\	NOUN
bracis-19038	384	9	)	)	PUNCT
bracis-19038	384	10	,	,	PUNCT
bracis-19038	384	11	we	we	PRON
bracis-19038	384	12	obtain	obtain	VERB
bracis-19038	384	13	\(\mathcal	\(\mathcal	ADJ
bracis-19038	384	14	b_i	b_i	PROPN
bracis-19038	384	15	=	=	SYM
bracis-19038	384	16	\mathcal	\mathcal	PROPN
bracis-19038	384	17	w_i	w_i	PROPN
bracis-19038	384	18	=	=	SYM
bracis-19038	384	19	2^i\	2^i\	NUM
bracis-19038	384	20	)	)	PUNCT
bracis-19038	384	21	,	,	PUNCT
bracis-19038	384	22	in	in	ADP
bracis-19038	384	23	which	which	PRON
bracis-19038	384	24	\(\mathcal	\(\mathcal	ADJ
bracis-19038	384	25	b_i\	b_i\	NOUN
bracis-19038	384	26	)	)	PUNCT
bracis-19038	384	27	is	be	AUX
bracis-19038	384	28	the	the	DET
bracis-19038	384	29	set	set	NOUN
bracis-19038	384	30	of	of	ADP
bracis-19038	384	31	all	all	DET
bracis-19038	384	32	best	well	ADV
bracis-19038	384	33	-	-	PUNCT
bracis-19038	384	34	ranked	rank	VERB
bracis-19038	384	35	options	option	NOUN
bracis-19038	384	36	in	in	ADP
bracis-19038	384	37	i	i	PRON
bracis-19038	384	38	and	and	CCONJ
bracis-19038	384	39	\(\mathcal	\(\mathcal	ADJ
bracis-19038	384	40	w_i\	w_i\	NOUN
bracis-19038	384	41	)	)	PUNCT
bracis-19038	384	42	is	be	AUX
bracis-19038	384	43	the	the	DET
bracis-19038	384	44	set	set	NOUN
bracis-19038	384	45	of	of	ADP
bracis-19038	384	46	all	all	DET
bracis-19038	384	47	worst	worst	ADV
bracis-19038	384	48	-	-	PUNCT
bracis-19038	384	49	ranked	rank	VERB
bracis-19038	384	50	options	option	NOUN
bracis-19038	384	51	in	in	ADP
bracis-19038	384	52	i	i	PRON
bracis-19038	384	53	w.r.t	w.r.t	VERB
bracis-19038	384	54	.	.	PUNCT
bracis-19038	385	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	385	2	\	\	NUM
bracis-19038	385	3	)	)	PUNCT
bracis-19038	385	4	.	.	PUNCT
bracis-19038	386	1	then	then	ADV
bracis-19038	386	2	for	for	ADP
bracis-19038	386	3	any	any	DET
bracis-19038	386	4	\	\	NOUN
bracis-19038	386	5	(	(	PUNCT
bracis-19038	386	6	ps	ps	NOUN
bracis-19038	386	7	\	\	ADJ
bracis-19038	386	8	)	)	PUNCT
bracis-19038	386	9	models	model	NOUN
bracis-19038	386	10	\(i_1\	\(i_1\	NOUN
bracis-19038	386	11	)	)	PUNCT
bracis-19038	386	12	and	and	CCONJ
bracis-19038	386	13	\(i_2\	\(i_2\	PROPN
bracis-19038	386	14	)	)	PUNCT
bracis-19038	386	15	of	of	ADP
bracis-19038	386	16	p	p	X
bracis-19038	386	17	,	,	PUNCT
bracis-19038	386	18	for	for	ADP
bracis-19038	386	19	any	any	DET
bracis-19038	386	20	\(o_1	\(o_1	PROPN
bracis-19038	386	21	\in	\in	PROPN
bracis-19038	386	22	\mathcal	\mathcal	PROPN
bracis-19038	386	23	b_{i_1	b_{i_1	NOUN
bracis-19038	386	24	}	}	PUNCT
bracis-19038	386	25	=	=	PUNCT
bracis-19038	386	26	\mathcal	\mathcal	NOUN
bracis-19038	386	27	w_{i_i	w_{i_i	PROPN
bracis-19038	386	28	}	}	PUNCT
bracis-19038	386	29	=	=	SYM
bracis-19038	386	30	2^{i_1}\	2^{i_1}\	NUM
bracis-19038	386	31	)	)	PUNCT
bracis-19038	386	32	and	and	CCONJ
bracis-19038	386	33	for	for	ADP
bracis-19038	386	34	any	any	DET
bracis-19038	386	35	\(o_2	\(o_2	PROPN
bracis-19038	386	36	\in	\in	PROPN
bracis-19038	386	37	\mathcal	\mathcal	PROPN
bracis-19038	386	38	b_{i_2	b_{i_2	PUNCT
bracis-19038	386	39	}	}	PUNCT
bracis-19038	386	40	=	=	SYM
bracis-19038	386	41	\mathcal	\mathcal	ADJ
bracis-19038	386	42	w_{i_2	w_{i_2	ADJ
bracis-19038	386	43	}	}	PUNCT
bracis-19038	386	44	=	=	SYM
bracis-19038	386	45	2^{i_2}\	2^{i_2}\	NUM
bracis-19038	386	46	)	)	PUNCT
bracis-19038	386	47	,	,	PUNCT
bracis-19038	386	48	it	it	PRON
bracis-19038	386	49	holds	hold	VERB
bracis-19038	386	50	\(o_2	\(o_2	PROPN
bracis-19038	386	51	\not	\not	ADV
bracis-19038	386	52	\prec	\prec	ADP
bracis-19038	386	53	o_1\	o_1\	PROPN
bracis-19038	386	54	)	)	PUNCT
bracis-19038	386	55	and	and	CCONJ
bracis-19038	386	56	\(o_1	\(o_1	PROPN
bracis-19038	386	57	\not	\not	ADV
bracis-19038	386	58	\prec	\prec	PROPN
bracis-19038	386	59	o_2\	o_2\	PROPN
bracis-19038	386	60	)	)	PUNCT
bracis-19038	386	61	according	accord	VERB
bracis-19038	386	62	to	to	ADP
bracis-19038	386	63	\(\varphi	\(\varphi	PROPN
bracis-19038	386	64	^*\	^*\	NUM
bracis-19038	386	65	)	)	PUNCT
bracis-19038	386	66	.	.	PUNCT
bracis-19038	387	1	hence	hence	ADV
bracis-19038	387	2	,	,	PUNCT
bracis-19038	387	3	for	for	ADP
bracis-19038	387	4	any	any	DET
bracis-19038	387	5	\(y	\(y	NUM
bracis-19038	387	6	\in	\in	PROPN
bracis-19038	387	7	\left\	\left\	PROPN
bracis-19038	387	8	{	{	PUNCT
bracis-19038	387	9	\forall	\forall	INTJ
bracis-19038	387	10	\forall	\forall	INTJ
bracis-19038	387	11	,	,	PUNCT
bracis-19038	387	12	\forall	\forall	DET
bracis-19038	387	13	\exists	\exist	NOUN
bracis-19038	387	14	,	,	PUNCT
bracis-19038	387	15	\exists	\exist	NOUN
bracis-19038	387	16	\forall	\forall	ADV
bracis-19038	387	17	,	,	PUNCT
bracis-19038	387	18	\exists	\exist	VERB
bracis-19038	387	19	\exists	\exist	NOUN
bracis-19038	387	20	\right\	\right\	ADV
bracis-19038	387	21	}	}	PUNCT
bracis-19038	387	22	\	\	NOUN
bracis-19038	387	23	)	)	PUNCT
bracis-19038	387	24	,	,	PUNCT
bracis-19038	387	25	we	we	PRON
bracis-19038	387	26	obtain	obtain	VERB
bracis-19038	387	27	$	$	SYM
bracis-19038	387	28	$	$	SYM
bracis-19038	387	29	\begin{aligned	\begin{aligne	VERB
bracis-19038	387	30	}	}	PUNCT
bracis-19038	387	31	\begin{gathered	\begin{gathere	VERB
bracis-19038	387	32	}	}	PUNCT
bracis-19038	387	33	\mathcal	\mathcal	ADJ
bracis-19038	387	34	b_{i_1	b_{i_1	NOUN
bracis-19038	387	35	}	}	PUNCT
bracis-19038	387	36	=	=	PUNCT
bracis-19038	387	37	\mathcal	\mathcal	NOUN
bracis-19038	387	38	w_{i_i	w_{i_i	PROPN
bracis-19038	387	39	}	}	PUNCT
bracis-19038	387	40	=	=	SYM
bracis-19038	387	41	2^{i_1	2^{i_1	NUM
bracis-19038	387	42	}	}	PUNCT
bracis-19038	387	43	\subseteq	\subseteq	PROPN
bracis-19038	387	44	^y	^y	ADJ
bracis-19038	387	45	\mathcal	\mathcal	ADJ
bracis-19038	387	46	b_{i_2	b_{i_2	PUNCT
bracis-19038	387	47	}	}	PUNCT
bracis-19038	387	48	=	=	SYM
bracis-19038	387	49	\mathcal	\mathcal	ADJ
bracis-19038	387	50	w_{i_2	w_{i_2	ADJ
bracis-19038	387	51	}	}	PUNCT
bracis-19038	387	52	=	=	SYM
bracis-19038	387	53	2^{i_2	2^{i_2	PROPN
bracis-19038	387	54	}	}	PUNCT
bracis-19038	387	55	\textit	\textit	NOUN
bracis-19038	387	56	{	{	PUNCT
bracis-19038	387	57	and	and	CCONJ
bracis-19038	387	58	}	}	PUNCT
bracis-19038	387	59	\\	\\	NOUN
bracis-19038	387	60	\mathcal	\mathcal	ADJ
bracis-19038	387	61	b_{i_2	b_{i_2	PUNCT
bracis-19038	387	62	}	}	PUNCT
bracis-19038	387	63	=	=	SYM
bracis-19038	387	64	\mathcal	\mathcal	ADJ
bracis-19038	387	65	w_{i_2	w_{i_2	ADJ
bracis-19038	387	66	}	}	PUNCT
bracis-19038	387	67	=	=	SYM
bracis-19038	387	68	2^{i_2	2^{i_2	PROPN
bracis-19038	387	69	}	}	PUNCT
bracis-19038	387	70	\subseteq	\subseteq	PROPN
bracis-19038	387	71	^y	^y	ADJ
bracis-19038	387	72	\mathcal	\mathcal	ADJ
bracis-19038	387	73	b_{i_1	b_{i_1	NOUN
bracis-19038	387	74	}	}	PUNCT
bracis-19038	387	75	=	=	PUNCT
bracis-19038	387	76	\mathcal	\mathcal	ADJ
bracis-19038	387	77	w_{i_1	w_{i_1	NOUN
bracis-19038	387	78	}	}	PUNCT
bracis-19038	387	79	=	=	SYM
bracis-19038	387	80	2^{i_1	2^{i_1	NOUN
bracis-19038	387	81	}	}	PUNCT
bracis-19038	387	82	\end{gathered	\end{gathere	VERB
bracis-19038	387	83	}	}	PUNCT
bracis-19038	387	84	\end{aligned}$$	\end{aligned}$$	X
bracis-19038	387	85	(	(	PUNCT
bracis-19038	387	86	1	1	NUM
bracis-19038	387	87	)	)	PUNCT
bracis-19038	387	88	from	from	ADP
bracis-19038	387	89	eq	eq	ADP
bracis-19038	387	90	.	.	PUNCT
bracis-19038	388	1	(	(	PUNCT
bracis-19038	388	2	1	1	NUM
bracis-19038	388	3	)	)	PUNCT
bracis-19038	388	4	,	,	PUNCT
bracis-19038	388	5	we	we	PRON
bracis-19038	388	6	infer	infer	VERB
bracis-19038	388	7	for	for	ADP
bracis-19038	388	8	each	each	DET
bracis-19038	388	9	\(x	\(x	ADJ
bracis-19038	388	10	\in	\in	PROPN
bracis-19038	388	11	\left\	\left\	PROPN
bracis-19038	388	12	{	{	PUNCT
bracis-19038	388	13	st	st	PROPN
bracis-19038	388	14	,	,	PUNCT
bracis-19038	388	15	opt	opt	NOUN
bracis-19038	388	16	,	,	PUNCT
bracis-19038	388	17	pes	pe	NOUN
bracis-19038	388	18	,	,	PUNCT
bracis-19038	388	19	opp	opp	PROPN
bracis-19038	388	20	\right\	\right\	ADV
bracis-19038	388	21	}	}	PUNCT
bracis-19038	388	22	\	\	NOUN
bracis-19038	388	23	)	)	PUNCT
bracis-19038	388	24	and	and	CCONJ
bracis-19038	388	25	for	for	ADP
bracis-19038	388	26	all	all	DET
bracis-19038	388	27	\(y	\(y	NUM
bracis-19038	388	28	\in	\in	PROPN
bracis-19038	388	29	\left\	\left\	PROPN
bracis-19038	388	30	{	{	PUNCT
bracis-19038	388	31	\forall	\forall	INTJ
bracis-19038	389	1	\forall	\forall	INTJ
bracis-19038	389	2	,	,	PUNCT
bracis-19038	389	3	\forall	\forall	DET
bracis-19038	389	4	\exists	\exist	NOUN
bracis-19038	389	5	,	,	PUNCT
bracis-19038	389	6	\exists	\exist	NOUN
bracis-19038	389	7	\forall	\forall	ADV
bracis-19038	389	8	,	,	PUNCT
bracis-19038	389	9	\exists	\exist	VERB
bracis-19038	389	10	\exists	\exist	NOUN
bracis-19038	389	11	\right\	\right\	ADV
bracis-19038	389	12	}	}	PUNCT
bracis-19038	389	13	\	\	NOUN
bracis-19038	389	14	)	)	PUNCT
bracis-19038	389	15	,	,	PUNCT
bracis-19038	389	16	it	it	PRON
bracis-19038	389	17	holds	hold	VERB
bracis-19038	389	18	\(i_1	\(i_1	PROPN
bracis-19038	389	19	\subseteq	\subseteq	PROPN
bracis-19038	389	20	^y_x	^y_x	NOUN
bracis-19038	389	21	i_2	i_2	ADJ
bracis-19038	389	22	\textit	\textit	PROPN
bracis-19038	389	23	{	{	PUNCT
bracis-19038	389	24	and	and	CCONJ
bracis-19038	389	25	}	}	PUNCT
bracis-19038	389	26	i_2	i_2	PROPN
bracis-19038	389	27	\subseteq	\subseteq	PROPN
bracis-19038	389	28	^y_x	^y_x	NUM
bracis-19038	389	29	i_1\	i_1\	PROPN
bracis-19038	389	30	)	)	PUNCT
bracis-19038	389	31	.	.	PUNCT
bracis-19038	390	1	consequently	consequently	ADV
bracis-19038	390	2	,	,	PUNCT
bracis-19038	390	3	for	for	ADP
bracis-19038	390	4	each	each	DET
bracis-19038	390	5	\(x	\(x	ADJ
bracis-19038	390	6	\in	\in	PROPN
bracis-19038	390	7	\left\	\left\	PROPN
bracis-19038	390	8	{	{	PUNCT
bracis-19038	390	9	st	st	PROPN
bracis-19038	390	10	,	,	PUNCT
bracis-19038	390	11	opt	opt	NOUN
bracis-19038	390	12	,	,	PUNCT
bracis-19038	390	13	pes	pe	NOUN
bracis-19038	390	14	,	,	PUNCT
bracis-19038	390	15	opp	opp	PROPN
bracis-19038	390	16	\right\	\right\	ADV
bracis-19038	390	17	}	}	PUNCT
bracis-19038	390	18	\	\	NOUN
bracis-19038	390	19	)	)	PUNCT
bracis-19038	390	20	and	and	CCONJ
bracis-19038	390	21	for	for	ADP
bracis-19038	390	22	all	all	DET
bracis-19038	390	23	\(y	\(y	NUM
bracis-19038	390	24	\in	\in	PROPN
bracis-19038	390	25	\left\	\left\	PROPN
bracis-19038	390	26	{	{	PUNCT
bracis-19038	390	27	\forall	\forall	INTJ
bracis-19038	390	28	\forall	\forall	INTJ
bracis-19038	390	29	,	,	PUNCT
bracis-19038	390	30	\forall	\forall	DET
bracis-19038	390	31	\exists	\exist	NOUN
bracis-19038	390	32	,	,	PUNCT
bracis-19038	390	33	\exists	\exist	NOUN
bracis-19038	390	34	\forall	\forall	ADV
bracis-19038	390	35	,	,	PUNCT
bracis-19038	390	36	\exists	\exist	VERB
bracis-19038	390	37	\exists	\exist	NOUN
bracis-19038	390	38	\right\	\right\	ADV
bracis-19038	390	39	}	}	PUNCT
bracis-19038	390	40	\	\	NOUN
bracis-19038	390	41	)	)	PUNCT
bracis-19038	390	42	,	,	PUNCT
bracis-19038	390	43	it	it	PRON
bracis-19038	390	44	holds	hold	VERB
bracis-19038	390	45	i	i	PRON
bracis-19038	390	46	is	be	AUX
bracis-19038	390	47	a	a	DET
bracis-19038	390	48	\	\	PROPN
bracis-19038	390	49	(	(	PUNCT
bracis-19038	390	50	ps	ps	PROPN
bracis-19038	390	51	\	\	ADJ
bracis-19038	390	52	)	)	PUNCT
bracis-19038	390	53	model	model	NOUN
bracis-19038	390	54	of	of	ADP
bracis-19038	390	55	p	p	PROPN
bracis-19038	390	56	iff	iff	PROPN
bracis-19038	390	57	i	i	PRON
bracis-19038	390	58	is	be	AUX
bracis-19038	390	59	a	a	DET
bracis-19038	390	60	\	\	PROPN
bracis-19038	390	61	(	(	PUNCT
bracis-19038	390	62	pps	pps	PROPN
bracis-19038	390	63	\	\	ADJ
bracis-19038	390	64	)	)	PUNCT
bracis-19038	390	65	model	model	NOUN
bracis-19038	390	66	of	of	ADP
bracis-19038	390	67	\((p	\((p	NOUN
bracis-19038	390	68	,	,	PUNCT
bracis-19038	390	69	\varphi	\varphi	PROPN
bracis-19038	390	70	)	)	PUNCT
bracis-19038	390	71	\	\	NOUN
bracis-19038	390	72	)	)	PUNCT
bracis-19038	390	73	w.r.t	w.r.t	NOUN
bracis-19038	390	74	.	.	PUNCT
bracis-19038	391	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	391	2	^y_x\	^y_x\	NUM
bracis-19038	391	3	)	)	PUNCT
bracis-19038	391	4	.	.	PUNCT
bracis-19038	392	1	after	after	ADP
bracis-19038	392	2	replacing	replace	VERB
bracis-19038	392	3	above	above	ADP
bracis-19038	392	4	\(i_1\	\(i_1\	NOUN
bracis-19038	392	5	)	)	PUNCT
bracis-19038	392	6	by	by	ADP
bracis-19038	392	7	\(i_1	\(i_1	PROPN
bracis-19038	392	8	i_2\	i_2\	NUM
bracis-19038	392	9	)	)	PUNCT
bracis-19038	392	10	and	and	CCONJ
bracis-19038	392	11	\(i_2\	\(i_2\	PROPN
bracis-19038	392	12	)	)	PUNCT
bracis-19038	392	13	by	by	ADP
bracis-19038	392	14	\(i_2	\(i_2	PROPN
bracis-19038	392	15	i_i\	i_i\	NOUN
bracis-19038	392	16	)	)	PUNCT
bracis-19038	392	17	,	,	PUNCT
bracis-19038	392	18	we	we	PRON
bracis-19038	392	19	obtain	obtain	VERB
bracis-19038	392	20	the	the	DET
bracis-19038	392	21	same	same	ADJ
bracis-19038	392	22	result	result	NOUN
bracis-19038	392	23	for	for	ADP
bracis-19038	392	24	\(\sqsubseteq	\(\sqsubseteq	ADJ
bracis-19038	392	25	^y_x\	^y_x\	NUM
bracis-19038	392	26	)	)	PUNCT
bracis-19038	392	27	.	.	PUNCT
bracis-19038	392	28	   	   	SPACE
bracis-19038	393	1	\(\square	\(\square	VERB
bracis-19038	393	2	\	\	NOUN
bracis-19038	393	3	)	)	PUNCT
bracis-19038	394	1	the	the	DET
bracis-19038	394	2	following	follow	VERB
bracis-19038	394	3	results	result	NOUN
bracis-19038	394	4	are	be	AUX
bracis-19038	394	5	immediate	immediate	ADJ
bracis-19038	394	6	:	:	PUNCT
bracis-19038	394	7	corollary	corollary	ADJ
bracis-19038	394	8	2	2	NUM
bracis-19038	394	9	let	let	VERB
bracis-19038	394	10	\((p	\((p	NOUN
bracis-19038	394	11	,	,	PUNCT
bracis-19038	394	12	\varphi	\varphi	PROPN
bracis-19038	394	13	)	)	PUNCT
bracis-19038	394	14	\	\	NOUN
bracis-19038	394	15	)	)	PUNCT
bracis-19038	394	16	be	be	AUX
bracis-19038	394	17	a	a	DET
bracis-19038	394	18	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	394	19	)	)	PUNCT
bracis-19038	394	20	such	such	ADJ
bracis-19038	394	21	that	that	SCONJ
bracis-19038	394	22	\(\varphi	\(\varphi	ADV
bracis-19038	394	23	=	=	SYM
bracis-19038	394	24	\emptyset	\emptyset	VERB
bracis-19038	394	25	\	\	NOUN
bracis-19038	394	26	)	)	PUNCT
bracis-19038	394	27	,	,	PUNCT
bracis-19038	394	28	i.e.	i.e.	X
bracis-19038	394	29	,	,	PUNCT
bracis-19038	394	30	\((p	\((p	NOUN
bracis-19038	394	31	,	,	PUNCT
bracis-19038	394	32	\varphi	\varphi	PROPN
bracis-19038	394	33	)	)	PUNCT
bracis-19038	394	34	\	\	NOUN
bracis-19038	394	35	)	)	PUNCT
bracis-19038	394	36	corresponds	correspond	VERB
bracis-19038	394	37	to	to	ADP
bracis-19038	394	38	the	the	DET
bracis-19038	394	39	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	394	40	)	)	PUNCT
bracis-19038	395	1	p.	p.	NOUN
bracis-19038	395	2	then	then	ADV
bracis-19038	395	3	\(\forall	\(\forall	ADV
bracis-19038	395	4	x	x	X
bracis-19038	395	5	\in	\in	PROPN
bracis-19038	395	6	\left\	\left\	PROPN
bracis-19038	395	7	{	{	PUNCT
bracis-19038	395	8	st	st	PROPN
bracis-19038	395	9	,	,	PUNCT
bracis-19038	395	10	opt	opt	NOUN
bracis-19038	395	11	,	,	PUNCT
bracis-19038	395	12	pes	pe	NOUN
bracis-19038	395	13	,	,	PUNCT
bracis-19038	395	14	opp	opp	PROPN
bracis-19038	395	15	\right\	\right\	ADV
bracis-19038	395	16	}	}	PUNCT
bracis-19038	395	17	\	\	NOUN
bracis-19038	395	18	)	)	PUNCT
bracis-19038	395	19	and	and	CCONJ
bracis-19038	395	20	\(\forall	\(\forall	ADV
bracis-19038	395	21	y	y	PROPN
bracis-19038	395	22	\in	\in	PROPN
bracis-19038	395	23	\left\	\left\	PROPN
bracis-19038	395	24	{	{	PUNCT
bracis-19038	395	25	\forall	\forall	INTJ
bracis-19038	396	1	\forall	\forall	INTJ
bracis-19038	396	2	,	,	PUNCT
bracis-19038	396	3	\forall	\forall	DET
bracis-19038	396	4	\exists	\exist	NOUN
bracis-19038	396	5	,	,	PUNCT
bracis-19038	396	6	\exists	\exist	NOUN
bracis-19038	396	7	\forall	\forall	ADV
bracis-19038	396	8	,	,	PUNCT
bracis-19038	396	9	\exists	\exist	NOUN
bracis-19038	396	10	\exists	\exist	NOUN
bracis-19038	396	11	\right\	\right\	ADV
bracis-19038	396	12	}	}	PUNCT
bracis-19038	396	13	\	\	NOUN
bracis-19038	396	14	)	)	PUNCT
bracis-19038	396	15	,	,	PUNCT
bracis-19038	396	16	it	it	PRON
bracis-19038	396	17	holds	hold	VERB
bracis-19038	396	18	i	i	PRON
bracis-19038	396	19	is	be	AUX
bracis-19038	396	20	a	a	DET
bracis-19038	396	21	well	well	ADV
bracis-19038	396	22	-	-	PUNCT
bracis-19038	396	23	founded	found	VERB
bracis-19038	396	24	model	model	NOUN
bracis-19038	396	25	of	of	ADP
bracis-19038	396	26	p	p	PROPN
bracis-19038	396	27	iff	iff	PROPN
bracis-19038	396	28	i	i	PRON
bracis-19038	396	29	is	be	AUX
bracis-19038	396	30	a	a	DET
bracis-19038	396	31	preferential	preferential	ADJ
bracis-19038	396	32	well	well	ADV
bracis-19038	396	33	-	-	PUNCT
bracis-19038	396	34	founded	found	VERB
bracis-19038	396	35	model	model	NOUN
bracis-19038	396	36	of	of	ADP
bracis-19038	396	37	\((p	\((p	NOUN
bracis-19038	396	38	,	,	PUNCT
bracis-19038	396	39	\varphi	\varphi	PROPN
bracis-19038	396	40	)	)	PUNCT
bracis-19038	396	41	\	\	NOUN
bracis-19038	396	42	)	)	PUNCT
bracis-19038	396	43	w.r.t	w.r.t	NOUN
bracis-19038	396	44	.	.	PUNCT
bracis-19038	397	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	397	2	^y_x\	^y_x\	NUM
bracis-19038	397	3	)	)	PUNCT
bracis-19038	398	1	iff	iff	PROPN
bracis-19038	398	2	i	i	PRON
bracis-19038	398	3	is	be	AUX
bracis-19038	398	4	a	a	DET
bracis-19038	398	5	preferential	preferential	ADJ
bracis-19038	398	6	well	well	ADV
bracis-19038	398	7	-	-	PUNCT
bracis-19038	398	8	founded	found	VERB
bracis-19038	398	9	model	model	NOUN
bracis-19038	398	10	of	of	ADP
bracis-19038	398	11	\((p	\((p	NOUN
bracis-19038	398	12	,	,	PUNCT
bracis-19038	398	13	\varphi	\varphi	PROPN
bracis-19038	398	14	)	)	PUNCT
bracis-19038	399	1	\	\	NOUN
bracis-19038	399	2	)	)	PUNCT
bracis-19038	399	3	w.r.t	w.r.t	NOUN
bracis-19038	399	4	.	.	PUNCT
bracis-19038	400	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	400	2	^y_x\	^y_x\	NUM
bracis-19038	400	3	)	)	PUNCT
bracis-19038	400	4	.	.	PUNCT
bracis-19038	401	1	i	i	PRON
bracis-19038	401	2	is	be	AUX
bracis-19038	401	3	a	a	DET
bracis-19038	401	4	regular	regular	ADJ
bracis-19038	401	5	model	model	NOUN
bracis-19038	401	6	of	of	ADP
bracis-19038	401	7	p	p	PROPN
bracis-19038	401	8	iff	iff	PROPN
bracis-19038	401	9	i	i	PRON
bracis-19038	401	10	is	be	AUX
bracis-19038	401	11	a	a	DET
bracis-19038	401	12	preferential	preferential	ADJ
bracis-19038	401	13	regular	regular	ADJ
bracis-19038	401	14	model	model	NOUN
bracis-19038	401	15	of	of	ADP
bracis-19038	401	16	\((p	\((p	NOUN
bracis-19038	401	17	,	,	PUNCT
bracis-19038	401	18	\varphi	\varphi	PROPN
bracis-19038	401	19	)	)	PUNCT
bracis-19038	401	20	\	\	NOUN
bracis-19038	401	21	)	)	PUNCT
bracis-19038	401	22	w.r.t	w.r.t	NOUN
bracis-19038	401	23	.	.	PUNCT
bracis-19038	402	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	402	2	^y_x\	^y_x\	NUM
bracis-19038	402	3	)	)	PUNCT
bracis-19038	403	1	iff	iff	PROPN
bracis-19038	403	2	i	i	PRON
bracis-19038	403	3	is	be	AUX
bracis-19038	403	4	a	a	DET
bracis-19038	403	5	preferential	preferential	ADJ
bracis-19038	403	6	regular	regular	ADJ
bracis-19038	403	7	model	model	NOUN
bracis-19038	403	8	of	of	ADP
bracis-19038	403	9	\((p	\((p	NOUN
bracis-19038	403	10	,	,	PUNCT
bracis-19038	403	11	\varphi	\varphi	PROPN
bracis-19038	403	12	)	)	PUNCT
bracis-19038	404	1	\	\	NOUN
bracis-19038	404	2	)	)	PUNCT
bracis-19038	404	3	w.r.t	w.r.t	NOUN
bracis-19038	404	4	.	.	PUNCT
bracis-19038	405	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	405	2	^y_x\	^y_x\	NUM
bracis-19038	405	3	)	)	PUNCT
bracis-19038	405	4	.	.	PUNCT
bracis-19038	406	1	i	i	PRON
bracis-19038	406	2	is	be	AUX
bracis-19038	406	3	a	a	DET
bracis-19038	406	4	stable	stable	ADJ
bracis-19038	406	5	model	model	NOUN
bracis-19038	406	6	of	of	ADP
bracis-19038	406	7	p	p	PROPN
bracis-19038	406	8	iff	iff	PROPN
bracis-19038	406	9	i	i	PRON
bracis-19038	406	10	is	be	AUX
bracis-19038	406	11	a	a	DET
bracis-19038	406	12	preferential	preferential	ADJ
bracis-19038	406	13	stable	stable	ADJ
bracis-19038	406	14	model	model	NOUN
bracis-19038	406	15	of	of	ADP
bracis-19038	406	16	\((p	\((p	NOUN
bracis-19038	406	17	,	,	PUNCT
bracis-19038	406	18	\varphi	\varphi	PROPN
bracis-19038	406	19	)	)	PUNCT
bracis-19038	406	20	\	\	NOUN
bracis-19038	406	21	)	)	PUNCT
bracis-19038	406	22	w.r.t	w.r.t	NOUN
bracis-19038	406	23	.	.	PUNCT
bracis-19038	407	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	407	2	^y_x\	^y_x\	NUM
bracis-19038	407	3	)	)	PUNCT
bracis-19038	408	1	iff	iff	PROPN
bracis-19038	408	2	i	i	PRON
bracis-19038	408	3	is	be	AUX
bracis-19038	408	4	a	a	DET
bracis-19038	408	5	preferential	preferential	ADJ
bracis-19038	408	6	stable	stable	ADJ
bracis-19038	408	7	model	model	NOUN
bracis-19038	408	8	of	of	ADP
bracis-19038	408	9	\((p	\((p	NOUN
bracis-19038	408	10	,	,	PUNCT
bracis-19038	408	11	\varphi	\varphi	PROPN
bracis-19038	408	12	)	)	PUNCT
bracis-19038	409	1	\	\	NOUN
bracis-19038	409	2	)	)	PUNCT
bracis-19038	409	3	w.r.t	w.r.t	NOUN
bracis-19038	409	4	.	.	PUNCT
bracis-19038	410	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	410	2	^y_x\	^y_x\	NUM
bracis-19038	410	3	)	)	PUNCT
bracis-19038	410	4	.	.	PUNCT
bracis-19038	411	1	i	i	PRON
bracis-19038	411	2	is	be	AUX
bracis-19038	411	3	an	an	DET
bracis-19038	411	4	l	l	ADJ
bracis-19038	411	5	-	-	ADJ
bracis-19038	411	6	stable	stable	ADJ
bracis-19038	411	7	model	model	NOUN
bracis-19038	411	8	of	of	ADP
bracis-19038	411	9	p	p	PROPN
bracis-19038	411	10	iff	iff	PROPN
bracis-19038	411	11	i	i	PRON
bracis-19038	411	12	is	be	AUX
bracis-19038	411	13	a	a	DET
bracis-19038	411	14	preferential	preferential	ADJ
bracis-19038	411	15	l	l	ADJ
bracis-19038	411	16	-	-	ADJ
bracis-19038	411	17	stable	stable	ADJ
bracis-19038	411	18	model	model	NOUN
bracis-19038	411	19	of	of	ADP
bracis-19038	411	20	\((p	\((p	NOUN
bracis-19038	411	21	,	,	PUNCT
bracis-19038	411	22	\varphi	\varphi	PROPN
bracis-19038	411	23	)	)	PUNCT
bracis-19038	411	24	\	\	NOUN
bracis-19038	411	25	)	)	PUNCT
bracis-19038	411	26	w.r.t	w.r.t	NOUN
bracis-19038	411	27	.	.	PUNCT
bracis-19038	412	1	\(\subseteq	\(\subseteq	PROPN
bracis-19038	412	2	^y_x\	^y_x\	NUM
bracis-19038	412	3	)	)	PUNCT
bracis-19038	413	1	iff	iff	PROPN
bracis-19038	413	2	i	i	PRON
bracis-19038	413	3	is	be	AUX
bracis-19038	413	4	a	a	DET
bracis-19038	413	5	preferential	preferential	ADJ
bracis-19038	413	6	l	l	ADJ
bracis-19038	413	7	-	-	ADJ
bracis-19038	413	8	stable	stable	ADJ
bracis-19038	413	9	model	model	NOUN
bracis-19038	413	10	of	of	ADP
bracis-19038	413	11	\((p	\((p	NOUN
bracis-19038	413	12	,	,	PUNCT
bracis-19038	413	13	\varphi	\varphi	PROPN
bracis-19038	413	14	)	)	PUNCT
bracis-19038	414	1	\	\	NOUN
bracis-19038	414	2	)	)	PUNCT
bracis-19038	414	3	w.r.t	w.r.t	NOUN
bracis-19038	414	4	.	.	PUNCT
bracis-19038	415	1	\(\sqsubseteq	\(\sqsubseteq	PROPN
bracis-19038	415	2	^y_x\	^y_x\	NUM
bracis-19038	415	3	)	)	PUNCT
bracis-19038	415	4	.	.	PUNCT
bracis-19038	416	1	proof	proof	NOUN
bracis-19038	416	2	these	these	DET
bracis-19038	416	3	results	result	NOUN
bracis-19038	416	4	follow	follow	VERB
bracis-19038	416	5	from	from	ADP
bracis-19038	416	6	definitions	definition	NOUN
bracis-19038	416	7	3	3	NUM
bracis-19038	416	8	and	and	CCONJ
bracis-19038	416	9	12	12	NUM
bracis-19038	416	10	and	and	CCONJ
bracis-19038	416	11	theorem	theorem	VERB
bracis-19038	416	12	2	2	NUM
bracis-19038	416	13	.	.	PUNCT
bracis-19038	417	1	both	both	DET
bracis-19038	417	2	the	the	DET
bracis-19038	417	3	relations	relation	NOUN
bracis-19038	417	4	\(\subseteq	\(\subseteq	PROPN
bracis-19038	417	5	^y_x\	^y_x\	NUM
bracis-19038	417	6	)	)	PUNCT
bracis-19038	417	7	and	and	CCONJ
bracis-19038	417	8	\(\sqsubseteq	\(\sqsubseteq	ADV
bracis-19038	417	9	^y_x\	^y_x\	NUM
bracis-19038	417	10	)	)	PUNCT
bracis-19038	417	11	have	have	VERB
bracis-19038	417	12	neither	neither	CCONJ
bracis-19038	417	13	a	a	DET
bracis-19038	417	14	monotonic	monotonic	ADJ
bracis-19038	417	15	nor	nor	CCONJ
bracis-19038	417	16	an	an	DET
bracis-19038	417	17	antitonic	antitonic	ADJ
bracis-19038	417	18	behaviour	behaviour	NOUN
bracis-19038	417	19	w.r.t	w.r.t	VERB
bracis-19038	417	20	.	.	PUNCT
bracis-19038	418	1	\(\varphi	\(\varphi	PUNCT
bracis-19038	418	2	\	\	NUM
bracis-19038	418	3	):	):	PUNCT
bracis-19038	418	4	theorem	theorem	ADJ
bracis-19038	418	5	3	3	NUM
bracis-19038	418	6	let	let	VERB
bracis-19038	418	7	\((p	\((p	NOUN
bracis-19038	418	8	,	,	PUNCT
bracis-19038	418	9	\varphi	\varphi	PROPN
bracis-19038	418	10	_	_	NOUN
bracis-19038	418	11	1)\	1)\	NUM
bracis-19038	418	12	)	)	PUNCT
bracis-19038	418	13	and	and	CCONJ
bracis-19038	418	14	\((p	\((p	NOUN
bracis-19038	418	15	,	,	PUNCT
bracis-19038	418	16	\varphi	\varphi	PROPN
bracis-19038	418	17	_	_	NOUN
bracis-19038	418	18	2)\	2)\	NUM
bracis-19038	418	19	)	)	PUNCT
bracis-19038	418	20	be	be	AUX
bracis-19038	418	21	\(\textit{plp}\)s	\(\textit{plp}\)s	ADJ
bracis-19038	418	22	.	.	PUNCT
bracis-19038	419	1	if	if	SCONJ
bracis-19038	419	2	\(\varphi	\(\varphi	PROPN
bracis-19038	419	3	_	_	PRON
bracis-19038	419	4	1	1	NUM
bracis-19038	419	5	\subseteq	\subseteq	PROPN
bracis-19038	419	6	\varphi	\varphi	PROPN
bracis-19038	419	7	_	_	PROPN
bracis-19038	419	8	2\	2\	NUM
bracis-19038	419	9	)	)	PUNCT
bracis-19038	419	10	,	,	PUNCT
bracis-19038	419	11	then	then	ADV
bracis-19038	419	12	\(\forall	\(\forall	ADV
bracis-19038	419	13	x	x	PART
bracis-19038	419	14	\in	\in	PROPN
bracis-19038	419	15	\	\	PROPN
bracis-19038	419	16	{	{	PUNCT
bracis-19038	419	17	st	st	PROPN
bracis-19038	419	18	,	,	PUNCT
bracis-19038	419	19	opt	opt	NOUN
bracis-19038	419	20	,	,	PUNCT
bracis-19038	419	21	\	\	ADJ
bracis-19038	419	22	)	)	PUNCT
bracis-19038	419	23	\	\	PROPN
bracis-19038	419	24	(	(	PUNCT
bracis-19038	419	25	pes	pe	NOUN
bracis-19038	419	26	,	,	PUNCT
bracis-19038	419	27	opp	opp	PROPN
bracis-19038	419	28	\}\	\}\	NOUN
bracis-19038	419	29	)	)	PUNCT
bracis-19038	419	30	and	and	CCONJ
bracis-19038	419	31	\(\forall	\(\forall	ADV
bracis-19038	419	32	y	y	PROPN
bracis-19038	419	33	\in	\in	PROPN
bracis-19038	419	34	\left\	\left\	PROPN
bracis-19038	419	35	{	{	PUNCT
bracis-19038	419	36	\forall	\forall	INTJ
bracis-19038	419	37	\forall	\forall	INTJ
bracis-19038	419	38	,	,	PUNCT
bracis-19038	419	39	\forall	\forall	DET
bracis-19038	419	40	\exists	\exist	NOUN
bracis-19038	419	41	,	,	PUNCT
bracis-19038	419	42	\exists	\exist	NOUN
bracis-19038	419	43	\forall	\forall	ADV
bracis-19038	419	44	,	,	PUNCT
bracis-19038	419	45	\exists	\exist	NOUN
bracis-19038	419	46	\exists	\exist	NOUN
bracis-19038	419	47	\right\	\right\	ADV
bracis-19038	419	48	}	}	PUNCT
bracis-19038	419	49	\	\	NOUN
bracis-19038	419	50	)	)	PUNCT
bracis-19038	419	51	,	,	PUNCT
bracis-19038	419	52	it	it	PRON
bracis-19038	419	53	does	do	AUX
bracis-19038	419	54	not	not	PART
bracis-19038	419	55	hold	hold	VERB
bracis-19038	419	56	in	in	ADP
bracis-19038	419	57	general	general	ADJ
bracis-19038	419	58	1	1	NUM
bracis-19038	419	59	.	.	PUNCT
bracis-19038	420	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	420	2	{	{	PUNCT
bracis-19038	420	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	420	4	_	_	DET
bracis-19038	420	5	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	420	6	^y_x	^y_x	NOUN
bracis-19038	420	7	}	}	PUNCT
bracis-19038	420	8	\subseteq	\subseteq	PROPN
bracis-19038	420	9	\mathcal	\mathcal	PROPN
bracis-19038	420	10	{	{	PUNCT
bracis-19038	420	11	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	420	12	_	_	PRON
bracis-19038	420	13	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	420	14	^y_x}\	^y_x}\	NUM
bracis-19038	420	15	)	)	PUNCT
bracis-19038	420	16	(	(	PUNCT
bracis-19038	420	17	resp	resp	NOUN
bracis-19038	420	18	.	.	PUNCT
bracis-19038	421	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	421	2	{	{	PUNCT
bracis-19038	421	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	421	4	_	_	PRON
bracis-19038	421	5	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	421	6	^y_x	^y_x	NOUN
bracis-19038	421	7	}	}	PUNCT
bracis-19038	421	8	\subseteq	\subseteq	PROPN
bracis-19038	421	9	\mathcal	\mathcal	PROPN
bracis-19038	421	10	{	{	PUNCT
bracis-19038	421	11	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	421	12	_	_	PRON
bracis-19038	421	13	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	421	14	^y_x}\	^y_x}\	NUM
bracis-19038	421	15	)	)	PUNCT
bracis-19038	421	16	)	)	PUNCT
bracis-19038	421	17	(	(	PUNCT
bracis-19038	421	18	monotonic	monotonic	ADJ
bracis-19038	421	19	)	)	PUNCT
bracis-19038	421	20	.	.	PUNCT
bracis-19038	422	1	2	2	X
bracis-19038	422	2	.	.	X
bracis-19038	422	3	\(\mathcal	\(\mathcal	ADJ
bracis-19038	422	4	{	{	PUNCT
bracis-19038	422	5	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	422	6	_	_	PRON
bracis-19038	422	7	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	422	8	^y_x	^y_x	NOUN
bracis-19038	422	9	}	}	PUNCT
bracis-19038	422	10	\subseteq	\subseteq	PROPN
bracis-19038	422	11	\mathcal	\mathcal	PROPN
bracis-19038	422	12	{	{	PUNCT
bracis-19038	422	13	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	422	14	_	_	PRON
bracis-19038	422	15	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	422	16	^y_x}\	^y_x}\	NUM
bracis-19038	422	17	)	)	PUNCT
bracis-19038	422	18	(	(	PUNCT
bracis-19038	422	19	resp	resp	NOUN
bracis-19038	422	20	.	.	PUNCT
bracis-19038	423	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	423	2	{	{	PUNCT
bracis-19038	423	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	423	4	_	_	PRON
bracis-19038	423	5	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	423	6	^y_x	^y_x	NOUN
bracis-19038	423	7	}	}	PUNCT
bracis-19038	423	8	\subseteq	\subseteq	PROPN
bracis-19038	423	9	\mathcal	\mathcal	PROPN
bracis-19038	423	10	{	{	PUNCT
bracis-19038	423	11	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	423	12	_	_	PRON
bracis-19038	423	13	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	423	14	^y_x}\	^y_x}\	NUM
bracis-19038	423	15	)	)	PUNCT
bracis-19038	423	16	)	)	PUNCT
bracis-19038	423	17	(	(	PUNCT
bracis-19038	423	18	antitonic	antitonic	PROPN
bracis-19038	423	19	)	)	PUNCT
bracis-19038	423	20	.	.	PUNCT
bracis-19038	424	1	proof	proof	NOUN
bracis-19038	424	2	let	let	VERB
bracis-19038	424	3	p	p	PRON
bracis-19038	424	4	be	be	AUX
bracis-19038	424	5	the	the	DET
bracis-19038	424	6	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	424	7	)	)	PUNCT
bracis-19038	425	1	\(\left\	\(\left\	PROPN
bracis-19038	425	2	{	{	PUNCT
bracis-19038	425	3	a	a	DET
bracis-19038	425	4	\leftarrow	\leftarrow	PROPN
bracis-19038	425	5	\mathtt	\mathtt	PROPN
bracis-19038	425	6	{	{	PUNCT
bracis-19038	425	7	not\	not\	PROPN
bracis-19038	425	8	}	}	PUNCT
bracis-19038	425	9	b	b	NOUN
bracis-19038	425	10	\quad	\quad	PROPN
bracis-19038	425	11	b	b	PROPN
bracis-19038	425	12	\leftarrow	\leftarrow	PROPN
bracis-19038	425	13	\mathtt	\mathtt	PROPN
bracis-19038	425	14	{	{	PUNCT
bracis-19038	425	15	not\	not\	PROPN
bracis-19038	425	16	}	}	PUNCT
bracis-19038	425	17	a\right\	a\right\	VERB
bracis-19038	425	18	}	}	PUNCT
bracis-19038	425	19	\	\	NOUN
bracis-19038	425	20	)	)	PUNCT
bracis-19038	425	21	,	,	PUNCT
bracis-19038	425	22	whose	whose	DET
bracis-19038	425	23	\	\	NOUN
bracis-19038	425	24	(	(	PUNCT
bracis-19038	425	25	ps	ps	PROPN
bracis-19038	425	26	\	\	ADJ
bracis-19038	425	27	)	)	PUNCT
bracis-19038	425	28	models	model	NOUN
bracis-19038	425	29	are	be	AUX
bracis-19038	425	30	\(\emptyset	\(\emptyset	ADJ
bracis-19038	425	31	\	\	PROPN
bracis-19038	425	32	)	)	PUNCT
bracis-19038	425	33	,	,	PUNCT
bracis-19038	425	34	\(\left\	\(\left\	PROPN
bracis-19038	425	35	{	{	PUNCT
bracis-19038	425	36	a\right\	a\right\	NOUN
bracis-19038	425	37	}	}	PUNCT
bracis-19038	425	38	\	\	NOUN
bracis-19038	425	39	)	)	PUNCT
bracis-19038	425	40	and	and	CCONJ
bracis-19038	425	41	\(\left\	\(\left\	PROPN
bracis-19038	425	42	{	{	PUNCT
bracis-19038	425	43	b\right\	b\right\	NOUN
bracis-19038	425	44	}	}	PUNCT
bracis-19038	425	45	\	\	NOUN
bracis-19038	425	46	)	)	PUNCT
bracis-19038	425	47	.	.	PUNCT
bracis-19038	426	1	firstly	firstly	ADV
bracis-19038	426	2	,	,	PUNCT
bracis-19038	426	3	we	we	PRON
bracis-19038	426	4	will	will	AUX
bracis-19038	426	5	show	show	VERB
bracis-19038	426	6	a	a	DET
bracis-19038	426	7	counterexample	counterexample	NOUN
bracis-19038	426	8	to	to	ADP
bracis-19038	426	9	the	the	DET
bracis-19038	426	10	statement	statement	NOUN
bracis-19038	426	11	\(\forall	\(\forall	ADV
bracis-19038	426	12	x	x	PART
bracis-19038	426	13	\in	\in	PROPN
bracis-19038	426	14	\	\	PROPN
bracis-19038	426	15	{	{	PUNCT
bracis-19038	426	16	st	st	PROPN
bracis-19038	426	17	,	,	PUNCT
bracis-19038	426	18	opt	opt	NOUN
bracis-19038	426	19	,	,	PUNCT
bracis-19038	426	20	\	\	ADJ
bracis-19038	426	21	)	)	PUNCT
bracis-19038	427	1	\	\	PROPN
bracis-19038	427	2	(	(	PUNCT
bracis-19038	427	3	pes	pe	NOUN
bracis-19038	427	4	,	,	PUNCT
bracis-19038	427	5	opp	opp	PROPN
bracis-19038	427	6	\}\	\}\	NOUN
bracis-19038	427	7	)	)	PUNCT
bracis-19038	427	8	and	and	CCONJ
bracis-19038	427	9	\(\forall	\(\forall	ADV
bracis-19038	427	10	y	y	PROPN
bracis-19038	427	11	\in	\in	PROPN
bracis-19038	427	12	\left\	\left\	PROPN
bracis-19038	427	13	{	{	PUNCT
bracis-19038	427	14	\forall	\forall	INTJ
bracis-19038	428	1	\forall	\forall	INTJ
bracis-19038	428	2	,	,	PUNCT
bracis-19038	428	3	\forall	\forall	DET
bracis-19038	428	4	\exists	\exist	NOUN
bracis-19038	428	5	,	,	PUNCT
bracis-19038	428	6	\exists	\exist	NOUN
bracis-19038	428	7	\forall	\forall	ADV
bracis-19038	428	8	,	,	PUNCT
bracis-19038	428	9	\exists	\exist	NOUN
bracis-19038	428	10	\exists	\exist	NOUN
bracis-19038	428	11	\right\	\right\	ADV
bracis-19038	428	12	}	}	PUNCT
bracis-19038	428	13	\	\	NOUN
bracis-19038	428	14	)	)	PUNCT
bracis-19038	428	15	,	,	PUNCT
bracis-19038	428	16	it	it	PRON
bracis-19038	428	17	holds	hold	VERB
bracis-19038	428	18	\(\mathcal	\(\mathcal	ADJ
bracis-19038	428	19	{	{	PUNCT
bracis-19038	428	20	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	428	21	_	_	DET
bracis-19038	428	22	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	428	23	^y_x	^y_x	NOUN
bracis-19038	428	24	}	}	PUNCT
bracis-19038	428	25	\subseteq	\subseteq	PROPN
bracis-19038	428	26	\mathcal	\mathcal	PROPN
bracis-19038	428	27	{	{	PUNCT
bracis-19038	428	28	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	428	29	_	_	PRON
bracis-19038	428	30	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	428	31	^y_x}\	^y_x}\	NUM
bracis-19038	428	32	)	)	PUNCT
bracis-19038	428	33	(	(	PUNCT
bracis-19038	428	34	resp	resp	NOUN
bracis-19038	428	35	.	.	PUNCT
bracis-19038	429	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	429	2	{	{	PUNCT
bracis-19038	429	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	429	4	_	_	PRON
bracis-19038	429	5	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	429	6	^y_x	^y_x	NOUN
bracis-19038	429	7	}	}	PUNCT
bracis-19038	429	8	\subseteq	\subseteq	PROPN
bracis-19038	429	9	\mathcal	\mathcal	PROPN
bracis-19038	429	10	{	{	PUNCT
bracis-19038	429	11	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	429	12	_	_	PRON
bracis-19038	429	13	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	429	14	^y_x}\	^y_x}\	NUM
bracis-19038	429	15	)	)	PUNCT
bracis-19038	429	16	)	)	PUNCT
bracis-19038	429	17	:	:	PUNCT
bracis-19038	429	18	let	let	VERB
bracis-19038	429	19	\(\varphi	\(\varphi	PROPN
bracis-19038	429	20	_	_	NOUN
bracis-19038	429	21	1	1	X
bracis-19038	429	22	=	=	SYM
bracis-19038	429	23	\emptyset	\emptyset	VERB
bracis-19038	429	24	\	\	NOUN
bracis-19038	429	25	)	)	PUNCT
bracis-19038	429	26	and	and	CCONJ
bracis-19038	429	27	\(\varphi	\(\varphi	PUNCT
bracis-19038	429	28	_	_	NOUN
bracis-19038	429	29	2	2	X
bracis-19038	429	30	=	=	SYM
bracis-19038	429	31	\left\	\left\	PROPN
bracis-19038	429	32	{	{	PUNCT
bracis-19038	429	33	\emptyset	\emptyset	VERB
bracis-19038	429	34	\preceq	\preceq	PROPN
bracis-19038	429	35	\left\	\left\	PROPN
bracis-19038	429	36	{	{	PUNCT
bracis-19038	429	37	b\right\	b\right\	NOUN
bracis-19038	429	38	}	}	PUNCT
bracis-19038	429	39	,	,	PUNCT
bracis-19038	429	40	\left\	\left\	PROPN
bracis-19038	429	41	{	{	PUNCT
bracis-19038	429	42	b\right\	b\right\	NOUN
bracis-19038	429	43	}	}	PUNCT
bracis-19038	429	44	\preceq	\preceq	PROPN
bracis-19038	429	45	\left\	\left\	PROPN
bracis-19038	429	46	{	{	PUNCT
bracis-19038	429	47	a\right\	a\right\	PROPN
bracis-19038	429	48	}	}	PUNCT
bracis-19038	429	49	\right\	\right\	ADJ
bracis-19038	429	50	}	}	PUNCT
bracis-19038	429	51	\	\	NOUN
bracis-19038	429	52	)	)	PUNCT
bracis-19038	429	53	.	.	PUNCT
bracis-19038	430	1	we	we	PRON
bracis-19038	430	2	have	have	VERB
bracis-19038	430	3	\(\forall	\(\forall	ADV
bracis-19038	430	4	x	x	PART
bracis-19038	430	5	\in	\in	PROPN
bracis-19038	430	6	\	\	PROPN
bracis-19038	430	7	{	{	PUNCT
bracis-19038	430	8	st	st	PROPN
bracis-19038	430	9	,	,	PUNCT
bracis-19038	430	10	opt	opt	NOUN
bracis-19038	430	11	,	,	PUNCT
bracis-19038	430	12	\	\	ADJ
bracis-19038	430	13	)	)	PUNCT
bracis-19038	431	1	\	\	PROPN
bracis-19038	431	2	(	(	PUNCT
bracis-19038	431	3	pes	pe	NOUN
bracis-19038	431	4	,	,	PUNCT
bracis-19038	431	5	opp	opp	PROPN
bracis-19038	431	6	\}\	\}\	NOUN
bracis-19038	431	7	)	)	PUNCT
bracis-19038	431	8	and	and	CCONJ
bracis-19038	431	9	\(\forall	\(\forall	ADV
bracis-19038	431	10	y	y	PROPN
bracis-19038	431	11	\in	\in	PROPN
bracis-19038	431	12	\left\	\left\	PROPN
bracis-19038	431	13	{	{	PUNCT
bracis-19038	431	14	\forall	\forall	INTJ
bracis-19038	432	1	\forall	\forall	INTJ
bracis-19038	432	2	,	,	PUNCT
bracis-19038	432	3	\forall	\forall	DET
bracis-19038	432	4	\exists	\exist	NOUN
bracis-19038	432	5	,	,	PUNCT
bracis-19038	432	6	\exists	\exist	NOUN
bracis-19038	432	7	\forall	\forall	ADV
bracis-19038	432	8	,	,	PUNCT
bracis-19038	432	9	\exists	\exist	NOUN
bracis-19038	432	10	\exists	\exist	NOUN
bracis-19038	432	11	\right\	\right\	ADV
bracis-19038	432	12	}	}	PUNCT
bracis-19038	432	13	\	\	NOUN
bracis-19038	432	14	)	)	PUNCT
bracis-19038	432	15	,	,	PUNCT
bracis-19038	432	16	it	it	PRON
bracis-19038	432	17	holds	hold	VERB
bracis-19038	432	18	\(\mathcal	\(\mathcal	ADJ
bracis-19038	432	19	{	{	PUNCT
bracis-19038	432	20	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	432	21	_	_	DET
bracis-19038	432	22	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	432	23	^y_x	^y_x	NOUN
bracis-19038	432	24	}	}	PUNCT
bracis-19038	432	25	=	=	SYM
bracis-19038	432	26	\mathcal	\mathcal	ADJ
bracis-19038	432	27	{	{	PUNCT
bracis-19038	432	28	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	432	29	_	_	PRON
bracis-19038	432	30	1)_{\sqsubseteq	1)_{\sqsubseteq	NUM
bracis-19038	432	31	^y_x	^y_x	VERB
bracis-19038	432	32	}	}	PUNCT
bracis-19038	432	33	=	=	SYM
bracis-19038	432	34	\	\	NOUN
bracis-19038	432	35	{	{	PUNCT
bracis-19038	432	36	\emptyset	\emptyset	VERB
bracis-19038	432	37	,	,	PUNCT
bracis-19038	432	38	\left\	\left\	PROPN
bracis-19038	432	39	{	{	PUNCT
bracis-19038	432	40	a\right\	a\right\	PROPN
bracis-19038	432	41	}	}	PUNCT
bracis-19038	432	42	,	,	PUNCT
bracis-19038	432	43	\	\	ADJ
bracis-19038	432	44	)	)	PUNCT
bracis-19038	433	1	\	\	PROPN
bracis-19038	433	2	(	(	PUNCT
bracis-19038	433	3	\left\	\left\	PROPN
bracis-19038	433	4	{	{	PUNCT
bracis-19038	433	5	b\right\	b\right\	NOUN
bracis-19038	433	6	}	}	PUNCT
bracis-19038	433	7	\}\	\}\	NOUN
bracis-19038	433	8	)	)	PUNCT
bracis-19038	433	9	and	and	CCONJ
bracis-19038	433	10	\(\mathcal	\(\mathcal	ADJ
bracis-19038	433	11	{	{	PUNCT
bracis-19038	433	12	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	433	13	_	_	DET
bracis-19038	433	14	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	433	15	^y_x	^y_x	NOUN
bracis-19038	433	16	}	}	PUNCT
bracis-19038	433	17	=	=	SYM
bracis-19038	433	18	\mathcal	\mathcal	ADJ
bracis-19038	433	19	{	{	PUNCT
bracis-19038	433	20	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	433	21	_	_	PRON
bracis-19038	433	22	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	433	23	^y_x	^y_x	NOUN
bracis-19038	433	24	}	}	PUNCT
bracis-19038	433	25	=	=	SYM
bracis-19038	433	26	\left\	\left\	PROPN
bracis-19038	433	27	{	{	PUNCT
bracis-19038	433	28	\left\	\left\	PROPN
bracis-19038	433	29	{	{	PUNCT
bracis-19038	433	30	a\right\	a\right\	PROPN
bracis-19038	433	31	}	}	PUNCT
bracis-19038	433	32	\right\	\right\	ADJ
bracis-19038	433	33	}	}	PUNCT
bracis-19038	433	34	\	\	NOUN
bracis-19038	433	35	)	)	PUNCT
bracis-19038	433	36	.	.	PUNCT
bracis-19038	434	1	consequently	consequently	ADV
bracis-19038	434	2	,	,	PUNCT
bracis-19038	434	3	$	$	SYM
bracis-19038	434	4	$	$	SYM
bracis-19038	434	5	\begin{aligned	\begin{aligne	VERB
bracis-19038	434	6	}	}	PUNCT
bracis-19038	434	7	\mathcal	\mathcal	ADJ
bracis-19038	434	8	{	{	PUNCT
bracis-19038	434	9	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	434	10	_	_	PRON
bracis-19038	434	11	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	434	12	^y_x	^y_x	NOUN
bracis-19038	434	13	}	}	PUNCT
bracis-19038	434	14	=	=	SYM
bracis-19038	434	15	\mathcal	\mathcal	ADJ
bracis-19038	434	16	{	{	PUNCT
bracis-19038	434	17	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	434	18	_	_	PRON
bracis-19038	434	19	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	434	20	^y_x	^y_x	NOUN
bracis-19038	434	21	}	}	PUNCT
bracis-19038	434	22	\not	\not	ADV
bracis-19038	434	23	\subseteq	\subseteq	PROPN
bracis-19038	434	24	\mathcal	\mathcal	PROPN
bracis-19038	434	25	{	{	PUNCT
bracis-19038	434	26	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	434	27	_	_	PRON
bracis-19038	434	28	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	434	29	^y_x	^y_x	NOUN
bracis-19038	434	30	}	}	PUNCT
bracis-19038	434	31	=	=	SYM
bracis-19038	434	32	\mathcal	\mathcal	ADJ
bracis-19038	434	33	{	{	PUNCT
bracis-19038	434	34	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	434	35	_	_	PRON
bracis-19038	434	36	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	434	37	^y_x	^y_x	NUM
bracis-19038	434	38	}	}	PUNCT
bracis-19038	434	39	\end{aligned}$$	\end{aligned}$$	ADP
bracis-19038	434	40	now	now	ADV
bracis-19038	434	41	we	we	PRON
bracis-19038	434	42	will	will	AUX
bracis-19038	434	43	show	show	VERB
bracis-19038	434	44	a	a	DET
bracis-19038	434	45	counterexample	counterexample	NOUN
bracis-19038	434	46	to	to	ADP
bracis-19038	434	47	\(\forall	\(\forall	ADV
bracis-19038	434	48	x	x	PART
bracis-19038	434	49	\in	\in	PROPN
bracis-19038	434	50	\	\	PROPN
bracis-19038	434	51	{	{	PUNCT
bracis-19038	434	52	st	st	PROPN
bracis-19038	434	53	,	,	PUNCT
bracis-19038	434	54	opt	opt	NOUN
bracis-19038	434	55	,	,	PUNCT
bracis-19038	434	56	\	\	ADJ
bracis-19038	434	57	)	)	PUNCT
bracis-19038	435	1	\	\	PROPN
bracis-19038	435	2	(	(	PUNCT
bracis-19038	435	3	pes	pe	NOUN
bracis-19038	435	4	,	,	PUNCT
bracis-19038	435	5	opp	opp	PROPN
bracis-19038	435	6	\}\	\}\	NOUN
bracis-19038	435	7	)	)	PUNCT
bracis-19038	435	8	and	and	CCONJ
bracis-19038	435	9	\(\forall	\(\forall	ADV
bracis-19038	435	10	y	y	PROPN
bracis-19038	435	11	\in	\in	PROPN
bracis-19038	435	12	\left\	\left\	PROPN
bracis-19038	435	13	{	{	PUNCT
bracis-19038	435	14	\forall	\forall	INTJ
bracis-19038	436	1	\forall	\forall	INTJ
bracis-19038	436	2	,	,	PUNCT
bracis-19038	436	3	\forall	\forall	DET
bracis-19038	436	4	\exists	\exist	NOUN
bracis-19038	436	5	,	,	PUNCT
bracis-19038	436	6	\exists	\exist	NOUN
bracis-19038	436	7	\forall	\forall	ADV
bracis-19038	436	8	,	,	PUNCT
bracis-19038	436	9	\exists	\exist	NOUN
bracis-19038	436	10	\exists	\exist	NOUN
bracis-19038	436	11	\right\	\right\	ADV
bracis-19038	436	12	}	}	PUNCT
bracis-19038	436	13	\	\	NOUN
bracis-19038	436	14	)	)	PUNCT
bracis-19038	436	15	,	,	PUNCT
bracis-19038	436	16	it	it	PRON
bracis-19038	436	17	holds	hold	VERB
bracis-19038	436	18	\(\mathcal	\(\mathcal	ADJ
bracis-19038	436	19	{	{	PUNCT
bracis-19038	436	20	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	436	21	_	_	DET
bracis-19038	436	22	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	436	23	^y_x	^y_x	NOUN
bracis-19038	436	24	}	}	PUNCT
bracis-19038	436	25	\subseteq	\subseteq	PROPN
bracis-19038	436	26	\mathcal	\mathcal	PROPN
bracis-19038	436	27	{	{	PUNCT
bracis-19038	436	28	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	436	29	_	_	PRON
bracis-19038	436	30	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	436	31	^y_x}\	^y_x}\	NUM
bracis-19038	436	32	)	)	PUNCT
bracis-19038	436	33	(	(	PUNCT
bracis-19038	436	34	resp	resp	NOUN
bracis-19038	436	35	.	.	PUNCT
bracis-19038	437	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	437	2	{	{	PUNCT
bracis-19038	437	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	437	4	_	_	PRON
bracis-19038	437	5	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	437	6	^y_x	^y_x	NOUN
bracis-19038	437	7	}	}	PUNCT
bracis-19038	437	8	\subseteq	\subseteq	PROPN
bracis-19038	437	9	\mathcal	\mathcal	PROPN
bracis-19038	437	10	{	{	PUNCT
bracis-19038	437	11	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	437	12	_	_	PRON
bracis-19038	437	13	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	437	14	^y_x}\	^y_x}\	NUM
bracis-19038	437	15	)	)	PUNCT
bracis-19038	437	16	):	):	PUNCT
bracis-19038	438	1	let	let	VERB
bracis-19038	438	2	\(\varphi	\(\varphi	PROPN
bracis-19038	438	3	_	_	NOUN
bracis-19038	438	4	1	1	X
bracis-19038	438	5	=	=	SYM
bracis-19038	438	6	\left\	\left\	PROPN
bracis-19038	438	7	{	{	PUNCT
bracis-19038	438	8	\emptyset	\emptyset	VERB
bracis-19038	438	9	\preceq	\preceq	PROPN
bracis-19038	438	10	\left\	\left\	PROPN
bracis-19038	438	11	{	{	PUNCT
bracis-19038	438	12	b\right\	b\right\	NOUN
bracis-19038	438	13	}	}	PUNCT
bracis-19038	438	14	,	,	PUNCT
bracis-19038	438	15	\left\	\left\	PROPN
bracis-19038	438	16	{	{	PUNCT
bracis-19038	438	17	b\right\	b\right\	NOUN
bracis-19038	438	18	}	}	PUNCT
bracis-19038	438	19	\preceq	\preceq	PROPN
bracis-19038	438	20	\left\	\left\	PROPN
bracis-19038	438	21	{	{	PUNCT
bracis-19038	438	22	a\right\	a\right\	PROPN
bracis-19038	438	23	}	}	PUNCT
bracis-19038	438	24	\right\	\right\	ADJ
bracis-19038	438	25	}	}	PUNCT
bracis-19038	438	26	\	\	NOUN
bracis-19038	438	27	)	)	PUNCT
bracis-19038	438	28	and	and	CCONJ
bracis-19038	438	29	\(\varphi	\(\varphi	PUNCT
bracis-19038	438	30	_	_	NOUN
bracis-19038	438	31	2	2	X
bracis-19038	438	32	=	=	SYM
bracis-19038	438	33	\left\	\left\	PROPN
bracis-19038	438	34	{	{	PUNCT
bracis-19038	438	35	\emptyset	\emptyset	VERB
bracis-19038	438	36	\preceq	\preceq	PROPN
bracis-19038	438	37	\left\	\left\	PROPN
bracis-19038	438	38	{	{	PUNCT
bracis-19038	438	39	b\right\	b\right\	NOUN
bracis-19038	438	40	}	}	PUNCT
bracis-19038	438	41	,	,	PUNCT
bracis-19038	438	42	\left\	\left\	PROPN
bracis-19038	438	43	{	{	PUNCT
bracis-19038	438	44	b\right\	b\right\	NOUN
bracis-19038	438	45	}	}	PUNCT
bracis-19038	438	46	\preceq	\preceq	PROPN
bracis-19038	438	47	\left\	\left\	PROPN
bracis-19038	438	48	{	{	PUNCT
bracis-19038	438	49	a\right\	a\right\	PROPN
bracis-19038	438	50	}	}	PUNCT
bracis-19038	438	51	,	,	PUNCT
bracis-19038	438	52	\left\	\left\	PROPN
bracis-19038	438	53	{	{	PUNCT
bracis-19038	438	54	a\right\	a\right\	PROPN
bracis-19038	438	55	}	}	PUNCT
bracis-19038	438	56	\preceq	\preceq	PROPN
bracis-19038	438	57	\emptyset	\emptyset	VERB
bracis-19038	438	58	\right\	\right\	ADV
bracis-19038	438	59	}	}	PUNCT
bracis-19038	438	60	\	\	NOUN
bracis-19038	438	61	)	)	PUNCT
bracis-19038	438	62	.	.	PUNCT
bracis-19038	439	1	we	we	PRON
bracis-19038	439	2	have	have	VERB
bracis-19038	439	3	\(\forall	\(\forall	ADV
bracis-19038	439	4	x	x	PART
bracis-19038	439	5	\in	\in	PROPN
bracis-19038	439	6	\	\	PROPN
bracis-19038	439	7	{	{	PUNCT
bracis-19038	439	8	st	st	PROPN
bracis-19038	439	9	,	,	PUNCT
bracis-19038	439	10	opt	opt	NOUN
bracis-19038	439	11	,	,	PUNCT
bracis-19038	439	12	\	\	ADJ
bracis-19038	439	13	)	)	PUNCT
bracis-19038	440	1	\	\	PROPN
bracis-19038	440	2	(	(	PUNCT
bracis-19038	440	3	pes	pe	NOUN
bracis-19038	440	4	,	,	PUNCT
bracis-19038	440	5	opp	opp	PROPN
bracis-19038	440	6	\}\	\}\	NOUN
bracis-19038	440	7	)	)	PUNCT
bracis-19038	440	8	and	and	CCONJ
bracis-19038	440	9	\(\forall	\(\forall	ADV
bracis-19038	440	10	y	y	PROPN
bracis-19038	440	11	\in	\in	PROPN
bracis-19038	440	12	\left\	\left\	PROPN
bracis-19038	440	13	{	{	PUNCT
bracis-19038	440	14	\forall	\forall	INTJ
bracis-19038	441	1	\forall	\forall	INTJ
bracis-19038	441	2	,	,	PUNCT
bracis-19038	441	3	\forall	\forall	DET
bracis-19038	441	4	\exists	\exist	NOUN
bracis-19038	441	5	,	,	PUNCT
bracis-19038	441	6	\exists	\exist	NOUN
bracis-19038	441	7	\forall	\forall	ADV
bracis-19038	441	8	,	,	PUNCT
bracis-19038	441	9	\exists	\exist	NOUN
bracis-19038	441	10	\exists	\exist	NOUN
bracis-19038	441	11	\right\	\right\	ADV
bracis-19038	441	12	}	}	PUNCT
bracis-19038	441	13	\	\	NOUN
bracis-19038	441	14	)	)	PUNCT
bracis-19038	441	15	,	,	PUNCT
bracis-19038	441	16	it	it	PRON
bracis-19038	441	17	holds	hold	VERB
bracis-19038	441	18	\(\mathcal	\(\mathcal	ADJ
bracis-19038	441	19	{	{	PUNCT
bracis-19038	441	20	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	441	21	_	_	DET
bracis-19038	441	22	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	441	23	^y_x	^y_x	NOUN
bracis-19038	441	24	}	}	PUNCT
bracis-19038	441	25	=	=	SYM
bracis-19038	441	26	\mathcal	\mathcal	ADJ
bracis-19038	441	27	{	{	PUNCT
bracis-19038	441	28	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	441	29	_	_	PRON
bracis-19038	441	30	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	441	31	^y_x	^y_x	VERB
bracis-19038	441	32	}	}	PUNCT
bracis-19038	441	33	=	=	SYM
bracis-19038	441	34	\left\	\left\	PROPN
bracis-19038	441	35	{	{	PUNCT
bracis-19038	441	36	\left\	\left\	PROPN
bracis-19038	441	37	{	{	PUNCT
bracis-19038	441	38	a\right\	a\right\	PROPN
bracis-19038	441	39	}	}	PUNCT
bracis-19038	441	40	\right\	\right\	ADJ
bracis-19038	441	41	}	}	PUNCT
bracis-19038	441	42	\	\	NOUN
bracis-19038	441	43	)	)	PUNCT
bracis-19038	441	44	and	and	CCONJ
bracis-19038	441	45	\(\mathcal	\(\mathcal	ADJ
bracis-19038	441	46	{	{	PUNCT
bracis-19038	441	47	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	441	48	_	_	PRON
bracis-19038	441	49	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	441	50	^y_x	^y_x	NOUN
bracis-19038	441	51	}	}	PUNCT
bracis-19038	441	52	=	=	SYM
bracis-19038	441	53	\mathcal	\mathcal	ADJ
bracis-19038	441	54	{	{	PUNCT
bracis-19038	441	55	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	441	56	_	_	PRON
bracis-19038	441	57	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	441	58	^y_x	^y_x	NOUN
bracis-19038	441	59	}	}	PUNCT
bracis-19038	441	60	=	=	SYM
bracis-19038	441	61	\left\	\left\	PROPN
bracis-19038	441	62	{	{	PUNCT
bracis-19038	441	63	\emptyset	\emptyset	X
bracis-19038	441	64	,	,	PUNCT
bracis-19038	441	65	\left\	\left\	PROPN
bracis-19038	441	66	{	{	PUNCT
bracis-19038	441	67	a\right\	a\right\	PROPN
bracis-19038	441	68	}	}	PUNCT
bracis-19038	441	69	,	,	PUNCT
bracis-19038	441	70	\left\	\left\	PROPN
bracis-19038	441	71	{	{	PUNCT
bracis-19038	441	72	b\right\	b\right\	NOUN
bracis-19038	441	73	}	}	PUNCT
bracis-19038	441	74	\right\	\right\	ADJ
bracis-19038	441	75	}	}	PUNCT
bracis-19038	441	76	\	\	NOUN
bracis-19038	441	77	)	)	PUNCT
bracis-19038	441	78	.	.	PUNCT
bracis-19038	442	1	consequently	consequently	ADV
bracis-19038	442	2	,	,	PUNCT
bracis-19038	442	3	$	$	SYM
bracis-19038	442	4	$	$	SYM
bracis-19038	442	5	\begin{aligned	\begin{aligne	VERB
bracis-19038	442	6	}	}	PUNCT
bracis-19038	442	7	\mathcal	\mathcal	ADJ
bracis-19038	442	8	{	{	PUNCT
bracis-19038	442	9	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	442	10	_	_	DET
bracis-19038	442	11	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	442	12	^y_x	^y_x	NOUN
bracis-19038	442	13	}	}	PUNCT
bracis-19038	442	14	=	=	SYM
bracis-19038	442	15	\mathcal	\mathcal	ADJ
bracis-19038	442	16	{	{	PUNCT
bracis-19038	442	17	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	442	18	_	_	DET
bracis-19038	442	19	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	442	20	^y_x	^y_x	NOUN
bracis-19038	442	21	}	}	PUNCT
bracis-19038	442	22	\not	\not	ADV
bracis-19038	442	23	\subseteq	\subseteq	PROPN
bracis-19038	442	24	\mathcal	\mathcal	PROPN
bracis-19038	442	25	{	{	PUNCT
bracis-19038	442	26	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	442	27	_	_	PRON
bracis-19038	442	28	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	442	29	^y_x	^y_x	NOUN
bracis-19038	442	30	}	}	PUNCT
bracis-19038	442	31	=	=	SYM
bracis-19038	442	32	\mathcal	\mathcal	ADJ
bracis-19038	442	33	{	{	PUNCT
bracis-19038	442	34	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	442	35	_	_	PRON
bracis-19038	442	36	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	442	37	^y_x	^y_x	NOUN
bracis-19038	442	38	}	}	PUNCT
bracis-19038	442	39	\end{aligned}$$	\end{aligned}$$	ADP
bracis-19038	443	1	we	we	PRON
bracis-19038	443	2	end	end	VERB
bracis-19038	443	3	up	up	ADP
bracis-19038	443	4	this	this	DET
bracis-19038	443	5	section	section	NOUN
bracis-19038	443	6	by	by	ADP
bracis-19038	443	7	showing	show	VERB
bracis-19038	443	8	inconsistency	inconsistency	NOUN
bracis-19038	443	9	options	option	NOUN
bracis-19038	443	10	do	do	AUX
bracis-19038	443	11	not	not	PART
bracis-19038	443	12	interfere	interfere	VERB
bracis-19038	443	13	in	in	ADP
bracis-19038	443	14	the	the	DET
bracis-19038	443	15	process	process	NOUN
bracis-19038	443	16	of	of	ADP
bracis-19038	443	17	selecting	select	VERB
bracis-19038	443	18	the	the	DET
bracis-19038	443	19	\	\	PROPN
bracis-19038	443	20	(	(	PUNCT
bracis-19038	443	21	pps	pps	PROPN
bracis-19038	443	22	\	\	ADJ
bracis-19038	443	23	)	)	PUNCT
bracis-19038	443	24	models	model	NOUN
bracis-19038	443	25	:	:	PUNCT
bracis-19038	443	26	theorem	theorem	NOUN
bracis-19038	443	27	4	4	NUM
bracis-19038	443	28	(	(	PUNCT
bracis-19038	443	29	invariant	invariant	ADJ
bracis-19038	443	30	to	to	PART
bracis-19038	443	31	inconsistency	inconsistency	VERB
bracis-19038	443	32	)	)	PUNCT
bracis-19038	443	33	let	let	VERB
bracis-19038	443	34	\((p	\((p	NOUN
bracis-19038	443	35	,	,	PUNCT
bracis-19038	443	36	\varphi	\varphi	PROPN
bracis-19038	443	37	_	_	NOUN
bracis-19038	443	38	1)\	1)\	NUM
bracis-19038	443	39	)	)	PUNCT
bracis-19038	443	40	and	and	CCONJ
bracis-19038	443	41	\((p	\((p	NOUN
bracis-19038	443	42	,	,	PUNCT
bracis-19038	443	43	\varphi	\varphi	PROPN
bracis-19038	443	44	_	_	NOUN
bracis-19038	443	45	2)\	2)\	NUM
bracis-19038	443	46	)	)	PUNCT
bracis-19038	443	47	be	be	AUX
bracis-19038	443	48	\(\textit{plp}\)s	\(\textit{plp}\)s	ADJ
bracis-19038	443	49	such	such	ADJ
bracis-19038	443	50	that	that	SCONJ
bracis-19038	443	51	\(\varphi	\(\varphi	PROPN
bracis-19038	443	52	_	_	ADJ
bracis-19038	443	53	2	2	X
bracis-19038	443	54	=	=	SYM
bracis-19038	443	55	\left\	\left\	PROPN
bracis-19038	443	56	{	{	PUNCT
bracis-19038	443	57	o_1	o_1	ADP
bracis-19038	443	58	\preceq	\preceq	PROPN
bracis-19038	443	59	o_2	o_2	NOUN
bracis-19038	443	60	\mid	\mid	ADP
bracis-19038	443	61	o_1	o_1	ADP
bracis-19038	443	62	\preceq	\preceq	PROPN
bracis-19038	443	63	o_2	o_2	NOUN
bracis-19038	443	64	\in	\in	PROPN
bracis-19038	443	65	\varphi	\varphi	PROPN
bracis-19038	443	66	_	_	PROPN
bracis-19038	443	67	1	1	NUM
bracis-19038	443	68	\textit	\textit	NOUN
bracis-19038	443	69	{	{	PUNCT
bracis-19038	443	70	and	and	CCONJ
bracis-19038	443	71	both	both	PRON
bracis-19038	443	72	}	}	PUNCT
bracis-19038	443	73	o_1	o_1	ADP
bracis-19038	443	74	\textit	\textit	NOUN
bracis-19038	443	75	{	{	PUNCT
bracis-19038	443	76	and	and	CCONJ
bracis-19038	443	77	}	}	PUNCT
bracis-19038	443	78	o_2	o_2	NOUN
bracis-19038	443	79	\textit	\textit	NOUN
bracis-19038	443	80	{	{	PUNCT
bracis-19038	443	81	are	be	AUX
bracis-19038	443	82	consistent}\right\	consistent}\right\	ADJ
bracis-19038	443	83	}	}	PUNCT
bracis-19038	443	84	\	\	NOUN
bracis-19038	443	85	)	)	PUNCT
bracis-19038	443	86	.	.	PUNCT
bracis-19038	444	1	then	then	ADV
bracis-19038	444	2	\(\forall	\(\forall	ADV
bracis-19038	444	3	x	x	X
bracis-19038	444	4	\in	\in	PROPN
bracis-19038	444	5	\left\	\left\	PROPN
bracis-19038	444	6	{	{	PUNCT
bracis-19038	444	7	st	st	PROPN
bracis-19038	444	8	,	,	PUNCT
bracis-19038	444	9	opt	opt	NOUN
bracis-19038	444	10	,	,	PUNCT
bracis-19038	444	11	pes	pe	NOUN
bracis-19038	444	12	,	,	PUNCT
bracis-19038	444	13	opp	opp	PROPN
bracis-19038	444	14	\right\	\right\	ADV
bracis-19038	444	15	}	}	PUNCT
bracis-19038	444	16	\	\	NOUN
bracis-19038	444	17	)	)	PUNCT
bracis-19038	444	18	and	and	CCONJ
bracis-19038	444	19	\(\forall	\(\forall	ADV
bracis-19038	444	20	y	y	PROPN
bracis-19038	444	21	\in	\in	PROPN
bracis-19038	444	22	\left\	\left\	PROPN
bracis-19038	444	23	{	{	PUNCT
bracis-19038	444	24	\forall	\forall	INTJ
bracis-19038	444	25	\forall	\forall	INTJ
bracis-19038	444	26	,	,	PUNCT
bracis-19038	444	27	\forall	\forall	DET
bracis-19038	444	28	\exists	\exist	NOUN
bracis-19038	444	29	,	,	PUNCT
bracis-19038	444	30	\exists	\exist	NOUN
bracis-19038	444	31	\forall	\forall	ADV
bracis-19038	444	32	,	,	PUNCT
bracis-19038	444	33	\exists	\exist	NOUN
bracis-19038	444	34	\exists	\exist	NOUN
bracis-19038	444	35	\right\	\right\	ADV
bracis-19038	444	36	}	}	PUNCT
bracis-19038	444	37	\	\	NOUN
bracis-19038	444	38	)	)	PUNCT
bracis-19038	444	39	,	,	PUNCT
bracis-19038	444	40	it	it	PRON
bracis-19038	444	41	holds	hold	VERB
bracis-19038	444	42	\(\mathcal	\(\mathcal	ADJ
bracis-19038	444	43	{	{	PUNCT
bracis-19038	444	44	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	444	45	_	_	DET
bracis-19038	444	46	1)_{\subseteq	1)_{\subseteq	NOUN
bracis-19038	444	47	^y_x	^y_x	NOUN
bracis-19038	444	48	}	}	PUNCT
bracis-19038	444	49	=	=	SYM
bracis-19038	444	50	\mathcal	\mathcal	ADJ
bracis-19038	444	51	{	{	PUNCT
bracis-19038	444	52	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	444	53	_	_	PRON
bracis-19038	444	54	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	444	55	^y_x}\	^y_x}\	NUM
bracis-19038	444	56	)	)	PUNCT
bracis-19038	444	57	(	(	PUNCT
bracis-19038	444	58	resp	resp	NOUN
bracis-19038	444	59	.	.	PUNCT
bracis-19038	445	1	\(\mathcal	\(\mathcal	ADJ
bracis-19038	445	2	{	{	PUNCT
bracis-19038	445	3	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	445	4	_	_	PRON
bracis-19038	445	5	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	445	6	^y_x	^y_x	VERB
bracis-19038	445	7	}	}	PUNCT
bracis-19038	445	8	=	=	SYM
bracis-19038	445	9	\mathcal	\mathcal	ADJ
bracis-19038	445	10	{	{	PUNCT
bracis-19038	445	11	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	445	12	_	_	PRON
bracis-19038	445	13	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	445	14	^y_x}\	^y_x}\	NUM
bracis-19038	445	15	)	)	PUNCT
bracis-19038	445	16	)	)	PUNCT
bracis-19038	445	17	.	.	PUNCT
bracis-19038	446	1	proof	proof	NOUN
bracis-19038	446	2	let	let	VERB
bracis-19038	446	3	\(i_1\	\(i_1\	PROPN
bracis-19038	446	4	)	)	PUNCT
bracis-19038	446	5	and	and	CCONJ
bracis-19038	446	6	\(i_2\	\(i_2\	PROPN
bracis-19038	446	7	)	)	PUNCT
bracis-19038	446	8	be	be	VERB
bracis-19038	446	9	a	a	DET
bracis-19038	446	10	\	\	PROPN
bracis-19038	446	11	(	(	PUNCT
bracis-19038	446	12	ps	ps	PROPN
bracis-19038	446	13	\	\	ADJ
bracis-19038	446	14	)	)	PUNCT
bracis-19038	446	15	model	model	NOUN
bracis-19038	446	16	of	of	ADP
bracis-19038	446	17	p.	p.	NOUN
bracis-19038	446	18	we	we	PRON
bracis-19038	446	19	will	will	AUX
bracis-19038	446	20	show	show	VERB
bracis-19038	446	21	\(i_1	\(i_1	PROPN
bracis-19038	446	22	\in	\in	PROPN
bracis-19038	446	23	\mathcal	\mathcal	PROPN
bracis-19038	446	24	{	{	PUNCT
bracis-19038	446	25	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	446	26	_	_	PRON
bracis-19038	446	27	1)_{\subseteq	1)_{\subseteq	NUM
bracis-19038	446	28	^y_x}\	^y_x}\	NUM
bracis-19038	446	29	)	)	PUNCT
bracis-19038	446	30	iff	iff	VERB
bracis-19038	446	31	\(i_1	\(i_1	PROPN
bracis-19038	446	32	\in	\in	PROPN
bracis-19038	446	33	\mathcal	\mathcal	PROPN
bracis-19038	446	34	{	{	PUNCT
bracis-19038	446	35	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	446	36	_	_	PRON
bracis-19038	446	37	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	446	38	^y_x}\	^y_x}\	NUM
bracis-19038	446	39	)	)	PUNCT
bracis-19038	446	40	(	(	PUNCT
bracis-19038	446	41	resp	resp	NOUN
bracis-19038	446	42	.	.	PUNCT
bracis-19038	447	1	\(i_1	\(i_1	NUM
bracis-19038	447	2	\in	\in	PROPN
bracis-19038	447	3	\mathcal	\mathcal	PROPN
bracis-19038	447	4	{	{	PUNCT
bracis-19038	447	5	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	447	6	_	_	PRON
bracis-19038	447	7	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	447	8	^y_x}\	^y_x}\	NUM
bracis-19038	447	9	)	)	PUNCT
bracis-19038	447	10	iff	iff	VERB
bracis-19038	447	11	\(i_1	\(i_1	PROPN
bracis-19038	447	12	\in	\in	PROPN
bracis-19038	447	13	\mathcal	\mathcal	PROPN
bracis-19038	447	14	{	{	PUNCT
bracis-19038	447	15	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	447	16	_	_	PRON
bracis-19038	447	17	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	447	18	^y_x}\	^y_x}\	NUM
bracis-19038	447	19	)	)	PUNCT
bracis-19038	447	20	)	)	PUNCT
bracis-19038	447	21	.	.	PUNCT
bracis-19038	448	1	as	as	SCONJ
bracis-19038	448	2	no	no	DET
bracis-19038	448	3	\	\	PROPN
bracis-19038	448	4	(	(	PUNCT
bracis-19038	448	5	ps	ps	PROPN
bracis-19038	448	6	\	\	ADJ
bracis-19038	448	7	)	)	PUNCT
bracis-19038	448	8	model	model	NOUN
bracis-19038	448	9	is	be	AUX
bracis-19038	448	10	inconsistent	inconsistent	ADJ
bracis-19038	448	11	,	,	PUNCT
bracis-19038	448	12	the	the	DET
bracis-19038	448	13	inconsistent	inconsistent	ADJ
bracis-19038	448	14	options	option	NOUN
bracis-19038	448	15	are	be	AUX
bracis-19038	448	16	neither	neither	CCONJ
bracis-19038	448	17	in	in	ADP
bracis-19038	448	18	the	the	DET
bracis-19038	448	19	set	set	ADJ
bracis-19038	448	20	\(\mathcal	\(\mathcal	ADJ
bracis-19038	448	21	b_{i_j}\	b_{i_j}\	PROPN
bracis-19038	448	22	)	)	PUNCT
bracis-19038	448	23	of	of	ADP
bracis-19038	448	24	all	all	DET
bracis-19038	448	25	best	well	ADV
bracis-19038	448	26	-	-	PUNCT
bracis-19038	448	27	ranked	rank	VERB
bracis-19038	448	28	options	option	NOUN
bracis-19038	448	29	of	of	ADP
bracis-19038	448	30	\(i_j\	\(i_j\	NOUN
bracis-19038	448	31	)	)	PUNCT
bracis-19038	448	32	nor	nor	CCONJ
bracis-19038	448	33	in	in	ADP
bracis-19038	448	34	the	the	DET
bracis-19038	448	35	set	set	ADJ
bracis-19038	448	36	\(\mathcal	\(\mathcal	ADJ
bracis-19038	448	37	w_{i_j}\	w_{i_j}\	NOUN
bracis-19038	448	38	)	)	PUNCT
bracis-19038	448	39	of	of	ADP
bracis-19038	448	40	all	all	DET
bracis-19038	448	41	worst	worst	ADV
bracis-19038	448	42	-	-	PUNCT
bracis-19038	448	43	ranked	rank	VERB
bracis-19038	448	44	options	option	NOUN
bracis-19038	448	45	of	of	ADP
bracis-19038	448	46	\(i_j\	\(i_j\	PROPN
bracis-19038	448	47	)	)	PUNCT
bracis-19038	448	48	with	with	ADP
bracis-19038	448	49	\(j	\(j	PROPN
bracis-19038	448	50	\in	\in	PROPN
bracis-19038	448	51	\left\	\left\	PROPN
bracis-19038	448	52	{	{	PUNCT
bracis-19038	448	53	1,2\right\	1,2\right\	NUM
bracis-19038	448	54	}	}	PUNCT
bracis-19038	448	55	\	\	NOUN
bracis-19038	448	56	)	)	PUNCT
bracis-19038	448	57	.	.	PUNCT
bracis-19038	449	1	this	this	PRON
bracis-19038	449	2	means	mean	VERB
bracis-19038	449	3	for	for	ADP
bracis-19038	449	4	each	each	DET
bracis-19038	449	5	\(o_1	\(o_1	PROPN
bracis-19038	449	6	\in	\in	PROPN
bracis-19038	449	7	\mathcal	\mathcal	PROPN
bracis-19038	449	8	b_{i_1	b_{i_1	NOUN
bracis-19038	449	9	}	}	PUNCT
bracis-19038	449	10	\cup	\cup	VERB
bracis-19038	449	11	\mathcal	\mathcal	ADJ
bracis-19038	449	12	w_{i_1}\	w_{i_1}\	NOUN
bracis-19038	449	13	)	)	PUNCT
bracis-19038	449	14	and	and	CCONJ
bracis-19038	449	15	for	for	ADP
bracis-19038	449	16	each	each	DET
bracis-19038	449	17	\(o_2	\(o_2	PROPN
bracis-19038	449	18	\in	\in	PROPN
bracis-19038	449	19	\mathcal	\mathcal	PROPN
bracis-19038	449	20	b_{i_2	b_{i_2	PUNCT
bracis-19038	449	21	}	}	PUNCT
bracis-19038	449	22	\cup	\cup	X
bracis-19038	449	23	\mathcal	\mathcal	ADJ
bracis-19038	449	24	w_{i_2}\	w_{i_2}\	NOUN
bracis-19038	449	25	)	)	PUNCT
bracis-19038	449	26	,	,	PUNCT
bracis-19038	449	27	it	it	PRON
bracis-19038	449	28	holds	hold	VERB
bracis-19038	449	29	\(o_2	\(o_2	PROPN
bracis-19038	449	30	\not	\not	ADV
bracis-19038	449	31	\prec	\prec	ADP
bracis-19038	449	32	o_1\	o_1\	PROPN
bracis-19038	449	33	)	)	PUNCT
bracis-19038	449	34	according	accord	VERB
bracis-19038	449	35	to	to	ADP
bracis-19038	449	36	\(\varphi	\(\varphi	PROPN
bracis-19038	449	37	_	_	NOUN
bracis-19038	449	38	1^*\	1^*\	NUM
bracis-19038	449	39	)	)	PUNCT
bracis-19038	449	40	iff	iff	PROPN
bracis-19038	449	41	\(o_2	\(o_2	PROPN
bracis-19038	449	42	\not	\not	ADV
bracis-19038	449	43	\prec	\prec	ADP
bracis-19038	449	44	o_1\	o_1\	PROPN
bracis-19038	449	45	)	)	PUNCT
bracis-19038	449	46	according	accord	VERB
bracis-19038	449	47	to	to	ADP
bracis-19038	449	48	\(\varphi	\(\varphi	PROPN
bracis-19038	449	49	_	_	NOUN
bracis-19038	449	50	2^*\	2^*\	NUM
bracis-19038	449	51	)	)	PUNCT
bracis-19038	449	52	.	.	PUNCT
bracis-19038	450	1	then	then	ADV
bracis-19038	450	2	\(\forall	\(\forall	ADV
bracis-19038	450	3	y	y	PROPN
bracis-19038	450	4	\in	\in	PROPN
bracis-19038	450	5	\left\	\left\	PROPN
bracis-19038	450	6	{	{	PUNCT
bracis-19038	450	7	\forall	\forall	INTJ
bracis-19038	450	8	\forall	\forall	INTJ
bracis-19038	450	9	,	,	PUNCT
bracis-19038	450	10	\forall	\forall	DET
bracis-19038	450	11	\exists	\exist	NOUN
bracis-19038	450	12	,	,	PUNCT
bracis-19038	450	13	\exists	\exist	NOUN
bracis-19038	450	14	\forall	\forall	ADV
bracis-19038	450	15	,	,	PUNCT
bracis-19038	450	16	\exists	\exist	NOUN
bracis-19038	450	17	\exists	\exist	NOUN
bracis-19038	450	18	\right\	\right\	ADV
bracis-19038	450	19	}	}	PUNCT
bracis-19038	450	20	\	\	NOUN
bracis-19038	450	21	)	)	PUNCT
bracis-19038	450	22	,	,	PUNCT
bracis-19038	450	23	it	it	PRON
bracis-19038	450	24	holds	hold	VERB
bracis-19038	450	25	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	26	b_{i_1	b_{i_1	NOUN
bracis-19038	450	27	}	}	PUNCT
bracis-19038	450	28	\subseteq	\subseteq	PROPN
bracis-19038	450	29	^y	^y	ADJ
bracis-19038	450	30	\mathcal	\mathcal	ADJ
bracis-19038	450	31	b_{i_2}\	b_{i_2}\	NOUN
bracis-19038	450	32	)	)	PUNCT
bracis-19038	450	33	in	in	ADP
bracis-19038	450	34	\(\varphi	\(\varphi	NOUN
bracis-19038	450	35	_	_	PRON
bracis-19038	450	36	1\	1\	NUM
bracis-19038	450	37	)	)	PUNCT
bracis-19038	450	38	iff	iff	PROPN
bracis-19038	450	39	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	40	b_{i_1	b_{i_1	NOUN
bracis-19038	450	41	}	}	PUNCT
bracis-19038	450	42	\subseteq	\subseteq	PROPN
bracis-19038	450	43	^y	^y	ADJ
bracis-19038	450	44	\mathcal	\mathcal	ADJ
bracis-19038	450	45	b_{i_2}\	b_{i_2}\	NOUN
bracis-19038	450	46	)	)	PUNCT
bracis-19038	450	47	in	in	ADP
bracis-19038	450	48	\(\varphi	\(\varphi	PROPN
bracis-19038	450	49	_	_	NOUN
bracis-19038	450	50	2\	2\	X
bracis-19038	450	51	)	)	PUNCT
bracis-19038	450	52	,	,	PUNCT
bracis-19038	450	53	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	54	b_{i_1	b_{i_1	NOUN
bracis-19038	450	55	}	}	PUNCT
bracis-19038	450	56	\subseteq	\subseteq	PROPN
bracis-19038	450	57	^y	^y	ADJ
bracis-19038	450	58	\mathcal	\mathcal	ADJ
bracis-19038	450	59	w_{i_2}\	w_{i_2}\	NOUN
bracis-19038	450	60	)	)	PUNCT
bracis-19038	450	61	in	in	ADP
bracis-19038	450	62	\(\varphi	\(\varphi	NOUN
bracis-19038	450	63	_	_	PRON
bracis-19038	450	64	1\	1\	NUM
bracis-19038	450	65	)	)	PUNCT
bracis-19038	450	66	iff	iff	PROPN
bracis-19038	450	67	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	68	b_{i_1	b_{i_1	NOUN
bracis-19038	450	69	}	}	PUNCT
bracis-19038	450	70	\subseteq	\subseteq	PROPN
bracis-19038	450	71	^y	^y	ADJ
bracis-19038	450	72	\mathcal	\mathcal	ADJ
bracis-19038	450	73	w_{i_2}\	w_{i_2}\	NOUN
bracis-19038	450	74	)	)	PUNCT
bracis-19038	450	75	in	in	ADP
bracis-19038	450	76	\(\varphi	\(\varphi	PROPN
bracis-19038	450	77	_	_	NOUN
bracis-19038	450	78	2\	2\	X
bracis-19038	450	79	)	)	PUNCT
bracis-19038	450	80	,	,	PUNCT
bracis-19038	450	81	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	82	w_{i_1	w_{i_1	NOUN
bracis-19038	450	83	}	}	PUNCT
bracis-19038	450	84	\subseteq	\subseteq	PROPN
bracis-19038	450	85	^y	^y	ADJ
bracis-19038	450	86	\mathcal	\mathcal	ADJ
bracis-19038	450	87	b_{i_2}\	b_{i_2}\	NOUN
bracis-19038	450	88	)	)	PUNCT
bracis-19038	450	89	in	in	ADP
bracis-19038	450	90	\(\varphi	\(\varphi	NOUN
bracis-19038	450	91	_	_	PRON
bracis-19038	450	92	1\	1\	NUM
bracis-19038	450	93	)	)	PUNCT
bracis-19038	450	94	iff	iff	PROPN
bracis-19038	450	95	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	96	w_{i_1	w_{i_1	NOUN
bracis-19038	450	97	}	}	PUNCT
bracis-19038	450	98	\subseteq	\subseteq	PROPN
bracis-19038	450	99	^y	^y	ADJ
bracis-19038	450	100	\mathcal	\mathcal	ADJ
bracis-19038	450	101	b_{i_2}\	b_{i_2}\	NOUN
bracis-19038	450	102	)	)	PUNCT
bracis-19038	450	103	in	in	ADP
bracis-19038	450	104	\(\varphi	\(\varphi	PROPN
bracis-19038	450	105	_	_	NOUN
bracis-19038	450	106	2\	2\	NUM
bracis-19038	450	107	)	)	PUNCT
bracis-19038	450	108	and	and	CCONJ
bracis-19038	450	109	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	110	w_{i_1	w_{i_1	NOUN
bracis-19038	450	111	}	}	PUNCT
bracis-19038	450	112	\subseteq	\subseteq	PROPN
bracis-19038	450	113	^y	^y	ADJ
bracis-19038	450	114	\mathcal	\mathcal	ADJ
bracis-19038	450	115	w_{i_2}\	w_{i_2}\	NOUN
bracis-19038	450	116	)	)	PUNCT
bracis-19038	450	117	in	in	ADP
bracis-19038	450	118	\(\varphi	\(\varphi	NOUN
bracis-19038	450	119	_	_	PRON
bracis-19038	450	120	1\	1\	NUM
bracis-19038	450	121	)	)	PUNCT
bracis-19038	450	122	iff	iff	PROPN
bracis-19038	450	123	\(\mathcal	\(\mathcal	ADJ
bracis-19038	450	124	w_{i_1	w_{i_1	NOUN
bracis-19038	450	125	}	}	PUNCT
bracis-19038	450	126	\subseteq	\subseteq	PROPN
bracis-19038	450	127	^y	^y	ADJ
bracis-19038	450	128	\mathcal	\mathcal	ADJ
bracis-19038	450	129	w_{i_2}\	w_{i_2}\	NOUN
bracis-19038	450	130	)	)	PUNCT
bracis-19038	450	131	in	in	ADP
bracis-19038	450	132	\(\varphi	\(\varphi	PROPN
bracis-19038	450	133	_	_	NOUN
bracis-19038	450	134	2\	2\	NUM
bracis-19038	450	135	)	)	PUNCT
bracis-19038	450	136	,	,	PUNCT
bracis-19038	450	137	i.e.	i.e.	X
bracis-19038	450	138	,	,	PUNCT
bracis-19038	450	139	\(\forall	\(\forall	ADV
bracis-19038	450	140	x	x	X
bracis-19038	450	141	\in	\in	PROPN
bracis-19038	450	142	\left\	\left\	PROPN
bracis-19038	450	143	{	{	PUNCT
bracis-19038	450	144	st	st	PROPN
bracis-19038	450	145	,	,	PUNCT
bracis-19038	450	146	opt	opt	NOUN
bracis-19038	450	147	,	,	PUNCT
bracis-19038	450	148	pes	pe	NOUN
bracis-19038	450	149	,	,	PUNCT
bracis-19038	450	150	opp	opp	PROPN
bracis-19038	450	151	\right\	\right\	ADV
bracis-19038	450	152	}	}	PUNCT
bracis-19038	450	153	\	\	NOUN
bracis-19038	450	154	)	)	PUNCT
bracis-19038	450	155	and	and	CCONJ
bracis-19038	450	156	\(\forall	\(\forall	ADV
bracis-19038	450	157	y	y	PROPN
bracis-19038	450	158	\in	\in	PROPN
bracis-19038	450	159	\left\	\left\	PROPN
bracis-19038	450	160	{	{	PUNCT
bracis-19038	450	161	\forall	\forall	INTJ
bracis-19038	451	1	\forall	\forall	INTJ
bracis-19038	451	2	,	,	PUNCT
bracis-19038	451	3	\forall	\forall	DET
bracis-19038	451	4	\exists	\exist	NOUN
bracis-19038	451	5	,	,	PUNCT
bracis-19038	451	6	\exists	\exist	NOUN
bracis-19038	451	7	\forall	\forall	ADV
bracis-19038	451	8	,	,	PUNCT
bracis-19038	451	9	\exists	\exist	NOUN
bracis-19038	451	10	\exists	\exist	NOUN
bracis-19038	451	11	\right\	\right\	ADV
bracis-19038	451	12	}	}	PUNCT
bracis-19038	451	13	\	\	NOUN
bracis-19038	451	14	)	)	PUNCT
bracis-19038	451	15	,	,	PUNCT
bracis-19038	451	16	it	it	PRON
bracis-19038	451	17	holds	hold	VERB
bracis-19038	451	18	\(i_1	\(i_1	PROPN
bracis-19038	451	19	\subseteq	\subseteq	PROPN
bracis-19038	451	20	_	_	PROPN
bracis-19038	451	21	x^y	x^y	NOUN
bracis-19038	451	22	i_2\	i_2\	PRON
bracis-19038	451	23	)	)	PUNCT
bracis-19038	451	24	in	in	ADP
bracis-19038	451	25	\(\varphi	\(\varphi	NOUN
bracis-19038	451	26	_	_	PRON
bracis-19038	451	27	1\	1\	NUM
bracis-19038	451	28	)	)	PUNCT
bracis-19038	451	29	iff	iff	VERB
bracis-19038	451	30	\(i_1	\(i_1	PROPN
bracis-19038	451	31	\subseteq	\subseteq	PROPN
bracis-19038	451	32	_	_	PUNCT
bracis-19038	451	33	x^y	x^y	NOUN
bracis-19038	451	34	i_2\	i_2\	PRON
bracis-19038	451	35	)	)	PUNCT
bracis-19038	451	36	in	in	ADP
bracis-19038	451	37	\(\varphi	\(\varphi	PROPN
bracis-19038	451	38	_	_	NOUN
bracis-19038	451	39	2\	2\	NUM
bracis-19038	451	40	)	)	PUNCT
bracis-19038	451	41	.	.	PUNCT
bracis-19038	452	1	hence	hence	ADV
bracis-19038	452	2	,	,	PUNCT
bracis-19038	452	3	\(i_1	\(i_1	PROPN
bracis-19038	452	4	\in	\in	PROPN
bracis-19038	452	5	\mathcal	\mathcal	PROPN
bracis-19038	452	6	{	{	PUNCT
bracis-19038	452	7	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	452	8	_	_	PRON
bracis-19038	452	9	1)_{\subseteq	1)_{\subseteq	NUM
bracis-19038	452	10	^y_x}\	^y_x}\	NUM
bracis-19038	452	11	)	)	PUNCT
bracis-19038	452	12	iff	iff	VERB
bracis-19038	452	13	\(i_1	\(i_1	PROPN
bracis-19038	452	14	\in	\in	PROPN
bracis-19038	452	15	\mathcal	\mathcal	PROPN
bracis-19038	452	16	{	{	PUNCT
bracis-19038	452	17	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	452	18	_	_	PRON
bracis-19038	452	19	2)_{\subseteq	2)_{\subseteq	NOUN
bracis-19038	452	20	^y_x}\	^y_x}\	NUM
bracis-19038	452	21	)	)	PUNCT
bracis-19038	452	22	.	.	PUNCT
bracis-19038	453	1	similarly	similarly	ADV
bracis-19038	453	2	we	we	PRON
bracis-19038	453	3	can	can	AUX
bracis-19038	453	4	prove	prove	VERB
bracis-19038	453	5	\(i_1	\(i_1	NUM
bracis-19038	453	6	\in	\in	PROPN
bracis-19038	453	7	\mathcal	\mathcal	PROPN
bracis-19038	453	8	{	{	PUNCT
bracis-19038	453	9	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	453	10	_	_	PRON
bracis-19038	453	11	1)_{\sqsubseteq	1)_{\sqsubseteq	NOUN
bracis-19038	453	12	^y_x}\	^y_x}\	NUM
bracis-19038	453	13	)	)	PUNCT
bracis-19038	453	14	iff	iff	VERB
bracis-19038	453	15	\(i_1	\(i_1	PROPN
bracis-19038	453	16	\in	\in	PROPN
bracis-19038	453	17	\mathcal	\mathcal	PROPN
bracis-19038	453	18	{	{	PUNCT
bracis-19038	453	19	pps}(p,\varphi	pps}(p,\varphi	PROPN
bracis-19038	453	20	_	_	PRON
bracis-19038	453	21	2)_{\sqsubseteq	2)_{\sqsubseteq	NOUN
bracis-19038	453	22	^y_x}\	^y_x}\	NUM
bracis-19038	453	23	)	)	PUNCT
bracis-19038	453	24	.	.	PUNCT
bracis-19038	453	25	   	   	SPACE
bracis-19038	453	26	\(\square	\(\square	VERB
bracis-19038	453	27	\	\	NOUN
bracis-19038	453	28	)	)	PUNCT
bracis-19038	453	29	6	6	NUM
bracis-19038	453	30	related	relate	VERB
bracis-19038	453	31	work	work	NOUN
bracis-19038	453	32	the	the	DET
bracis-19038	453	33	first	first	ADJ
bracis-19038	453	34	studies	study	NOUN
bracis-19038	453	35	on	on	ADP
bracis-19038	453	36	preference	preference	NOUN
bracis-19038	453	37	information	information	NOUN
bracis-19038	453	38	in	in	ADP
bracis-19038	453	39	non	non	ADJ
bracis-19038	453	40	-	-	ADJ
bracis-19038	453	41	monotonic	monotonic	ADJ
bracis-19038	453	42	reasoning	reasoning	NOUN
bracis-19038	453	43	involved	involve	VERB
bracis-19038	453	44	the	the	DET
bracis-19038	453	45	idea	idea	NOUN
bracis-19038	453	46	of	of	ADP
bracis-19038	453	47	specificity	specificity	NOUN
bracis-19038	453	48	[	[	X
bracis-19038	453	49	22	22	NUM
bracis-19038	453	50	]	]	PUNCT
bracis-19038	453	51	:	:	PUNCT
bracis-19038	453	52	given	give	VERB
bracis-19038	453	53	two	two	NUM
bracis-19038	453	54	conflicting	conflicting	ADJ
bracis-19038	453	55	conclusions	conclusion	NOUN
bracis-19038	453	56	obtained	obtain	VERB
bracis-19038	453	57	from	from	ADP
bracis-19038	453	58	the	the	DET
bracis-19038	453	59	same	same	ADJ
bracis-19038	453	60	initial	initial	ADJ
bracis-19038	453	61	information	information	NOUN
bracis-19038	453	62	but	but	CCONJ
bracis-19038	453	63	resorting	resort	VERB
bracis-19038	453	64	to	to	ADP
bracis-19038	453	65	different	different	ADJ
bracis-19038	453	66	inference	inference	NOUN
bracis-19038	453	67	rules	rule	NOUN
bracis-19038	453	68	,	,	PUNCT
bracis-19038	453	69	one	one	PRON
bracis-19038	453	70	should	should	AUX
bracis-19038	453	71	prefer	prefer	VERB
bracis-19038	453	72	the	the	DET
bracis-19038	453	73	more	more	ADV
bracis-19038	453	74	specific	specific	ADJ
bracis-19038	453	75	.	.	PUNCT
bracis-19038	454	1	following	follow	VERB
bracis-19038	454	2	a	a	DET
bracis-19038	454	3	related	related	ADJ
bracis-19038	454	4	point	point	NOUN
bracis-19038	454	5	of	of	ADP
bracis-19038	454	6	view	view	NOUN
bracis-19038	454	7	,	,	PUNCT
bracis-19038	454	8	in	in	ADP
bracis-19038	454	9	[	[	X
bracis-19038	454	10	23	23	NUM
bracis-19038	454	11	]	]	PUNCT
bracis-19038	454	12	,	,	PUNCT
bracis-19038	454	13	they	they	PRON
bracis-19038	454	14	introduced	introduce	VERB
bracis-19038	454	15	preference	preference	NOUN
bracis-19038	454	16	between	between	ADP
bracis-19038	454	17	predicates	predicate	NOUN
bracis-19038	454	18	in	in	ADP
bracis-19038	454	19	the	the	DET
bracis-19038	454	20	context	context	NOUN
bracis-19038	454	21	of	of	ADP
bracis-19038	454	22	circumscription	circumscription	NOUN
bracis-19038	454	23	.	.	PUNCT
bracis-19038	455	1	preference	preference	NOUN
bracis-19038	455	2	(	(	PUNCT
bracis-19038	455	3	usually	usually	ADV
bracis-19038	455	4	based	base	VERB
bracis-19038	455	5	on	on	ADP
bracis-19038	455	6	simplicity	simplicity	NOUN
bracis-19038	455	7	measures	measure	NOUN
bracis-19038	455	8	)	)	PUNCT
bracis-19038	455	9	is	be	AUX
bracis-19038	455	10	also	also	ADV
bracis-19038	455	11	employed	employ	VERB
bracis-19038	455	12	in	in	ADP
bracis-19038	455	13	[	[	X
bracis-19038	455	14	24	24	NUM
bracis-19038	455	15	]	]	PUNCT
bracis-19038	455	16	to	to	PART
bracis-19038	455	17	select	select	VERB
bracis-19038	455	18	the	the	DET
bracis-19038	455	19	most	most	ADV
bracis-19038	455	20	preferable	preferable	ADJ
bracis-19038	455	21	explanations	explanation	NOUN
bracis-19038	455	22	in	in	ADP
bracis-19038	455	23	abductive	abductive	ADJ
bracis-19038	455	24	systems	system	NOUN
bracis-19038	455	25	.	.	PUNCT
bracis-19038	456	1	with	with	ADP
bracis-19038	456	2	respect	respect	NOUN
bracis-19038	456	3	to	to	ADP
bracis-19038	456	4	preferences	preference	NOUN
bracis-19038	456	5	in	in	ADP
bracis-19038	456	6	logic	logic	NOUN
bracis-19038	456	7	programming	programming	NOUN
bracis-19038	456	8	,	,	PUNCT
bracis-19038	456	9	we	we	PRON
bracis-19038	456	10	find	find	VERB
bracis-19038	456	11	a	a	DET
bracis-19038	456	12	plethora	plethora	NOUN
bracis-19038	456	13	of	of	ADP
bracis-19038	456	14	proposals	proposal	NOUN
bracis-19038	456	15	(	(	PUNCT
bracis-19038	456	16	see	see	VERB
bracis-19038	456	17	[	[	X
bracis-19038	456	18	2,3,4,5,6,7,8,9,10,11,12	2,3,4,5,6,7,8,9,10,11,12	NUM
bracis-19038	456	19	]	]	X
bracis-19038	456	20	for	for	ADP
bracis-19038	456	21	a	a	DET
bracis-19038	456	22	non	non	X
bracis-19038	456	23	exhaustive	exhaustive	ADJ
bracis-19038	456	24	list	list	NOUN
bracis-19038	456	25	)	)	PUNCT
bracis-19038	456	26	.	.	PUNCT
bracis-19038	457	1	in	in	ADP
bracis-19038	457	2	[	[	X
bracis-19038	457	3	2	2	NUM
bracis-19038	457	4	]	]	PUNCT
bracis-19038	457	5	and	and	CCONJ
bracis-19038	457	6	[	[	X
bracis-19038	457	7	3	3	NUM
bracis-19038	457	8	]	]	PUNCT
bracis-19038	457	9	,	,	PUNCT
bracis-19038	457	10	they	they	PRON
bracis-19038	457	11	extend	extend	VERB
bracis-19038	457	12	respectively	respectively	ADV
bracis-19038	457	13	the	the	DET
bracis-19038	457	14	well	well	ADV
bracis-19038	457	15	-	-	PUNCT
bracis-19038	457	16	founded	found	VERB
bracis-19038	457	17	semantics	semantic	NOUN
bracis-19038	457	18	and	and	CCONJ
bracis-19038	457	19	the	the	DET
bracis-19038	457	20	answer	answer	NOUN
bracis-19038	457	21	sets	set	VERB
bracis-19038	457	22	semantics	semantic	NOUN
bracis-19038	457	23	[	[	X
bracis-19038	457	24	25	25	NUM
bracis-19038	457	25	]	]	PUNCT
bracis-19038	457	26	for	for	SCONJ
bracis-19038	457	27	logic	logic	NOUN
bracis-19038	457	28	programs	program	NOUN
bracis-19038	457	29	to	to	PART
bracis-19038	457	30	represent	represent	VERB
bracis-19038	457	31	preference	preference	NOUN
bracis-19038	457	32	between	between	ADP
bracis-19038	457	33	rules	rule	NOUN
bracis-19038	457	34	in	in	ADP
bracis-19038	457	35	the	the	DET
bracis-19038	457	36	language	language	NOUN
bracis-19038	457	37	and	and	CCONJ
bracis-19038	457	38	resort	resort	VERB
bracis-19038	457	39	to	to	ADP
bracis-19038	457	40	such	such	ADJ
bracis-19038	457	41	information	information	NOUN
bracis-19038	457	42	to	to	PART
bracis-19038	457	43	obtain	obtain	VERB
bracis-19038	457	44	new	new	ADJ
bracis-19038	457	45	conclusions	conclusion	NOUN
bracis-19038	457	46	.	.	PUNCT
bracis-19038	458	1	unlike	unlike	ADP
bracis-19038	458	2	the	the	DET
bracis-19038	458	3	semantics	semantic	NOUN
bracis-19038	458	4	in	in	ADP
bracis-19038	458	5	[	[	X
bracis-19038	458	6	3	3	NUM
bracis-19038	458	7	]	]	PUNCT
bracis-19038	458	8	,	,	PUNCT
bracis-19038	458	9	which	which	PRON
bracis-19038	458	10	allows	allow	VERB
bracis-19038	458	11	multiple	multiple	ADJ
bracis-19038	458	12	preferred	preferred	ADJ
bracis-19038	458	13	answer	answer	NOUN
bracis-19038	458	14	sets	set	NOUN
bracis-19038	458	15	even	even	ADV
bracis-19038	458	16	for	for	ADP
bracis-19038	458	17	some	some	DET
bracis-19038	458	18	fully	fully	ADV
bracis-19038	458	19	prioritised	prioritise	VERB
bracis-19038	458	20	programs	program	NOUN
bracis-19038	458	21	,	,	PUNCT
bracis-19038	458	22	the	the	DET
bracis-19038	458	23	semantics	semantic	NOUN
bracis-19038	458	24	in	in	ADP
bracis-19038	458	25	[	[	X
bracis-19038	458	26	10	10	NUM
bracis-19038	458	27	]	]	SYM
bracis-19038	458	28	selects	select	NOUN
bracis-19038	458	29	at	at	ADP
bracis-19038	458	30	most	most	ADV
bracis-19038	458	31	one	one	NUM
bracis-19038	458	32	preferred	preferred	ADJ
bracis-19038	458	33	answer	answer	NOUN
bracis-19038	458	34	set	set	VERB
bracis-19038	458	35	for	for	ADP
bracis-19038	458	36	all	all	DET
bracis-19038	458	37	fully	fully	ADV
bracis-19038	458	38	prioritised	prioritise	VERB
bracis-19038	458	39	programs	program	NOUN
bracis-19038	458	40	.	.	PUNCT
bracis-19038	459	1	furthermore	furthermore	ADV
bracis-19038	459	2	,	,	PUNCT
bracis-19038	459	3	for	for	ADP
bracis-19038	459	4	a	a	DET
bracis-19038	459	5	large	large	ADJ
bracis-19038	459	6	class	class	NOUN
bracis-19038	459	7	of	of	ADP
bracis-19038	459	8	programs	program	NOUN
bracis-19038	459	9	guaranteed	guarantee	VERB
bracis-19038	459	10	to	to	PART
bracis-19038	459	11	have	have	VERB
bracis-19038	459	12	an	an	DET
bracis-19038	459	13	answer	answer	NOUN
bracis-19038	459	14	set	set	NOUN
bracis-19038	459	15	,	,	PUNCT
bracis-19038	459	16	the	the	DET
bracis-19038	459	17	existence	existence	NOUN
bracis-19038	459	18	of	of	ADP
bracis-19038	459	19	a	a	DET
bracis-19038	459	20	preferred	preferred	ADJ
bracis-19038	459	21	answer	answer	NOUN
bracis-19038	459	22	set	set	NOUN
bracis-19038	459	23	is	be	AUX
bracis-19038	459	24	also	also	ADV
bracis-19038	459	25	guaranteed	guarantee	VERB
bracis-19038	459	26	.	.	PUNCT
bracis-19038	460	1	in	in	ADP
bracis-19038	460	2	ordered	order	VERB
bracis-19038	460	3	logic	logic	NOUN
bracis-19038	460	4	programming	programming	NOUN
bracis-19038	460	5	[	[	X
bracis-19038	460	6	5	5	NUM
bracis-19038	460	7	]	]	PUNCT
bracis-19038	460	8	,	,	PUNCT
bracis-19038	460	9	cr	cr	PROPN
bracis-19038	460	10	-	-	PUNCT
bracis-19038	460	11	prolog	prolog	NOUN
bracis-19038	460	12	[	[	X
bracis-19038	460	13	6	6	NUM
bracis-19038	460	14	]	]	PUNCT
bracis-19038	460	15	,	,	PUNCT
bracis-19038	460	16	logic	logic	NOUN
bracis-19038	460	17	programming	programming	NOUN
bracis-19038	460	18	with	with	ADP
bracis-19038	460	19	ordered	order	VERB
bracis-19038	460	20	disjunction	disjunction	NOUN
bracis-19038	460	21	[	[	X
bracis-19038	460	22	7	7	NUM
bracis-19038	460	23	]	]	PUNCT
bracis-19038	460	24	,	,	PUNCT
bracis-19038	460	25	answer	answer	NOUN
bracis-19038	460	26	set	set	VERB
bracis-19038	460	27	optimization	optimization	NOUN
bracis-19038	460	28	[	[	X
bracis-19038	460	29	8	8	NUM
bracis-19038	460	30	]	]	PUNCT
bracis-19038	460	31	,	,	PUNCT
bracis-19038	460	32	possibilistic	possibilistic	ADJ
bracis-19038	460	33	answer	answer	NOUN
bracis-19038	460	34	set	set	VERB
bracis-19038	460	35	programming	programming	NOUN
bracis-19038	460	36	[	[	X
bracis-19038	460	37	9	9	NUM
bracis-19038	460	38	]	]	PUNCT
bracis-19038	460	39	,	,	PUNCT
bracis-19038	460	40	preference	preference	NOUN
bracis-19038	460	41	is	be	AUX
bracis-19038	460	42	handled	handle	VERB
bracis-19038	460	43	to	to	PART
bracis-19038	460	44	evaluate	evaluate	VERB
bracis-19038	460	45	the	the	DET
bracis-19038	460	46	preferred	prefer	VERB
bracis-19038	460	47	answer	answer	NOUN
bracis-19038	460	48	sets	set	NOUN
bracis-19038	460	49	by	by	ADP
bracis-19038	460	50	specifying	specify	VERB
bracis-19038	460	51	the	the	DET
bracis-19038	460	52	precedence	precedence	NOUN
bracis-19038	460	53	over	over	ADP
bracis-19038	460	54	the	the	DET
bracis-19038	460	55	rules	rule	NOUN
bracis-19038	460	56	or	or	CCONJ
bracis-19038	460	57	the	the	DET
bracis-19038	460	58	literals	literal	NOUN
bracis-19038	460	59	in	in	ADP
bracis-19038	460	60	rules	rule	NOUN
bracis-19038	460	61	heads	head	NOUN
bracis-19038	460	62	.	.	PUNCT
bracis-19038	461	1	a	a	DET
bracis-19038	461	2	logic	logic	NOUN
bracis-19038	461	3	programming	programming	NOUN
bracis-19038	461	4	language	language	NOUN
bracis-19038	461	5	preflog	preflog	NOUN
bracis-19038	461	6	based	base	VERB
bracis-19038	461	7	on	on	ADP
bracis-19038	461	8	an	an	DET
bracis-19038	461	9	infinite	infinite	NOUN
bracis-19038	461	10	-	-	PUNCT
bracis-19038	461	11	valued	value	VERB
bracis-19038	461	12	logic	logic	NOUN
bracis-19038	461	13	has	have	AUX
bracis-19038	461	14	been	be	AUX
bracis-19038	461	15	conceived	conceive	VERB
bracis-19038	461	16	in	in	ADP
bracis-19038	461	17	[	[	X
bracis-19038	461	18	11	11	NUM
bracis-19038	461	19	]	]	PUNCT
bracis-19038	461	20	to	to	PART
bracis-19038	461	21	support	support	VERB
bracis-19038	461	22	operators	operator	NOUN
bracis-19038	461	23	for	for	ADP
bracis-19038	461	24	expressing	express	VERB
bracis-19038	461	25	preferences	preference	NOUN
bracis-19038	461	26	.	.	PUNCT
bracis-19038	462	1	despite	despite	SCONJ
bracis-19038	462	2	the	the	DET
bracis-19038	462	3	infinite	infinite	ADV
bracis-19038	462	4	-	-	PUNCT
bracis-19038	462	5	valued	value	VERB
bracis-19038	462	6	truth	truth	NOUN
bracis-19038	462	7	domain	domain	NOUN
bracis-19038	462	8	,	,	PUNCT
bracis-19038	462	9	it	it	PRON
bracis-19038	462	10	can	can	AUX
bracis-19038	462	11	be	be	AUX
bracis-19038	462	12	defined	define	VERB
bracis-19038	462	13	a	a	DET
bracis-19038	462	14	terminating	terminate	VERB
bracis-19038	462	15	bottom	bottom	ADJ
bracis-19038	462	16	-	-	PUNCT
bracis-19038	462	17	up	up	ADP
bracis-19038	462	18	proof	proof	NOUN
bracis-19038	462	19	procedure	procedure	NOUN
bracis-19038	462	20	for	for	ADP
bracis-19038	462	21	implementing	implement	VERB
bracis-19038	462	22	a	a	DET
bracis-19038	462	23	significant	significant	ADJ
bracis-19038	462	24	fragment	fragment	NOUN
bracis-19038	462	25	of	of	ADP
bracis-19038	462	26	the	the	DET
bracis-19038	462	27	language	language	NOUN
bracis-19038	462	28	.	.	PUNCT
bracis-19038	463	1	for	for	ADP
bracis-19038	463	2	continuous	continuous	ADJ
bracis-19038	463	3	operators	operator	NOUN
bracis-19038	463	4	,	,	PUNCT
bracis-19038	463	5	a	a	DET
bracis-19038	463	6	least	least	ADJ
bracis-19038	463	7	herbrand	herbrand	NOUN
bracis-19038	463	8	model	model	NOUN
bracis-19038	463	9	is	be	AUX
bracis-19038	463	10	guaranteed	guarantee	VERB
bracis-19038	463	11	to	to	PART
bracis-19038	463	12	exist	exist	VERB
bracis-19038	463	13	.	.	PUNCT
bracis-19038	464	1	in	in	ADP
bracis-19038	464	2	[	[	X
bracis-19038	464	3	12	12	NUM
bracis-19038	464	4	]	]	PUNCT
bracis-19038	464	5	,	,	PUNCT
bracis-19038	464	6	it	it	PRON
bracis-19038	464	7	is	be	AUX
bracis-19038	464	8	proposed	propose	VERB
bracis-19038	464	9	a	a	DET
bracis-19038	464	10	logic	logic	NOUN
bracis-19038	464	11	programming	programming	NOUN
bracis-19038	464	12	paradigm	paradigm	NOUN
bracis-19038	464	13	to	to	PART
bracis-19038	464	14	combine	combine	VERB
bracis-19038	464	15	non	non	ADJ
bracis-19038	464	16	-	-	ADJ
bracis-19038	464	17	monotonic	monotonic	ADJ
bracis-19038	464	18	reasoning	reasoning	NOUN
bracis-19038	464	19	with	with	ADP
bracis-19038	464	20	epistemic	epistemic	ADJ
bracis-19038	464	21	preferential	preferential	ADJ
bracis-19038	464	22	reasoning	reasoning	NOUN
bracis-19038	464	23	.	.	PUNCT
bracis-19038	465	1	in	in	ADP
bracis-19038	465	2	this	this	DET
bracis-19038	465	3	proposal	proposal	NOUN
bracis-19038	465	4	,	,	PUNCT
bracis-19038	465	5	the	the	DET
bracis-19038	465	6	relation	relation	NOUN
bracis-19038	465	7	of	of	ADP
bracis-19038	465	8	preferences	preference	NOUN
bracis-19038	465	9	between	between	ADP
bracis-19038	465	10	atoms	atom	NOUN
bracis-19038	465	11	can	can	AUX
bracis-19038	465	12	occur	occur	VERB
bracis-19038	465	13	in	in	ADP
bracis-19038	465	14	the	the	DET
bracis-19038	465	15	body	body	NOUN
bracis-19038	465	16	of	of	ADP
bracis-19038	465	17	the	the	DET
bracis-19038	465	18	rules	rule	NOUN
bracis-19038	465	19	and	and	CCONJ
bracis-19038	465	20	can	can	AUX
bracis-19038	465	21	be	be	AUX
bracis-19038	465	22	employed	employ	VERB
bracis-19038	465	23	to	to	PART
bracis-19038	465	24	possibly	possibly	ADV
bracis-19038	465	25	generate	generate	VERB
bracis-19038	465	26	new	new	ADJ
bracis-19038	465	27	models	model	NOUN
bracis-19038	465	28	.	.	PUNCT
bracis-19038	466	1	an	an	DET
bracis-19038	466	2	approach	approach	NOUN
bracis-19038	466	3	closer	close	ADV
bracis-19038	466	4	in	in	ADP
bracis-19038	466	5	spirit	spirit	PROPN
bracis-19038	466	6	to	to	ADP
bracis-19038	466	7	ours	ours	PRON
bracis-19038	466	8	is	be	AUX
bracis-19038	466	9	[	[	X
bracis-19038	466	10	4	4	NUM
bracis-19038	466	11	]	]	PUNCT
bracis-19038	466	12	,	,	PUNCT
bracis-19038	466	13	where	where	SCONJ
bracis-19038	466	14	the	the	DET
bracis-19038	466	15	authors	author	NOUN
bracis-19038	466	16	introduced	introduce	VERB
bracis-19038	466	17	a	a	DET
bracis-19038	466	18	framework	framework	NOUN
bracis-19038	466	19	of	of	ADP
bracis-19038	466	20	prioritised	prioritise	VERB
bracis-19038	466	21	logic	logic	NOUN
bracis-19038	466	22	programming	programming	NOUN
bracis-19038	466	23	to	to	PART
bracis-19038	466	24	represent	represent	VERB
bracis-19038	466	25	priority	priority	NOUN
bracis-19038	466	26	information	information	NOUN
bracis-19038	466	27	explicitly	explicitly	ADV
bracis-19038	466	28	in	in	ADP
bracis-19038	466	29	a	a	DET
bracis-19038	466	30	program	program	NOUN
bracis-19038	466	31	.	.	PUNCT
bracis-19038	467	1	differently	differently	ADV
bracis-19038	467	2	of	of	ADP
bracis-19038	467	3	us	we	PRON
bracis-19038	467	4	,	,	PUNCT
bracis-19038	467	5	however	however	ADV
bracis-19038	467	6	,	,	PUNCT
bracis-19038	467	7	they	they	PRON
bracis-19038	467	8	restrain	restrain	VERB
bracis-19038	467	9	the	the	DET
bracis-19038	467	10	preference	preference	NOUN
bracis-19038	467	11	relation	relation	NOUN
bracis-19038	467	12	to	to	ADP
bracis-19038	467	13	literals	literal	NOUN
bracis-19038	467	14	only	only	ADV
bracis-19038	467	15	,	,	PUNCT
bracis-19038	467	16	whereas	whereas	SCONJ
bracis-19038	467	17	we	we	PRON
bracis-19038	467	18	have	have	AUX
bracis-19038	467	19	defined	define	VERB
bracis-19038	467	20	the	the	DET
bracis-19038	467	21	preference	preference	NOUN
bracis-19038	467	22	relation	relation	NOUN
bracis-19038	467	23	over	over	ADP
bracis-19038	467	24	sets	set	NOUN
bracis-19038	467	25	of	of	ADP
bracis-19038	467	26	literals	literal	NOUN
bracis-19038	467	27	.	.	PUNCT
bracis-19038	468	1	as	as	ADP
bracis-19038	468	2	consequence	consequence	NOUN
bracis-19038	468	3	,	,	PUNCT
bracis-19038	468	4	in	in	ADP
bracis-19038	468	5	order	order	NOUN
bracis-19038	468	6	to	to	PART
bracis-19038	468	7	express	express	VERB
bracis-19038	468	8	in	in	ADP
bracis-19038	468	9	a	a	DET
bracis-19038	468	10	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	468	11	)	)	PUNCT
bracis-19038	468	12	\((p	\((p	NOUN
bracis-19038	468	13	,	,	PUNCT
bracis-19038	468	14	\varphi	\varphi	PROPN
bracis-19038	468	15	)	)	PUNCT
bracis-19038	468	16	\	\	NOUN
bracis-19038	468	17	)	)	PUNCT
bracis-19038	468	18	the	the	DET
bracis-19038	468	19	complex	complex	ADJ
bracis-19038	468	20	forms	form	NOUN
bracis-19038	468	21	of	of	ADP
bracis-19038	468	22	preferences	preference	NOUN
bracis-19038	468	23	expounded	expound	VERB
bracis-19038	468	24	in	in	ADP
bracis-19038	468	25	sect	sect	NOUN
bracis-19038	468	26	.	.	PUNCT
bracis-19038	468	27	 	 	SPACE
bracis-19038	468	28	4	4	NUM
bracis-19038	468	29	,	,	PUNCT
bracis-19038	468	30	they	they	PRON
bracis-19038	468	31	have	have	VERB
bracis-19038	468	32	to	to	PART
bracis-19038	468	33	change	change	VERB
bracis-19038	468	34	the	the	DET
bracis-19038	468	35	program	program	NOUN
bracis-19038	468	36	p	p	NOUN
bracis-19038	468	37	with	with	ADP
bracis-19038	468	38	the	the	DET
bracis-19038	468	39	introduction	introduction	NOUN
bracis-19038	468	40	of	of	ADP
bracis-19038	468	41	new	new	ADJ
bracis-19038	468	42	atoms	atom	NOUN
bracis-19038	468	43	as	as	ADV
bracis-19038	468	44	well	well	ADV
bracis-19038	468	45	as	as	ADP
bracis-19038	468	46	the	the	DET
bracis-19038	468	47	set	set	NOUN
bracis-19038	468	48	\(\varphi	\(\varphi	NOUN
bracis-19038	468	49	\	\	NOUN
bracis-19038	468	50	)	)	PUNCT
bracis-19038	468	51	of	of	ADP
bracis-19038	468	52	priorities	priority	NOUN
bracis-19038	468	53	.	.	PUNCT
bracis-19038	469	1	furthermore	furthermore	ADV
bracis-19038	469	2	,	,	PUNCT
bracis-19038	469	3	they	they	PRON
bracis-19038	469	4	defined	define	VERB
bracis-19038	469	5	a	a	DET
bracis-19038	469	6	unique	unique	ADJ
bracis-19038	469	7	semantics	semantic	NOUN
bracis-19038	469	8	to	to	PART
bracis-19038	469	9	determine	determine	VERB
bracis-19038	469	10	the	the	DET
bracis-19038	469	11	preferred	preferred	ADJ
bracis-19038	469	12	answer	answer	NOUN
bracis-19038	469	13	sets	set	NOUN
bracis-19038	469	14	.	.	PUNCT
bracis-19038	470	1	in	in	ADP
bracis-19038	470	2	contradistinction	contradistinction	NOUN
bracis-19038	470	3	,	,	PUNCT
bracis-19038	470	4	we	we	PRON
bracis-19038	470	5	introduced	introduce	VERB
bracis-19038	470	6	32	32	NUM
bracis-19038	470	7	different	different	ADJ
bracis-19038	470	8	criteria	criterion	NOUN
bracis-19038	470	9	(	(	PUNCT
bracis-19038	470	10	semantics	semantic	NOUN
bracis-19038	470	11	)	)	PUNCT
bracis-19038	470	12	to	to	PART
bracis-19038	470	13	establish	establish	VERB
bracis-19038	470	14	preference	preference	NOUN
bracis-19038	470	15	between	between	ADP
bracis-19038	470	16	partial	partial	ADJ
bracis-19038	470	17	stable	stable	ADJ
bracis-19038	470	18	models	model	NOUN
bracis-19038	470	19	(	(	PUNCT
bracis-19038	470	20	which	which	PRON
bracis-19038	470	21	allow	allow	VERB
bracis-19038	470	22	defining	define	VERB
bracis-19038	470	23	32	32	NUM
bracis-19038	470	24	different	different	ADJ
bracis-19038	470	25	ways	way	NOUN
bracis-19038	470	26	of	of	ADP
bracis-19038	470	27	selecting	select	VERB
bracis-19038	470	28	the	the	DET
bracis-19038	470	29	preferred	prefer	VERB
bracis-19038	470	30	answer	answer	NOUN
bracis-19038	470	31	sets	set	NOUN
bracis-19038	470	32	)	)	PUNCT
bracis-19038	470	33	.	.	PUNCT
bracis-19038	471	1	in	in	ADP
bracis-19038	471	2	this	this	DET
bracis-19038	471	3	sense	sense	NOUN
bracis-19038	471	4	,	,	PUNCT
bracis-19038	471	5	our	our	PRON
bracis-19038	471	6	work	work	NOUN
bracis-19038	471	7	offers	offer	VERB
bracis-19038	471	8	a	a	DET
bracis-19038	471	9	more	more	ADV
bracis-19038	471	10	comprehensive	comprehensive	ADJ
bracis-19038	471	11	and	and	CCONJ
bracis-19038	471	12	systematic	systematic	ADJ
bracis-19038	471	13	treatment	treatment	NOUN
bracis-19038	471	14	to	to	PART
bracis-19038	471	15	deal	deal	VERB
bracis-19038	471	16	with	with	ADP
bracis-19038	471	17	preferences	preference	NOUN
bracis-19038	471	18	in	in	ADP
bracis-19038	471	19	logic	logic	NOUN
bracis-19038	471	20	programming	programming	NOUN
bracis-19038	471	21	.	.	PUNCT
bracis-19038	472	1	7	7	NUM
bracis-19038	472	2	conclusion	conclusion	NOUN
bracis-19038	472	3	and	and	CCONJ
bracis-19038	472	4	future	future	ADJ
bracis-19038	472	5	works	work	NOUN
bracis-19038	472	6	prioritised	prioritise	VERB
bracis-19038	472	7	logic	logic	NOUN
bracis-19038	472	8	programs	program	NOUN
bracis-19038	472	9	(	(	PUNCT
bracis-19038	472	10	\(\textit{plp}\)s	\(\textit{plp}\)s	ADJ
bracis-19038	472	11	)	)	PUNCT
bracis-19038	473	1	[	[	X
bracis-19038	473	2	4	4	NUM
bracis-19038	473	3	]	]	PUNCT
bracis-19038	473	4	are	be	AUX
bracis-19038	473	5	obtained	obtain	VERB
bracis-19038	473	6	from	from	ADP
bracis-19038	473	7	normal	normal	ADJ
bracis-19038	473	8	logic	logic	NOUN
bracis-19038	473	9	programs	program	NOUN
bracis-19038	473	10	(	(	PUNCT
bracis-19038	473	11	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	473	12	)	)	PUNCT
bracis-19038	473	13	)	)	PUNCT
bracis-19038	473	14	by	by	ADP
bracis-19038	473	15	including	include	VERB
bracis-19038	473	16	priorities	priority	NOUN
bracis-19038	473	17	between	between	ADP
bracis-19038	473	18	literals	literal	NOUN
bracis-19038	473	19	(	(	PUNCT
bracis-19038	473	20	an	an	DET
bracis-19038	473	21	atom	atom	NOUN
bracis-19038	473	22	or	or	CCONJ
bracis-19038	473	23	its	its	PRON
bracis-19038	473	24	negation	negation	NOUN
bracis-19038	473	25	)	)	PUNCT
bracis-19038	473	26	.	.	PUNCT
bracis-19038	474	1	in	in	ADP
bracis-19038	474	2	this	this	DET
bracis-19038	474	3	paper	paper	NOUN
bracis-19038	474	4	,	,	PUNCT
bracis-19038	474	5	we	we	PRON
bracis-19038	474	6	have	have	AUX
bracis-19038	474	7	presented	present	VERB
bracis-19038	474	8	a	a	DET
bracis-19038	474	9	more	more	ADV
bracis-19038	474	10	general	general	ADJ
bracis-19038	474	11	notion	notion	NOUN
bracis-19038	474	12	of	of	ADP
bracis-19038	474	13	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	474	14	)	)	PUNCT
bracis-19038	474	15	when	when	SCONJ
bracis-19038	474	16	compared	compare	VERB
bracis-19038	474	17	with	with	ADP
bracis-19038	474	18	that	that	DET
bracis-19038	474	19	version	version	NOUN
bracis-19038	474	20	in	in	ADP
bracis-19038	474	21	[	[	X
bracis-19038	474	22	4	4	NUM
bracis-19038	474	23	]	]	PUNCT
bracis-19038	474	24	.	.	PUNCT
bracis-19038	475	1	our	our	PRON
bracis-19038	475	2	proposal	proposal	NOUN
bracis-19038	475	3	has	have	VERB
bracis-19038	475	4	two	two	NUM
bracis-19038	475	5	main	main	ADJ
bracis-19038	475	6	distinguishing	distinguishing	NOUN
bracis-19038	475	7	features	feature	NOUN
bracis-19038	475	8	:	:	PUNCT
bracis-19038	475	9	a	a	X
bracis-19038	475	10	)	)	PUNCT
bracis-19038	475	11	it	it	PRON
bracis-19038	475	12	encompasses	encompass	VERB
bracis-19038	475	13	not	not	PART
bracis-19038	475	14	only	only	ADV
bracis-19038	475	15	priorities	priority	NOUN
bracis-19038	475	16	between	between	ADP
bracis-19038	475	17	literals	literal	NOUN
bracis-19038	475	18	(	(	PUNCT
bracis-19038	475	19	atoms	atom	NOUN
bracis-19038	475	20	or	or	CCONJ
bracis-19038	475	21	its	its	PRON
bracis-19038	475	22	negation	negation	NOUN
bracis-19038	475	23	)	)	PUNCT
bracis-19038	475	24	,	,	PUNCT
bracis-19038	475	25	but	but	CCONJ
bracis-19038	475	26	also	also	ADV
bracis-19038	475	27	between	between	ADP
bracis-19038	475	28	sets	set	NOUN
bracis-19038	475	29	of	of	ADP
bracis-19038	475	30	literals	literal	NOUN
bracis-19038	475	31	.	.	PUNCT
bracis-19038	476	1	as	as	ADP
bracis-19038	476	2	consequence	consequence	NOUN
bracis-19038	476	3	,	,	PUNCT
bracis-19038	476	4	we	we	PRON
bracis-19038	476	5	can	can	AUX
bracis-19038	476	6	represent	represent	VERB
bracis-19038	476	7	compactly	compactly	ADV
bracis-19038	476	8	complex	complex	ADJ
bracis-19038	476	9	forms	form	NOUN
bracis-19038	476	10	of	of	ADP
bracis-19038	476	11	preference	preference	NOUN
bracis-19038	476	12	.	.	PUNCT
bracis-19038	477	1	b	b	X
bracis-19038	477	2	)	)	PUNCT
bracis-19038	477	3	concerning	concern	VERB
bracis-19038	477	4	its	its	PRON
bracis-19038	477	5	semantics	semantic	NOUN
bracis-19038	477	6	,	,	PUNCT
bracis-19038	477	7	we	we	PRON
bracis-19038	477	8	have	have	AUX
bracis-19038	477	9	provided	provide	VERB
bracis-19038	477	10	a	a	DET
bracis-19038	477	11	comprehensive	comprehensive	ADJ
bracis-19038	477	12	and	and	CCONJ
bracis-19038	477	13	systematic	systematic	ADJ
bracis-19038	477	14	mechanism	mechanism	NOUN
bracis-19038	477	15	to	to	PART
bracis-19038	477	16	select	select	VERB
bracis-19038	477	17	the	the	DET
bracis-19038	477	18	most	most	ADV
bracis-19038	477	19	preferable	preferable	ADJ
bracis-19038	477	20	partial	partial	ADJ
bracis-19038	477	21	stable	stable	ADJ
bracis-19038	477	22	models	model	NOUN
bracis-19038	477	23	(	(	PUNCT
bracis-19038	477	24	\	\	PROPN
bracis-19038	477	25	(	(	PUNCT
bracis-19038	477	26	pps	pps	NOUN
bracis-19038	477	27	\	\	ADJ
bracis-19038	477	28	)	)	PUNCT
bracis-19038	477	29	models	model	NOUN
bracis-19038	477	30	)	)	PUNCT
bracis-19038	477	31	.	.	PUNCT
bracis-19038	478	1	indeed	indeed	ADV
bracis-19038	478	2	,	,	PUNCT
bracis-19038	478	3	by	by	ADP
bracis-19038	478	4	combining	combine	VERB
bracis-19038	478	5	well	well	ADV
bracis-19038	478	6	-	-	PUNCT
bracis-19038	478	7	known	know	VERB
bracis-19038	478	8	criteria	criterion	NOUN
bracis-19038	478	9	found	find	VERB
bracis-19038	478	10	in	in	ADP
bracis-19038	478	11	the	the	DET
bracis-19038	478	12	literature	literature	NOUN
bracis-19038	478	13	,	,	PUNCT
bracis-19038	478	14	we	we	PRON
bracis-19038	478	15	have	have	AUX
bracis-19038	478	16	defined	define	VERB
bracis-19038	478	17	32	32	NUM
bracis-19038	478	18	different	different	ADJ
bracis-19038	478	19	manners	manner	NOUN
bracis-19038	478	20	of	of	ADP
bracis-19038	478	21	selecting	select	VERB
bracis-19038	478	22	the	the	DET
bracis-19038	478	23	\	\	PROPN
bracis-19038	478	24	(	(	PUNCT
bracis-19038	478	25	pps	pps	NOUN
bracis-19038	478	26	\	\	ADJ
bracis-19038	478	27	)	)	PUNCT
bracis-19038	478	28	models	model	NOUN
bracis-19038	478	29	.	.	PUNCT
bracis-19038	479	1	as	as	SCONJ
bracis-19038	479	2	the	the	DET
bracis-19038	479	3	most	most	ADV
bracis-19038	479	4	important	important	ADJ
bracis-19038	479	5	semantics	semantic	NOUN
bracis-19038	479	6	in	in	ADP
bracis-19038	479	7	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	479	8	)	)	PUNCT
bracis-19038	479	9	are	be	AUX
bracis-19038	479	10	based	base	VERB
bracis-19038	479	11	on	on	ADP
bracis-19038	479	12	partial	partial	ADJ
bracis-19038	479	13	stable	stable	ADJ
bracis-19038	479	14	models	model	NOUN
bracis-19038	479	15	,	,	PUNCT
bracis-19038	479	16	we	we	PRON
bracis-19038	479	17	are	be	AUX
bracis-19038	479	18	also	also	ADV
bracis-19038	479	19	equipped	equip	VERB
bracis-19038	479	20	with	with	ADP
bracis-19038	479	21	32	32	NUM
bracis-19038	479	22	different	different	ADJ
bracis-19038	479	23	manners	manner	NOUN
bracis-19038	479	24	of	of	ADP
bracis-19038	479	25	selecting	select	VERB
bracis-19038	479	26	the	the	DET
bracis-19038	479	27	most	most	ADV
bracis-19038	479	28	preferred	preferred	ADJ
bracis-19038	479	29	models	model	NOUN
bracis-19038	479	30	according	accord	VERB
bracis-19038	479	31	to	to	ADP
bracis-19038	479	32	them	they	PRON
bracis-19038	479	33	.	.	PUNCT
bracis-19038	480	1	besides	besides	SCONJ
bracis-19038	480	2	,	,	PUNCT
bracis-19038	480	3	we	we	PRON
bracis-19038	480	4	have	have	AUX
bracis-19038	480	5	proved	prove	VERB
bracis-19038	480	6	some	some	DET
bracis-19038	480	7	properties	property	NOUN
bracis-19038	480	8	of	of	ADP
bracis-19038	480	9	these	these	DET
bracis-19038	480	10	\(\textit{plp}\)s	\(\textit{plp}\)s	NOUN
bracis-19038	480	11	and	and	CCONJ
bracis-19038	480	12	guaranteed	guarantee	VERB
bracis-19038	480	13	these	these	DET
bracis-19038	480	14	semantics	semantic	NOUN
bracis-19038	480	15	for	for	ADP
bracis-19038	480	16	\(\textit{plp}\	\(\textit{plp}\	NOUN
bracis-19038	480	17	)	)	PUNCT
bracis-19038	480	18	generalise	generalise	VERB
bracis-19038	480	19	their	their	PRON
bracis-19038	480	20	counterparts	counterpart	NOUN
bracis-19038	480	21	for	for	ADP
bracis-19038	480	22	\(\textit{nlp}\	\(\textit{nlp}\	NOUN
bracis-19038	480	23	)	)	PUNCT
bracis-19038	480	24	.	.	PUNCT
bracis-19038	481	1	future	future	ADJ
bracis-19038	481	2	directions	direction	NOUN
bracis-19038	481	3	include	include	VERB
bracis-19038	481	4	investigating	investigate	VERB
bracis-19038	481	5	computational	computational	ADJ
bracis-19038	481	6	complexity	complexity	NOUN
bracis-19038	481	7	issues	issue	NOUN
bracis-19038	481	8	on	on	ADP
bracis-19038	481	9	\(\textit{plp}\)s	\(\textit{plp}\)s	NOUN
bracis-19038	481	10	and	and	CCONJ
bracis-19038	481	11	exploiting	exploit	VERB
bracis-19038	481	12	the	the	DET
bracis-19038	481	13	consequence	consequence	NOUN
bracis-19038	481	14	of	of	ADP
bracis-19038	481	15	introducing	introduce	VERB
bracis-19038	481	16	preference	preference	NOUN
bracis-19038	481	17	on	on	ADP
bracis-19038	481	18	paraconsistent	paraconsistent	NOUN
bracis-19038	481	19	semantics	semantic	NOUN
bracis-19038	481	20	found	find	VERB
bracis-19038	481	21	in	in	ADP
bracis-19038	481	22	logic	logic	NOUN
bracis-19038	481	23	programming	programming	NOUN
bracis-19038	481	24	.	.	PUNCT
bracis-19038	482	1	we	we	PRON
bracis-19038	482	2	also	also	ADV
bracis-19038	482	3	intend	intend	VERB
bracis-19038	482	4	to	to	PART
bracis-19038	482	5	study	study	VERB
bracis-19038	482	6	how	how	SCONJ
bracis-19038	482	7	to	to	PART
bracis-19038	482	8	work	work	VERB
bracis-19038	482	9	with	with	ADP
bracis-19038	482	10	dynamic	dynamic	ADJ
bracis-19038	482	11	preferences	preference	NOUN
bracis-19038	482	12	along	along	ADP
bracis-19038	482	13	with	with	ADP
bracis-19038	482	14	the	the	DET
bracis-19038	482	15	resulting	result	VERB
bracis-19038	482	16	semantics	semantic	NOUN
bracis-19038	482	17	.	.	PUNCT
bracis-19038	483	1	references	reference	NOUN
bracis-19038	483	2	pigozzi	pigozzi	VERB
bracis-19038	483	3	,	,	PUNCT
bracis-19038	483	4	g.	g.	PROPN
bracis-19038	483	5	,	,	PUNCT
bracis-19038	483	6	tsoukias	tsoukia	NOUN
bracis-19038	483	7	,	,	PUNCT
bracis-19038	483	8	a.	a.	NOUN
bracis-19038	483	9	,	,	PUNCT
bracis-19038	483	10	viappiani	viappiani	NOUN
bracis-19038	483	11	,	,	PUNCT
bracis-19038	483	12	p.	p.	NOUN
bracis-19038	483	13	:	:	PUNCT
bracis-19038	484	1	preferences	preference	NOUN
bracis-19038	484	2	in	in	ADP
bracis-19038	484	3	artificial	artificial	ADJ
bracis-19038	484	4	intelligence	intelligence	NOUN
bracis-19038	484	5	.	.	PUNCT
bracis-19038	485	1	ann	ann	PROPN
bracis-19038	485	2	.	.	PUNCT
bracis-19038	485	3	math	math	PROPN
bracis-19038	485	4	.	.	PUNCT
bracis-19038	486	1	artif	artif	INTJ
bracis-19038	486	2	.	.	PUNCT
bracis-19038	487	1	intell	intell	PROPN
bracis-19038	487	2	.	.	PUNCT
bracis-19038	488	1	77(3	77(3	X
bracis-19038	488	2	)	)	PUNCT
bracis-19038	488	3	,	,	PUNCT
bracis-19038	488	4	361–401	361–401	NUM
bracis-19038	488	5	(	(	PUNCT
bracis-19038	488	6	2016	2016	NUM
bracis-19038	488	7	)	)	PUNCT
bracis-19038	488	8	google	google	PROPN
bracis-19038	488	9	scholar	scholar	NOUN
bracis-19038	488	10	  	  	SPACE
bracis-19038	488	11	brewka	brewka	NOUN
bracis-19038	488	12	,	,	PUNCT
bracis-19038	488	13	g.	g.	NOUN
bracis-19038	488	14	:	:	PUNCT
bracis-19038	488	15	well	well	ADV
bracis-19038	488	16	-	-	PUNCT
bracis-19038	488	17	founded	found	VERB
bracis-19038	488	18	semantics	semantic	NOUN
bracis-19038	488	19	for	for	ADP
bracis-19038	488	20	extended	extended	ADJ
bracis-19038	488	21	logic	logic	NOUN
bracis-19038	488	22	programs	program	NOUN
bracis-19038	488	23	with	with	ADP
bracis-19038	488	24	dynamic	dynamic	ADJ
bracis-19038	488	25	preferences	preference	NOUN
bracis-19038	488	26	.	.	PUNCT
bracis-19038	489	1	j.	j.	PROPN
bracis-19038	489	2	artif	artif	PROPN
bracis-19038	489	3	.	.	PUNCT
bracis-19038	490	1	intell	intell	PROPN
bracis-19038	490	2	.	.	PUNCT
bracis-19038	491	1	res	re	NOUN
bracis-19038	491	2	.	.	PROPN
bracis-19038	492	1	4	4	NUM
bracis-19038	492	2	,	,	PUNCT
bracis-19038	492	3	19–36	19–36	NUM
bracis-19038	492	4	(	(	PUNCT
bracis-19038	492	5	1996	1996	NUM
bracis-19038	492	6	)	)	PUNCT
bracis-19038	492	7	google	google	PROPN
bracis-19038	492	8	scholar	scholar	NOUN
bracis-19038	492	9	  	  	SPACE
bracis-19038	492	10	brewka	brewka	NOUN
bracis-19038	492	11	,	,	PUNCT
bracis-19038	492	12	g.	g.	PROPN
bracis-19038	492	13	,	,	PUNCT
bracis-19038	492	14	eiter	eiter	PROPN
bracis-19038	492	15	,	,	PUNCT
bracis-19038	492	16	t.	t.	PROPN
bracis-19038	492	17	:	:	PUNCT
bracis-19038	492	18	preferred	preferred	ADJ
bracis-19038	492	19	answer	answer	NOUN
bracis-19038	492	20	sets	set	NOUN
bracis-19038	492	21	for	for	ADP
bracis-19038	492	22	extended	extended	ADJ
bracis-19038	492	23	logic	logic	NOUN
bracis-19038	492	24	programs	program	NOUN
bracis-19038	492	25	.	.	PUNCT
bracis-19038	493	1	artif	artif	INTJ
bracis-19038	493	2	.	.	PUNCT
bracis-19038	494	1	intell	intell	PROPN
bracis-19038	494	2	.	.	PUNCT
bracis-19038	495	1	109(1–2	109(1–2	NUM
bracis-19038	495	2	)	)	PUNCT
bracis-19038	495	3	,	,	PUNCT
bracis-19038	495	4	297–356	297–356	NUM
bracis-19038	495	5	(	(	PUNCT
bracis-19038	495	6	1999	1999	NUM
bracis-19038	495	7	)	)	PUNCT
bracis-19038	495	8	google	google	PROPN
bracis-19038	495	9	scholar	scholar	NOUN
bracis-19038	495	10	  	  	SPACE
bracis-19038	495	11	sakama	sakama	NOUN
bracis-19038	495	12	,	,	PUNCT
bracis-19038	495	13	c.	c.	PROPN
bracis-19038	495	14	,	,	PUNCT
bracis-19038	495	15	inoue	inoue	PROPN
bracis-19038	495	16	,	,	PUNCT
bracis-19038	495	17	k.	k.	PROPN
bracis-19038	495	18	:	:	PUNCT
bracis-19038	495	19	prioritized	prioritize	VERB
bracis-19038	495	20	logic	logic	NOUN
bracis-19038	495	21	programming	programming	NOUN
bracis-19038	495	22	and	and	CCONJ
bracis-19038	495	23	its	its	PRON
bracis-19038	495	24	application	application	NOUN
bracis-19038	495	25	to	to	ADP
bracis-19038	495	26	commonsense	commonsense	ADJ
bracis-19038	495	27	reasoning	reasoning	NOUN
bracis-19038	495	28	.	.	PUNCT
bracis-19038	496	1	artif	artif	INTJ
bracis-19038	496	2	.	.	PUNCT
bracis-19038	497	1	intell	intell	PROPN
bracis-19038	497	2	.	.	PUNCT
bracis-19038	498	1	123(1–2	123(1–2	X
bracis-19038	498	2	)	)	PUNCT
bracis-19038	498	3	,	,	PUNCT
bracis-19038	498	4	185–222	185–222	NUM
bracis-19038	498	5	(	(	PUNCT
bracis-19038	498	6	2000	2000	NUM
bracis-19038	498	7	)	)	PUNCT
bracis-19038	498	8	google	google	PROPN
bracis-19038	498	9	scholar	scholar	NOUN
bracis-19038	498	10	  	  	SPACE
bracis-19038	498	11	schaub	schaub	PROPN
bracis-19038	498	12	,	,	PUNCT
bracis-19038	498	13	t.	t.	PROPN
bracis-19038	498	14	,	,	PUNCT
bracis-19038	498	15	wang	wang	PROPN
bracis-19038	498	16	,	,	PUNCT
bracis-19038	498	17	k.	k.	PROPN
bracis-19038	498	18	:	:	PUNCT
bracis-19038	498	19	a	a	DET
bracis-19038	498	20	semantic	semantic	ADJ
bracis-19038	498	21	framework	framework	NOUN
bracis-19038	498	22	for	for	ADP
bracis-19038	498	23	preference	preference	NOUN
bracis-19038	498	24	handling	handle	VERB
bracis-19038	498	25	in	in	ADP
bracis-19038	498	26	answer	answer	NOUN
bracis-19038	498	27	set	set	VERB
bracis-19038	498	28	programming	programming	NOUN
bracis-19038	498	29	.	.	PUNCT
bracis-19038	499	1	arxiv	arxiv	PROPN
bracis-19038	499	2	preprint	preprint	NOUN
bracis-19038	499	3	cs/0301023	cs/0301023	PROPN
bracis-19038	499	4	(	(	PUNCT
bracis-19038	499	5	2003	2003	NUM
bracis-19038	499	6	)	)	PUNCT
bracis-19038	499	7	google	google	PROPN
bracis-19038	499	8	scholar	scholar	NOUN
bracis-19038	499	9	  	  	SPACE
bracis-19038	499	10	balduccini	balduccini	NOUN
bracis-19038	499	11	,	,	PUNCT
bracis-19038	499	12	m.	m.	NOUN
bracis-19038	499	13	,	,	PUNCT
bracis-19038	499	14	gelfond	gelfond	NOUN
bracis-19038	499	15	,	,	PUNCT
bracis-19038	499	16	m.	m.	NOUN
bracis-19038	499	17	:	:	PUNCT
bracis-19038	499	18	logic	logic	NOUN
bracis-19038	499	19	programs	program	NOUN
bracis-19038	499	20	with	with	ADP
bracis-19038	499	21	consistency	consistency	NOUN
bracis-19038	499	22	-	-	PUNCT
bracis-19038	499	23	restoring	restore	VERB
bracis-19038	499	24	rules	rule	NOUN
bracis-19038	499	25	.	.	PUNCT
bracis-19038	500	1	in	in	ADP
bracis-19038	500	2	:	:	PUNCT
bracis-19038	500	3	international	international	ADJ
bracis-19038	500	4	symposium	symposium	NOUN
bracis-19038	500	5	on	on	ADP
bracis-19038	500	6	logical	logical	ADJ
bracis-19038	500	7	formalization	formalization	NOUN
bracis-19038	500	8	of	of	ADP
bracis-19038	500	9	commonsense	commonsense	ADJ
bracis-19038	500	10	reasoning	reasoning	NOUN
bracis-19038	500	11	,	,	PUNCT
bracis-19038	500	12	aaai	aaai	PROPN
bracis-19038	500	13	2003	2003	NUM
bracis-19038	500	14	spring	spring	NOUN
bracis-19038	500	15	symposium	symposium	NOUN
bracis-19038	500	16	series	series	NOUN
bracis-19038	500	17	,	,	PUNCT
bracis-19038	500	18	vol	vol	NOUN
bracis-19038	500	19	.	.	PROPN
bracis-19038	501	1	102	102	NUM
bracis-19038	501	2	(	(	PUNCT
bracis-19038	501	3	2003	2003	NUM
bracis-19038	501	4	)	)	PUNCT
bracis-19038	501	5	google	google	NOUN
bracis-19038	501	6	scholar	scholar	NOUN
bracis-19038	501	7	  	  	SPACE
bracis-19038	501	8	brewka	brewka	NOUN
bracis-19038	501	9	,	,	PUNCT
bracis-19038	501	10	g.	g.	NOUN
bracis-19038	501	11	,	,	PUNCT
bracis-19038	501	12	niemelä	niemelä	NOUN
bracis-19038	501	13	,	,	PUNCT
bracis-19038	501	14	i.	i.	NOUN
bracis-19038	501	15	,	,	PUNCT
bracis-19038	501	16	syrjänen	syrjänen	NOUN
bracis-19038	501	17	,	,	PUNCT
bracis-19038	501	18	t.	t.	NOUN
bracis-19038	501	19	:	:	PUNCT
bracis-19038	501	20	logic	logic	NOUN
bracis-19038	501	21	programs	program	NOUN
bracis-19038	501	22	with	with	ADP
bracis-19038	501	23	ordered	order	VERB
bracis-19038	501	24	disjunction	disjunction	NOUN
bracis-19038	501	25	.	.	PUNCT
bracis-19038	502	1	comput	comput	NOUN
bracis-19038	502	2	.	.	PUNCT
bracis-19038	503	1	intell	intell	PROPN
bracis-19038	503	2	.	.	PUNCT
bracis-19038	504	1	20(2	20(2	NUM
bracis-19038	504	2	)	)	PUNCT
bracis-19038	504	3	,	,	PUNCT
bracis-19038	504	4	335–357	335–357	NUM
bracis-19038	504	5	(	(	PUNCT
bracis-19038	504	6	2004	2004	NUM
bracis-19038	504	7	)	)	PUNCT
bracis-19038	504	8	google	google	PROPN
bracis-19038	504	9	scholar	scholar	NOUN
bracis-19038	504	10	  	  	SPACE
bracis-19038	504	11	brewka	brewka	NOUN
bracis-19038	504	12	,	,	PUNCT
bracis-19038	504	13	g.	g.	NOUN
bracis-19038	504	14	:	:	PUNCT
bracis-19038	504	15	answer	answer	NOUN
bracis-19038	504	16	sets	set	NOUN
bracis-19038	504	17	and	and	CCONJ
bracis-19038	504	18	qualitative	qualitative	ADJ
bracis-19038	504	19	optimization	optimization	NOUN
bracis-19038	504	20	.	.	PUNCT
bracis-19038	505	1	logic	logic	NOUN
bracis-19038	505	2	j.	j.	PROPN
bracis-19038	505	3	igpl	igpl	PROPN
bracis-19038	505	4	14(3	14(3	NUM
bracis-19038	505	5	)	)	PUNCT
bracis-19038	505	6	,	,	PUNCT
bracis-19038	505	7	413–433	413–433	NUM
bracis-19038	505	8	(	(	PUNCT
bracis-19038	505	9	2006	2006	NUM
bracis-19038	505	10	)	)	PUNCT
bracis-19038	505	11	google	google	PROPN
bracis-19038	505	12	scholar	scholar	NOUN
bracis-19038	505	13	  	  	SPACE
bracis-19038	505	14	nicolas	nicolas	PROPN
bracis-19038	505	15	,	,	PUNCT
bracis-19038	505	16	p.	p.	PROPN
bracis-19038	505	17	,	,	PUNCT
bracis-19038	505	18	garcia	garcia	PROPN
bracis-19038	505	19	,	,	PUNCT
bracis-19038	505	20	l.	l.	PROPN
bracis-19038	505	21	,	,	PUNCT
bracis-19038	505	22	stéphan	stéphan	ADP
bracis-19038	505	23	,	,	PUNCT
bracis-19038	505	24	i.	i.	NOUN
bracis-19038	505	25	,	,	PUNCT
bracis-19038	505	26	lefèvre	lefèvre	NOUN
bracis-19038	505	27	,	,	PUNCT
bracis-19038	505	28	c.	c.	NOUN
bracis-19038	505	29	:	:	PUNCT
bracis-19038	505	30	possibilistic	possibilistic	ADJ
bracis-19038	505	31	uncertainty	uncertainty	NOUN
bracis-19038	505	32	handling	handle	VERB
bracis-19038	505	33	for	for	ADP
bracis-19038	505	34	answer	answer	NOUN
bracis-19038	505	35	set	set	VERB
bracis-19038	505	36	programming	programming	NOUN
bracis-19038	505	37	.	.	PUNCT
bracis-19038	506	1	ann	ann	PROPN
bracis-19038	506	2	.	.	PUNCT
bracis-19038	506	3	math	math	PROPN
bracis-19038	506	4	.	.	PUNCT
bracis-19038	507	1	artif	artif	INTJ
bracis-19038	507	2	.	.	PUNCT
bracis-19038	508	1	intell	intell	PROPN
bracis-19038	508	2	.	.	PUNCT
bracis-19038	509	1	47(1	47(1	NUM
bracis-19038	509	2	)	)	PUNCT
bracis-19038	509	3	,	,	PUNCT
bracis-19038	509	4	139–181	139–181	NUM
bracis-19038	509	5	(	(	PUNCT
bracis-19038	509	6	2006	2006	NUM
bracis-19038	509	7	)	)	PUNCT
bracis-19038	509	8	article	article	NOUN
bracis-19038	509	9	  	  	SPACE
bracis-19038	509	10	mathscinet	mathscinet	NOUN
bracis-19038	509	11	  	  	SPACE
bracis-19038	509	12	google	google	PROPN
bracis-19038	509	13	scholar	scholar	NOUN
bracis-19038	509	14	  	  	SPACE
bracis-19038	509	15	gabaldon	gabaldon	NOUN
bracis-19038	509	16	,	,	PUNCT
bracis-19038	509	17	a.	a.	NOUN
bracis-19038	509	18	:	:	PUNCT
bracis-19038	509	19	a	a	DET
bracis-19038	509	20	selective	selective	ADJ
bracis-19038	509	21	semantics	semantic	NOUN
bracis-19038	509	22	for	for	ADP
bracis-19038	509	23	logic	logic	NOUN
bracis-19038	509	24	programs	program	NOUN
bracis-19038	509	25	with	with	ADP
bracis-19038	509	26	preferences	preference	NOUN
bracis-19038	509	27	.	.	PUNCT
bracis-19038	510	1	in	in	ADP
bracis-19038	510	2	:	:	PUNCT
bracis-19038	510	3	del	del	PROPN
bracis-19038	510	4	cerro	cerro	PROPN
bracis-19038	510	5	,	,	PUNCT
bracis-19038	510	6	l.f	l.f	PROPN
bracis-19038	510	7	.	.	PROPN
bracis-19038	510	8	,	,	PUNCT
bracis-19038	510	9	herzig	herzig	PROPN
bracis-19038	510	10	,	,	PUNCT
bracis-19038	510	11	a.	a.	NOUN
bracis-19038	510	12	,	,	PUNCT
bracis-19038	510	13	mengin	mengin	NOUN
bracis-19038	510	14	,	,	PUNCT
bracis-19038	510	15	j.	j.	PROPN
bracis-19038	510	16	(	(	PUNCT
bracis-19038	510	17	eds	eds	PROPN
bracis-19038	510	18	.	.	PUNCT
bracis-19038	510	19	)	)	PUNCT
bracis-19038	510	20	jelia	jelia	PROPN
bracis-19038	510	21	2012	2012	NUM
bracis-19038	510	22	.	.	PUNCT
bracis-19038	511	1	lncs	lncs	PROPN
bracis-19038	511	2	(	(	PUNCT
bracis-19038	511	3	lnai	lnai	ADJ
bracis-19038	511	4	)	)	PUNCT
bracis-19038	511	5	,	,	PUNCT
bracis-19038	511	6	vol	vol	NOUN
bracis-19038	511	7	.	.	NOUN
bracis-19038	511	8	7519	7519	NUM
bracis-19038	511	9	,	,	PUNCT
bracis-19038	511	10	pp	pp	ADJ
bracis-19038	511	11	.	.	PUNCT
bracis-19038	512	1	215–227	215–227	NUM
bracis-19038	512	2	.	.	PUNCT
bracis-19038	512	3	springer	springer	NOUN
bracis-19038	512	4	,	,	PUNCT
bracis-19038	512	5	heidelberg	heidelberg	PROPN
bracis-19038	512	6	(	(	PUNCT
bracis-19038	512	7	2012	2012	NUM
bracis-19038	512	8	)	)	PUNCT
bracis-19038	512	9	.	.	PUNCT
bracis-19038	513	1	https://doi.org/10.1007/978-3-642-33353-8_17	https://doi.org/10.1007/978-3-642-33353-8_17	NOUN
bracis-19038	513	2	rondogiannis	rondogiannis	VERB
bracis-19038	513	3	,	,	PUNCT
bracis-19038	513	4	p.	p.	NOUN
bracis-19038	513	5	,	,	PUNCT
bracis-19038	513	6	troumpoukis	troumpoukis	PROPN
bracis-19038	513	7	,	,	PUNCT
bracis-19038	513	8	a.	a.	NOUN
bracis-19038	513	9	:	:	PUNCT
bracis-19038	513	10	expressing	express	VERB
bracis-19038	513	11	preferences	preference	NOUN
bracis-19038	513	12	in	in	ADP
bracis-19038	513	13	logic	logic	NOUN
bracis-19038	513	14	programming	programming	NOUN
bracis-19038	513	15	using	use	VERB
bracis-19038	513	16	an	an	DET
bracis-19038	513	17	infinite	infinite	ADV
bracis-19038	513	18	-	-	PUNCT
bracis-19038	513	19	valued	value	VERB
bracis-19038	513	20	logic	logic	NOUN
bracis-19038	513	21	.	.	PUNCT
bracis-19038	514	1	in	in	ADP
bracis-19038	514	2	:	:	PUNCT
bracis-19038	514	3	proceedings	proceeding	NOUN
bracis-19038	514	4	of	of	ADP
bracis-19038	514	5	the	the	DET
bracis-19038	514	6	17th	17th	ADJ
bracis-19038	514	7	international	international	ADJ
bracis-19038	514	8	symposium	symposium	NOUN
bracis-19038	514	9	on	on	ADP
bracis-19038	514	10	principles	principle	NOUN
bracis-19038	514	11	and	and	CCONJ
bracis-19038	514	12	practice	practice	NOUN
bracis-19038	514	13	of	of	ADP
bracis-19038	514	14	declarative	declarative	ADJ
bracis-19038	514	15	programming	programming	NOUN
bracis-19038	514	16	,	,	PUNCT
bracis-19038	514	17	pp	pp	ADJ
bracis-19038	514	18	.	.	PUNCT
bracis-19038	515	1	208–219	208–219	NUM
bracis-19038	515	2	(	(	PUNCT
bracis-19038	515	3	2015	2015	NUM
bracis-19038	515	4	)	)	PUNCT
bracis-19038	515	5	google	google	PROPN
bracis-19038	515	6	scholar	scholar	NOUN
bracis-19038	515	7	  	  	SPACE
bracis-19038	515	8	zhang	zhang	PROPN
bracis-19038	515	9	,	,	PUNCT
bracis-19038	515	10	z.	z.	PROPN
bracis-19038	515	11	:	:	PUNCT
bracis-19038	515	12	introspecting	introspect	VERB
bracis-19038	515	13	preferences	preference	NOUN
bracis-19038	515	14	in	in	ADP
bracis-19038	515	15	answer	answer	NOUN
bracis-19038	515	16	set	set	VERB
bracis-19038	515	17	programming	programming	NOUN
bracis-19038	515	18	.	.	PUNCT
bracis-19038	516	1	in	in	ADP
bracis-19038	516	2	:	:	PUNCT
bracis-19038	516	3	34th	34th	ADJ
bracis-19038	516	4	international	international	ADJ
bracis-19038	516	5	conference	conference	NOUN
bracis-19038	516	6	on	on	ADP
bracis-19038	516	7	logic	logic	NOUN
bracis-19038	516	8	programming	programming	NOUN
bracis-19038	516	9	(	(	PUNCT
bracis-19038	516	10	iclp	iclp	PROPN
bracis-19038	516	11	2018	2018	NUM
bracis-19038	516	12	)	)	PUNCT
bracis-19038	516	13	(	(	PUNCT
bracis-19038	516	14	2018	2018	NUM
bracis-19038	516	15	)	)	PUNCT
bracis-19038	516	16	google	google	PROPN
bracis-19038	516	17	scholar	scholar	NOUN
bracis-19038	516	18	  	  	SPACE
bracis-19038	516	19	kaci	kaci	PROPN
bracis-19038	516	20	,	,	PUNCT
bracis-19038	516	21	s.	s.	PROPN
bracis-19038	516	22	:	:	PUNCT
bracis-19038	516	23	working	work	VERB
bracis-19038	516	24	with	with	ADP
bracis-19038	516	25	preferences	preference	NOUN
bracis-19038	516	26	:	:	PUNCT
bracis-19038	516	27	less	less	ADJ
bracis-19038	516	28	is	be	AUX
bracis-19038	516	29	more	more	ADJ
bracis-19038	516	30	.	.	PUNCT
bracis-19038	517	1	springer	springer	NOUN
bracis-19038	517	2	science	science	NOUN
bracis-19038	517	3	and	and	CCONJ
bracis-19038	517	4	business	business	NOUN
bracis-19038	517	5	media	medium	NOUN
bracis-19038	517	6	,	,	PUNCT
bracis-19038	517	7	2011	2011	NUM
bracis-19038	517	8	.	.	PUNCT
bracis-19038	518	1	https://doi.org/10.1007/978-3-642-17280-9_5	https://doi.org/10.1007/978-3-642-17280-9_5	PROPN
bracis-19038	518	2	przymusinski	przymusinski	ADJ
bracis-19038	518	3	,	,	PUNCT
bracis-19038	518	4	t.	t.	PROPN
bracis-19038	518	5	:	:	PUNCT
bracis-19038	519	1	the	the	DET
bracis-19038	519	2	well	well	ADV
bracis-19038	519	3	-	-	PUNCT
bracis-19038	519	4	founded	found	VERB
bracis-19038	519	5	semantics	semantic	NOUN
bracis-19038	519	6	coincides	coincide	VERB
bracis-19038	519	7	with	with	ADP
bracis-19038	519	8	the	the	DET
bracis-19038	519	9	three	three	NUM
bracis-19038	519	10	-	-	PUNCT
bracis-19038	519	11	valued	value	VERB
bracis-19038	519	12	stable	stable	ADJ
bracis-19038	519	13	semantics	semantic	NOUN
bracis-19038	519	14	.	.	PUNCT
bracis-19038	520	1	fundam	fundam	PROPN
bracis-19038	520	2	.	.	PUNCT
bracis-19038	520	3	inf	inf	PROPN
bracis-19038	520	4	.	.	PUNCT
bracis-19038	521	1	13(4	13(4	NUM
bracis-19038	521	2	)	)	PUNCT
bracis-19038	521	3	,	,	PUNCT
bracis-19038	521	4	445–463	445–463	NUM
bracis-19038	521	5	(	(	PUNCT
bracis-19038	521	6	1990	1990	NUM
bracis-19038	521	7	)	)	PUNCT
bracis-19038	521	8	google	google	PROPN
bracis-19038	521	9	scholar	scholar	NOUN
bracis-19038	521	10	  	  	SPACE
bracis-19038	521	11	eiter	eiter	NOUN
bracis-19038	521	12	,	,	PUNCT
bracis-19038	521	13	t.	t.	PROPN
bracis-19038	521	14	,	,	PUNCT
bracis-19038	521	15	leone	leone	NOUN
bracis-19038	521	16	,	,	PUNCT
bracis-19038	521	17	n.	n.	NOUN
bracis-19038	521	18	,	,	PUNCT
bracis-19038	521	19	sacca	sacca	PROPN
bracis-19038	521	20	,	,	PUNCT
bracis-19038	521	21	d.	d.	PROPN
bracis-19038	521	22	:	:	PUNCT
bracis-19038	521	23	on	on	ADP
bracis-19038	521	24	the	the	DET
bracis-19038	521	25	partial	partial	ADJ
bracis-19038	521	26	semantics	semantic	NOUN
bracis-19038	521	27	for	for	ADP
bracis-19038	521	28	disjunctive	disjunctive	ADJ
bracis-19038	521	29	deductive	deductive	ADJ
bracis-19038	521	30	databases	database	NOUN
bracis-19038	521	31	.	.	PUNCT
bracis-19038	522	1	ann	ann	PROPN
bracis-19038	522	2	.	.	PUNCT
bracis-19038	522	3	math	math	PROPN
bracis-19038	522	4	.	.	PUNCT
bracis-19038	523	1	artif	artif	INTJ
bracis-19038	523	2	.	.	PUNCT
bracis-19038	524	1	intell	intell	PROPN
bracis-19038	524	2	.	.	PUNCT
bracis-19038	525	1	19(1	19(1	NUM
bracis-19038	525	2	)	)	PUNCT
bracis-19038	525	3	,	,	PUNCT
bracis-19038	525	4	59–96	59–96	NUM
bracis-19038	525	5	(	(	PUNCT
bracis-19038	525	6	1997	1997	NUM
bracis-19038	525	7	)	)	PUNCT
bracis-19038	525	8	article	article	NOUN
bracis-19038	525	9	  	  	SPACE
bracis-19038	525	10	mathscinet	mathscinet	NOUN
bracis-19038	525	11	  	  	SPACE
bracis-19038	525	12	google	google	PROPN
bracis-19038	525	13	scholar	scholar	NOUN
bracis-19038	525	14	  	  	SPACE
bracis-19038	525	15	van	van	PROPN
bracis-19038	525	16	der	der	PROPN
bracis-19038	525	17	t.	t.	PROPN
bracis-19038	525	18	,	,	PUNCT
bracis-19038	525	19	leendert	leendert	ADJ
bracis-19038	525	20	,	,	PUNCT
bracis-19038	525	21	w.e	w.e	PROPN
bracis-19038	525	22	.	.	PROPN
bracis-19038	525	23	:	:	PUNCT
bracis-19038	526	1	parameters	parameter	NOUN
bracis-19038	526	2	for	for	ADP
bracis-19038	526	3	utilitarian	utilitarian	ADJ
bracis-19038	526	4	desires	desire	NOUN
bracis-19038	526	5	in	in	ADP
bracis-19038	526	6	a	a	DET
bracis-19038	526	7	qualitative	qualitative	ADJ
bracis-19038	526	8	decision	decision	NOUN
bracis-19038	526	9	theory	theory	NOUN
bracis-19038	526	10	.	.	PUNCT
bracis-19038	527	1	appl	appl	PROPN
bracis-19038	527	2	.	.	PUNCT
bracis-19038	528	1	intelli	intelli	PROPN
bracis-19038	528	2	.	.	PUNCT
bracis-19038	529	1	14(3	14(3	NUM
bracis-19038	529	2	)	)	PUNCT
bracis-19038	529	3	,	,	PUNCT
bracis-19038	529	4	285–301	285–301	NUM
bracis-19038	529	5	(	(	PUNCT
bracis-19038	529	6	2001	2001	NUM
bracis-19038	529	7	)	)	PUNCT
bracis-19038	529	8	google	google	PROPN
bracis-19038	529	9	scholar	scholar	NOUN
bracis-19038	529	10	  	  	SPACE
bracis-19038	529	11	benferhat	benferhat	PROPN
bracis-19038	529	12	,	,	PUNCT
bracis-19038	529	13	s.	s.	PROPN
bracis-19038	529	14	,	,	PUNCT
bracis-19038	529	15	dubois	dubois	PROPN
bracis-19038	529	16	,	,	PUNCT
bracis-19038	529	17	d.	d.	PROPN
bracis-19038	529	18	,	,	PUNCT
bracis-19038	529	19	kaci	kaci	PROPN
bracis-19038	529	20	,	,	PUNCT
bracis-19038	529	21	s.	s.	PROPN
bracis-19038	529	22	,	,	PUNCT
bracis-19038	529	23	prade	prade	NOUN
bracis-19038	529	24	,	,	PUNCT
bracis-19038	529	25	h.	h.	NOUN
bracis-19038	529	26	:	:	PUNCT
bracis-19038	529	27	bipolar	bipolar	ADJ
bracis-19038	529	28	representation	representation	NOUN
bracis-19038	529	29	and	and	CCONJ
bracis-19038	529	30	fusion	fusion	NOUN
bracis-19038	529	31	of	of	ADP
bracis-19038	529	32	preferences	preference	NOUN
bracis-19038	529	33	on	on	ADP
bracis-19038	529	34	the	the	DET
bracis-19038	529	35	possibilistic	possibilistic	ADJ
bracis-19038	529	36	logic	logic	NOUN
bracis-19038	529	37	framework	framework	NOUN
bracis-19038	529	38	.	.	PUNCT
bracis-19038	530	1	kr	kr	PROPN
bracis-19038	530	2	,	,	PUNCT
bracis-19038	530	3	2	2	NUM
bracis-19038	530	4	,	,	PUNCT
bracis-19038	530	5	421–432	421–432	NUM
bracis-19038	530	6	(	(	PUNCT
bracis-19038	530	7	2002	2002	NUM
bracis-19038	530	8	)	)	PUNCT
bracis-19038	530	9	google	google	PROPN
bracis-19038	530	10	scholar	scholar	NOUN
bracis-19038	530	11	  	  	SPACE
bracis-19038	530	12	benferhat	benferhat	PROPN
bracis-19038	530	13	,	,	PUNCT
bracis-19038	530	14	s.	s.	PROPN
bracis-19038	530	15	,	,	PUNCT
bracis-19038	530	16	dubois	dubois	PROPN
bracis-19038	530	17	,	,	PUNCT
bracis-19038	530	18	d.	d.	PROPN
bracis-19038	530	19	,	,	PUNCT
bracis-19038	530	20	kaci	kaci	PROPN
bracis-19038	530	21	,	,	PUNCT
bracis-19038	530	22	s.	s.	PROPN
bracis-19038	530	23	,	,	PUNCT
bracis-19038	530	24	prade	prade	NOUN
bracis-19038	530	25	,	,	PUNCT
bracis-19038	530	26	h.	h.	NOUN
bracis-19038	530	27	:	:	PUNCT
bracis-19038	530	28	bipolar	bipolar	ADJ
bracis-19038	530	29	possibilistic	possibilistic	ADJ
bracis-19038	530	30	representations	representation	NOUN
bracis-19038	530	31	.	.	PUNCT
bracis-19038	531	1	in	in	ADP
bracis-19038	531	2	:	:	PUNCT
bracis-19038	531	3	18th	18th	ADJ
bracis-19038	531	4	international	international	ADJ
bracis-19038	531	5	conference	conference	NOUN
bracis-19038	531	6	on	on	ADP
bracis-19038	531	7	uncertainty	uncertainty	NOUN
bracis-19038	531	8	in	in	ADP
bracis-19038	531	9	artificial	artificial	ADJ
bracis-19038	531	10	intelligence	intelligence	NOUN
bracis-19038	531	11	,	,	PUNCT
bracis-19038	531	12	pp	pp	ADV
bracis-19038	531	13	.	.	PUNCT
bracis-19038	532	1	45–52	45–52	NUM
bracis-19038	532	2	(	(	PUNCT
bracis-19038	532	3	2002	2002	NUM
bracis-19038	532	4	)	)	PUNCT
bracis-19038	532	5	google	google	PROPN
bracis-19038	532	6	scholar	scholar	NOUN
bracis-19038	532	7	  	  	SPACE
bracis-19038	532	8	lang	lang	PROPN
bracis-19038	532	9	,	,	PUNCT
bracis-19038	532	10	j.	j.	PROPN
bracis-19038	532	11	,	,	PUNCT
bracis-19038	532	12	van	van	PROPN
bracis-19038	532	13	der	der	PROPN
bracis-19038	532	14	torre	torre	PROPN
bracis-19038	532	15	,	,	PUNCT
bracis-19038	532	16	l.	l.	PROPN
bracis-19038	532	17	,	,	PUNCT
bracis-19038	532	18	weydert	weydert	PROPN
bracis-19038	532	19	,	,	PUNCT
bracis-19038	532	20	e.	e.	PROPN
bracis-19038	532	21	:	:	PUNCT
bracis-19038	532	22	utilitarian	utilitarian	ADJ
bracis-19038	532	23	desires	desire	NOUN
bracis-19038	532	24	.	.	PUNCT
bracis-19038	533	1	auton	auton	PROPN
bracis-19038	533	2	.	.	PUNCT
bracis-19038	534	1	agents	agent	NOUN
bracis-19038	534	2	multi	multi	ADJ
bracis-19038	534	3	-	-	ADJ
bracis-19038	534	4	agent	agent	ADJ
bracis-19038	534	5	syst	syst	NOUN
bracis-19038	534	6	.	.	PUNCT
bracis-19038	535	1	5(3	5(3	NUM
bracis-19038	535	2	)	)	PUNCT
bracis-19038	535	3	,	,	PUNCT
bracis-19038	535	4	329–363	329–363	NUM
bracis-19038	535	5	(	(	PUNCT
bracis-19038	535	6	2002	2002	NUM
bracis-19038	535	7	)	)	PUNCT
bracis-19038	535	8	google	google	PROPN
bracis-19038	535	9	scholar	scholar	NOUN
bracis-19038	535	10	  	  	SPACE
bracis-19038	536	1	benferhat	benferhat	PROPN
bracis-19038	536	2	,	,	PUNCT
bracis-19038	536	3	s.	s.	PROPN
bracis-19038	536	4	,	,	PUNCT
bracis-19038	536	5	dubois	dubois	PROPN
bracis-19038	536	6	,	,	PUNCT
bracis-19038	536	7	d.	d.	PROPN
bracis-19038	536	8	,	,	PUNCT
bracis-19038	536	9	kaci	kaci	PROPN
bracis-19038	536	10	,	,	PUNCT
bracis-19038	536	11	s.	s.	PROPN
bracis-19038	536	12	,	,	PUNCT
bracis-19038	536	13	prade	prade	NOUN
bracis-19038	536	14	,	,	PUNCT
bracis-19038	536	15	h.	h.	NOUN
bracis-19038	536	16	:	:	PUNCT
bracis-19038	536	17	bipolar	bipolar	ADJ
bracis-19038	536	18	possibility	possibility	NOUN
bracis-19038	536	19	theory	theory	NOUN
bracis-19038	536	20	in	in	ADP
bracis-19038	536	21	preference	preference	NOUN
bracis-19038	536	22	modeling	modeling	NOUN
bracis-19038	536	23	:	:	PUNCT
bracis-19038	536	24	representation	representation	NOUN
bracis-19038	536	25	,	,	PUNCT
bracis-19038	536	26	fusion	fusion	NOUN
bracis-19038	536	27	and	and	CCONJ
bracis-19038	536	28	optimal	optimal	ADJ
bracis-19038	536	29	solutions	solution	NOUN
bracis-19038	536	30	.	.	PUNCT
bracis-19038	537	1	inf	inf	PROPN
bracis-19038	537	2	.	.	PUNCT
bracis-19038	537	3	fusion	fusion	PROPN
bracis-19038	537	4	7(1	7(1	NUM
bracis-19038	537	5	)	)	PUNCT
bracis-19038	537	6	,	,	PUNCT
bracis-19038	537	7	135–150	135–150	NUM
bracis-19038	537	8	(	(	PUNCT
bracis-19038	537	9	2006	2006	NUM
bracis-19038	537	10	)	)	PUNCT
bracis-19038	537	11	google	google	PROPN
bracis-19038	537	12	scholar	scholar	NOUN
bracis-19038	537	13	  	  	SPACE
bracis-19038	537	14	bistarelli	bistarelli	PROPN
bracis-19038	537	15	,	,	PUNCT
bracis-19038	537	16	s.	s.	PROPN
bracis-19038	537	17	,	,	PUNCT
bracis-19038	537	18	pini	pini	PROPN
bracis-19038	537	19	,	,	PUNCT
bracis-19038	537	20	m.	m.	NOUN
bracis-19038	537	21	,	,	PUNCT
bracis-19038	537	22	rossi	rossi	PROPN
bracis-19038	537	23	,	,	PUNCT
bracis-19038	537	24	f.	f.	PROPN
bracis-19038	537	25	,	,	PUNCT
bracis-19038	537	26	venable	venable	PROPN
bracis-19038	537	27	,	,	PUNCT
bracis-19038	537	28	k.	k.	PROPN
bracis-19038	537	29	:	:	PUNCT
bracis-19038	537	30	from	from	ADP
bracis-19038	537	31	soft	soft	ADJ
bracis-19038	537	32	constraints	constraint	NOUN
bracis-19038	537	33	to	to	ADP
bracis-19038	537	34	bipolar	bipolar	ADJ
bracis-19038	537	35	preferences	preference	NOUN
bracis-19038	537	36	:	:	PUNCT
bracis-19038	537	37	modelling	model	VERB
bracis-19038	537	38	framework	framework	NOUN
bracis-19038	537	39	and	and	CCONJ
bracis-19038	537	40	solving	solving	NOUN
bracis-19038	537	41	issues	issue	NOUN
bracis-19038	537	42	.	.	PUNCT
bracis-19038	538	1	j.	j.	PROPN
bracis-19038	538	2	exp	exp	PROPN
bracis-19038	538	3	.	.	PROPN
bracis-19038	538	4	theoret	theoret	PROPN
bracis-19038	538	5	.	.	PUNCT
bracis-19038	539	1	artif	artif	INTJ
bracis-19038	539	2	.	.	PUNCT
bracis-19038	540	1	intell	intell	PROPN
bracis-19038	540	2	.	.	PUNCT
bracis-19038	541	1	22(2	22(2	VERB
bracis-19038	541	2	)	)	PUNCT
bracis-19038	542	1	,	,	PUNCT
bracis-19038	542	2	135–158	135–158	NUM
bracis-19038	542	3	(	(	PUNCT
bracis-19038	542	4	2010	2010	NUM
bracis-19038	542	5	)	)	PUNCT
bracis-19038	542	6	google	google	PROPN
bracis-19038	542	7	scholar	scholar	NOUN
bracis-19038	542	8	  	  	SPACE
bracis-19038	542	9	poole	poole	NOUN
bracis-19038	542	10	,	,	PUNCT
bracis-19038	542	11	d.	d.	PROPN
bracis-19038	542	12	:	:	PUNCT
bracis-19038	542	13	on	on	ADP
bracis-19038	542	14	the	the	DET
bracis-19038	542	15	comparison	comparison	NOUN
bracis-19038	542	16	of	of	ADP
bracis-19038	542	17	theories	theory	NOUN
bracis-19038	542	18	:	:	PUNCT
bracis-19038	542	19	preferring	prefer	VERB
bracis-19038	542	20	the	the	DET
bracis-19038	542	21	most	most	ADV
bracis-19038	542	22	specific	specific	ADJ
bracis-19038	542	23	explanation	explanation	NOUN
bracis-19038	542	24	.	.	PUNCT
bracis-19038	543	1	in	in	ADP
bracis-19038	543	2	:	:	PUNCT
bracis-19038	543	3	9th	9th	ADJ
bracis-19038	543	4	international	international	ADJ
bracis-19038	543	5	joint	joint	ADJ
bracis-19038	543	6	conference	conference	NOUN
bracis-19038	543	7	on	on	ADP
bracis-19038	543	8	artificial	artificial	ADJ
bracis-19038	543	9	intelligence	intelligence	NOUN
bracis-19038	543	10	,	,	PUNCT
bracis-19038	543	11	vol	vol	NOUN
bracis-19038	543	12	.	.	PROPN
bracis-19038	543	13	85	85	NUM
bracis-19038	543	14	,	,	PUNCT
bracis-19038	543	15	pp	pp	ADJ
bracis-19038	543	16	.	.	PUNCT
bracis-19038	544	1	144–147	144–147	NUM
bracis-19038	544	2	(	(	PUNCT
bracis-19038	544	3	1985	1985	NUM
bracis-19038	544	4	)	)	PUNCT
bracis-19038	544	5	google	google	PROPN
bracis-19038	544	6	scholar	scholar	NOUN
bracis-19038	544	7	  	  	SPACE
bracis-19038	544	8	lifschitz	lifschitz	NOUN
bracis-19038	544	9	,	,	PUNCT
bracis-19038	544	10	v.	v.	ADP
bracis-19038	544	11	:	:	PUNCT
bracis-19038	544	12	computing	compute	VERB
bracis-19038	544	13	circumscription	circumscription	NOUN
bracis-19038	544	14	.	.	PUNCT
bracis-19038	545	1	in	in	ADP
bracis-19038	545	2	:	:	PUNCT
bracis-19038	545	3	international	international	ADJ
bracis-19038	545	4	joint	joint	ADJ
bracis-19038	545	5	conference	conference	NOUN
bracis-19038	545	6	on	on	ADP
bracis-19038	545	7	artificial	artificial	ADJ
bracis-19038	545	8	intelligence	intelligence	NOUN
bracis-19038	545	9	(	(	PUNCT
bracis-19038	545	10	ijcai	ijcai	NOUN
bracis-19038	545	11	)	)	PUNCT
bracis-19038	545	12	,	,	PUNCT
bracis-19038	545	13	vol	vol	NOUN
bracis-19038	545	14	.	.	PROPN
bracis-19038	545	15	85	85	NUM
bracis-19038	545	16	,	,	PUNCT
bracis-19038	545	17	pp	pp	ADJ
bracis-19038	545	18	.	.	PUNCT
bracis-19038	546	1	121–127	121–127	NUM
bracis-19038	546	2	(	(	PUNCT
bracis-19038	546	3	1985	1985	NUM
bracis-19038	546	4	)	)	PUNCT
bracis-19038	546	5	google	google	PROPN
bracis-19038	546	6	scholar	scholar	NOUN
bracis-19038	546	7	  	  	SPACE
bracis-19038	546	8	eiter	eiter	NOUN
bracis-19038	546	9	,	,	PUNCT
bracis-19038	546	10	t.	t.	PROPN
bracis-19038	546	11	,	,	PUNCT
bracis-19038	546	12	gottlob	gottlob	NOUN
bracis-19038	546	13	,	,	PUNCT
bracis-19038	546	14	g.	g.	PROPN
bracis-19038	546	15	:	:	PUNCT
bracis-19038	546	16	the	the	DET
bracis-19038	546	17	complexity	complexity	NOUN
bracis-19038	546	18	of	of	ADP
bracis-19038	546	19	logic	logic	NOUN
bracis-19038	546	20	-	-	PUNCT
bracis-19038	546	21	based	base	VERB
bracis-19038	546	22	abduction	abduction	NOUN
bracis-19038	546	23	.	.	PUNCT
bracis-19038	547	1	j.	j.	PROPN
bracis-19038	547	2	acm	acm	PROPN
bracis-19038	547	3	(	(	PUNCT
bracis-19038	547	4	jacm	jacm	PROPN
bracis-19038	547	5	)	)	PUNCT
bracis-19038	547	6	42(1	42(1	NOUN
bracis-19038	547	7	)	)	PUNCT
bracis-19038	547	8	,	,	PUNCT
bracis-19038	547	9	3–42	3–42	PROPN
bracis-19038	547	10	(	(	PUNCT
bracis-19038	547	11	1995	1995	NUM
bracis-19038	547	12	)	)	PUNCT
bracis-19038	547	13	google	google	NOUN
bracis-19038	547	14	scholar	scholar	NOUN
bracis-19038	547	15	  	  	SPACE
bracis-19038	547	16	gelfond	gelfond	NOUN
bracis-19038	547	17	,	,	PUNCT
bracis-19038	547	18	m.	m.	NOUN
bracis-19038	547	19	,	,	PUNCT
bracis-19038	547	20	lifschitz	lifschitz	PROPN
bracis-19038	547	21	,	,	PUNCT
bracis-19038	547	22	v.	v.	ADP
bracis-19038	547	23	:	:	PUNCT
bracis-19038	547	24	classical	classical	ADJ
bracis-19038	547	25	negation	negation	NOUN
bracis-19038	547	26	in	in	ADP
bracis-19038	547	27	logic	logic	NOUN
bracis-19038	547	28	programs	program	NOUN
bracis-19038	547	29	and	and	CCONJ
bracis-19038	547	30	disjunctive	disjunctive	ADJ
bracis-19038	547	31	databases	database	NOUN
bracis-19038	547	32	.	.	PUNCT
bracis-19038	548	1	new	new	ADJ
bracis-19038	548	2	gener	gener	PROPN
bracis-19038	548	3	.	.	PUNCT
bracis-19038	549	1	comput	comput	NOUN
bracis-19038	549	2	.	.	PUNCT
bracis-19038	550	1	9(3–4	9(3–4	NUM
bracis-19038	550	2	)	)	PUNCT
bracis-19038	550	3	,	,	PUNCT
bracis-19038	550	4	365–385	365–385	NUM
bracis-19038	550	5	(	(	PUNCT
bracis-19038	550	6	1991	1991	NUM
bracis-19038	550	7	)	)	PUNCT
bracis-19038	550	8	google	google	NOUN
bracis-19038	550	9	scholar	scholar	NOUN
bracis-19038	550	10	  	  	SPACE
bracis-19038	550	11	download	download	NOUN
bracis-19038	550	12	references	reference	NOUN
bracis-19038	550	13	author	author	NOUN
bracis-19038	550	14	information	information	NOUN
bracis-19038	550	15	authors	author	NOUN
bracis-19038	550	16	and	and	CCONJ
bracis-19038	550	17	affiliations	affiliation	NOUN
bracis-19038	550	18	department	department	PROPN
bracis-19038	550	19	of	of	ADP
bracis-19038	550	20	computer	computer	NOUN
bracis-19038	550	21	science	science	NOUN
bracis-19038	550	22	,	,	PUNCT
bracis-19038	550	23	federal	federal	ADJ
bracis-19038	550	24	university	university	PROPN
bracis-19038	550	25	of	of	ADP
bracis-19038	550	26	ceará	ceará	NOUN
bracis-19038	550	27	,	,	PUNCT
bracis-19038	550	28	fortaleza	fortaleza	PROPN
bracis-19038	550	29	,	,	PUNCT
bracis-19038	550	30	brazil	brazil	PROPN
bracis-19038	550	31	renan	renan	PROPN
bracis-19038	550	32	cordeiro	cordeiro	PROPN
bracis-19038	550	33	,	,	PUNCT
bracis-19038	550	34	 	 	SPACE
bracis-19038	550	35	guilherme	guilherme	PROPN
bracis-19038	550	36	fernandes	fernandes	PROPN
bracis-19038	550	37	 	 	SPACE
bracis-19038	550	38	&	&	CCONJ
bracis-19038	550	39	 	 	SPACE
bracis-19038	550	40	joão	joão	PROPN
bracis-19038	550	41	alcântara	alcântara	PROPN
bracis-19038	550	42	instituto	instituto	PROPN
bracis-19038	550	43	federal	federal	PROPN
bracis-19038	550	44	de	de	PROPN
bracis-19038	550	45	educação	educação	PROPN
bracis-19038	550	46	,	,	PUNCT
bracis-19038	550	47	ciência	ciência	PROPN
bracis-19038	550	48	e	e	NOUN
bracis-19038	550	49	tecnologia	tecnologia	NOUN
bracis-19038	550	50	do	do	VERB
bracis-19038	550	51	ceará	ceará	NOUN
bracis-19038	550	52	(	(	PUNCT
bracis-19038	550	53	ifce	ifce	PROPN
bracis-19038	550	54	)	)	PUNCT
bracis-19038	550	55	,	,	PUNCT
bracis-19038	550	56	ce-040	ce-040	PROPN
bracis-19038	550	57	,	,	PUNCT
bracis-19038	550	58	km	km	NOUN
bracis-19038	550	59	137,1	137,1	NOUN
bracis-19038	550	60	 	 	SPACE
bracis-19038	550	61	s	s	PROPN
bracis-19038	550	62	/	/	SYM
bracis-19038	550	63	n	n	CCONJ
bracis-19038	550	64	,	,	PUNCT
bracis-19038	550	65	aracati	aracati	NOUN
bracis-19038	550	66	,	,	PUNCT
bracis-19038	550	67	rodovia	rodovia	PROPN
bracis-19038	550	68	,	,	PUNCT
bracis-19038	550	69	ce	ce	PROPN
bracis-19038	550	70	,	,	PUNCT
bracis-19038	550	71	brazil	brazil	PROPN
bracis-19038	550	72	henrique	henrique	PROPN
bracis-19038	550	73	viana	viana	PROPN
bracis-19038	550	74	authors	authors	PROPN
bracis-19038	550	75	renan	renan	PROPN
bracis-19038	550	76	cordeiroview	cordeiroview	PROPN
bracis-19038	550	77	author	author	NOUN
bracis-19038	550	78	publications	publication	NOUN
bracis-19038	550	79	search	search	NOUN
bracis-19038	550	80	author	author	NOUN
bracis-19038	550	81	on	on	ADP
bracis-19038	550	82	:	:	PUNCT
bracis-19038	550	83	pubmed	pubmed	PROPN
bracis-19038	550	84	 	 	SPACE
bracis-19038	550	85	google	google	PROPN
bracis-19038	550	86	scholar	scholar	NOUN
bracis-19038	550	87	guilherme	guilherme	PROPN
bracis-19038	550	88	fernandesview	fernandesview	NOUN
bracis-19038	550	89	author	author	NOUN
bracis-19038	550	90	publications	publication	NOUN
bracis-19038	550	91	search	search	NOUN
bracis-19038	550	92	author	author	NOUN
bracis-19038	550	93	on	on	ADP
bracis-19038	550	94	:	:	PUNCT
bracis-19038	550	95	pubmed	pubmed	PROPN
bracis-19038	550	96	 	 	SPACE
bracis-19038	550	97	google	google	PROPN
bracis-19038	550	98	scholar	scholar	PROPN
bracis-19038	550	99	joão	joão	PROPN
bracis-19038	550	100	alcântaraview	alcântaraview	PROPN
bracis-19038	550	101	author	author	NOUN
bracis-19038	550	102	publications	publication	VERB
bracis-19038	550	103	search	search	NOUN
bracis-19038	550	104	author	author	NOUN
bracis-19038	550	105	on	on	ADP
bracis-19038	550	106	:	:	PUNCT
bracis-19038	550	107	pubmed	pubmed	PROPN
bracis-19038	550	108	 	 	SPACE
bracis-19038	550	109	google	google	PROPN
bracis-19038	550	110	scholar	scholar	PROPN
bracis-19038	550	111	henrique	henrique	PROPN
bracis-19038	550	112	vianaview	vianaview	PROPN
bracis-19038	550	113	author	author	NOUN
bracis-19038	550	114	publications	publication	NOUN
bracis-19038	550	115	search	search	NOUN
bracis-19038	550	116	author	author	NOUN
bracis-19038	550	117	on	on	ADP
bracis-19038	550	118	:	:	PUNCT
bracis-19038	550	119	pubmed	pubmed	PROPN
bracis-19038	550	120	 	 	SPACE
bracis-19038	550	121	google	google	PROPN
bracis-19038	550	122	scholar	scholar	NOUN
bracis-19038	550	123	corresponding	correspond	VERB
bracis-19038	550	124	author	author	NOUN
bracis-19038	550	125	correspondence	correspondence	NOUN
bracis-19038	550	126	to	to	ADP
bracis-19038	550	127	joão	joão	PROPN
bracis-19038	550	128	alcântara	alcântara	PROPN
bracis-19038	550	129	.	.	PUNCT
bracis-19038	551	1	editor	editor	NOUN
bracis-19038	551	2	information	information	NOUN
bracis-19038	551	3	editors	editor	NOUN
bracis-19038	551	4	and	and	CCONJ
bracis-19038	551	5	affiliations	affiliation	NOUN
bracis-19038	551	6	universidade	universidade	PROPN
bracis-19038	551	7	federal	federal	PROPN
bracis-19038	551	8	de	de	X
bracis-19038	551	9	sergipe	sergipe	PROPN
bracis-19038	551	10	,	,	PUNCT
bracis-19038	551	11	são	são	NOUN
bracis-19038	551	12	cristóvão	cristóvão	PROPN
bracis-19038	551	13	,	,	PUNCT
bracis-19038	551	14	brazil	brazil	PROPN
bracis-19038	551	15	andré	andré	PROPN
bracis-19038	551	16	britto	britto	PROPN
bracis-19038	551	17	universidade	universidade	PROPN
bracis-19038	551	18	de	de	PROPN
bracis-19038	551	19	são	são	PROPN
bracis-19038	551	20	paulo	paulo	PROPN
bracis-19038	551	21	,	,	PUNCT
bracis-19038	551	22	são	são	PROPN
bracis-19038	551	23	paulo	paulo	PROPN
bracis-19038	551	24	,	,	PUNCT
bracis-19038	551	25	brazil	brazil	PROPN
bracis-19038	551	26	karina	karina	PROPN
bracis-19038	551	27	valdivia	valdivia	PROPN
bracis-19038	551	28	delgado	delgado	VERB
bracis-19038	551	29	rights	right	NOUN
bracis-19038	551	30	and	and	CCONJ
bracis-19038	551	31	permissions	permission	NOUN
bracis-19038	551	32	reprints	reprint	NOUN
bracis-19038	551	33	and	and	CCONJ
bracis-19038	551	34	permissions	permission	VERB
bracis-19038	551	35	copyright	copyright	NOUN
bracis-19038	551	36	information	information	NOUN
bracis-19038	551	37	©	©	PROPN
bracis-19038	551	38	2021	2021	NUM
bracis-19038	551	39	springer	springer	NOUN
bracis-19038	551	40	nature	nature	NOUN
bracis-19038	551	41	switzerland	switzerland	PROPN
bracis-19038	551	42	ag	ag	PROPN
bracis-19038	551	43	about	about	ADP
bracis-19038	551	44	this	this	DET
bracis-19038	551	45	paper	paper	NOUN
bracis-19038	551	46	cite	cite	VERB
bracis-19038	551	47	this	this	DET
bracis-19038	551	48	paper	paper	NOUN
bracis-19038	551	49	cordeiro	cordeiro	PROPN
bracis-19038	551	50	,	,	PUNCT
bracis-19038	551	51	r.	r.	PROPN
bracis-19038	551	52	,	,	PUNCT
bracis-19038	551	53	fernandes	fernande	NOUN
bracis-19038	551	54	,	,	PUNCT
bracis-19038	551	55	g.	g.	PROPN
bracis-19038	551	56	,	,	PUNCT
bracis-19038	551	57	alcântara	alcântara	ADJ
bracis-19038	551	58	,	,	PUNCT
bracis-19038	551	59	j.	j.	PROPN
bracis-19038	551	60	,	,	PUNCT
bracis-19038	551	61	viana	viana	PROPN
bracis-19038	551	62	,	,	PUNCT
bracis-19038	551	63	h.	h.	PROPN
bracis-19038	551	64	(	(	PUNCT
bracis-19038	551	65	2021	2021	NUM
bracis-19038	551	66	)	)	PUNCT
bracis-19038	551	67	.	.	PUNCT
bracis-19038	552	1	a	a	DET
bracis-19038	552	2	systematic	systematic	ADJ
bracis-19038	552	3	approach	approach	NOUN
bracis-19038	552	4	to	to	PART
bracis-19038	552	5	define	define	VERB
bracis-19038	552	6	semantics	semantic	NOUN
bracis-19038	552	7	for	for	ADP
bracis-19038	552	8	prioritised	prioritise	VERB
bracis-19038	552	9	logic	logic	NOUN
bracis-19038	552	10	programs	program	NOUN
bracis-19038	552	11	.	.	PUNCT
bracis-19038	553	1	in	in	ADP
bracis-19038	553	2	:	:	PUNCT
bracis-19038	553	3	britto	britto	PROPN
bracis-19038	553	4	,	,	PUNCT
bracis-19038	553	5	a.	a.	PROPN
bracis-19038	553	6	,	,	PUNCT
bracis-19038	553	7	valdivia	valdivia	PROPN
bracis-19038	553	8	delgado	delgado	PROPN
bracis-19038	553	9	,	,	PUNCT
bracis-19038	553	10	k.	k.	PROPN
bracis-19038	553	11	(	(	PUNCT
bracis-19038	553	12	eds	eds	PROPN
bracis-19038	553	13	)	)	PUNCT
bracis-19038	553	14	intelligent	intelligent	ADJ
bracis-19038	553	15	systems	system	NOUN
bracis-19038	553	16	.	.	PUNCT
bracis-19038	554	1	bracis	bracis	PROPN
bracis-19038	554	2	2021	2021	NUM
bracis-19038	554	3	.	.	PUNCT
bracis-19038	555	1	lecture	lecture	NOUN
bracis-19038	555	2	notes	note	NOUN
bracis-19038	555	3	in	in	ADP
bracis-19038	555	4	computer	computer	NOUN
bracis-19038	555	5	science	science	NOUN
bracis-19038	555	6	(	(	PUNCT
bracis-19038	555	7	)	)	PUNCT
bracis-19038	555	8	,	,	PUNCT
bracis-19038	555	9	vol	vol	NOUN
bracis-19038	555	10	13073	13073	NUM
bracis-19038	555	11	.	.	PUNCT
bracis-19038	556	1	springer	springer	NOUN
bracis-19038	556	2	,	,	PUNCT
bracis-19038	556	3	cham	cham	PROPN
bracis-19038	556	4	.	.	PUNCT
bracis-19038	557	1	https://doi.org/10.1007/978-3-030-91702-9_20	https://doi.org/10.1007/978-3-030-91702-9_20	NOUN
bracis-19038	557	2	download	download	VERB
bracis-19038	557	3	citation	citation	NOUN
bracis-19038	557	4	.ris	.ris	PUNCT
bracis-19038	557	5	.enw	.enw	PROPN
bracis-19038	558	1	.bib	.bib	PUNCT
bracis-19038	559	1	doi	doi	PROPN
bracis-19038	559	2	:	:	PUNCT
bracis-19038	559	3	https://doi.org/10.1007/978-3-030-91702-9_20	https://doi.org/10.1007/978-3-030-91702-9_20	NOUN
bracis-19038	559	4	published	publish	VERB
bracis-19038	559	5	:	:	PUNCT
bracis-19038	559	6	28	28	NUM
bracis-19038	559	7	november	november	PROPN
bracis-19038	559	8	2021	2021	NUM
bracis-19038	559	9	publisher	publisher	NOUN
bracis-19038	559	10	name	name	NOUN
bracis-19038	559	11	:	:	PUNCT
bracis-19038	559	12	springer	springer	NOUN
bracis-19038	559	13	,	,	PUNCT
bracis-19038	559	14	cham	cham	PROPN
bracis-19038	559	15	print	print	PROPN
bracis-19038	559	16	isbn	isbn	PROPN
bracis-19038	559	17	:	:	PUNCT
bracis-19038	559	18	978	978	NUM
bracis-19038	559	19	-	-	SYM
bracis-19038	559	20	3	3	NUM
bracis-19038	559	21	-	-	PUNCT
bracis-19038	559	22	030	030	NUM
bracis-19038	559	23	-	-	PUNCT
bracis-19038	559	24	91701	91701	NUM
bracis-19038	559	25	-	-	SYM
bracis-19038	559	26	2	2	NUM
bracis-19038	559	27	online	online	ADJ
bracis-19038	559	28	isbn	isbn	NOUN
bracis-19038	559	29	:	:	PUNCT
bracis-19038	559	30	978	978	NUM
bracis-19038	559	31	-	-	SYM
bracis-19038	559	32	3	3	NUM
bracis-19038	559	33	-	-	PUNCT
bracis-19038	559	34	030	030	NUM
bracis-19038	559	35	-	-	PUNCT
bracis-19038	559	36	91702	91702	NUM
bracis-19038	559	37	-	-	SYM
bracis-19038	559	38	9	9	NUM
bracis-19038	559	39	ebook	ebook	NOUN
bracis-19038	559	40	packages	package	NOUN
bracis-19038	559	41	:	:	PUNCT
bracis-19038	559	42	computer	computer	NOUN
bracis-19038	559	43	sciencecomputer	sciencecomputer	NOUN
bracis-19038	559	44	science	science	NOUN
bracis-19038	559	45	(	(	PUNCT
bracis-19038	559	46	r0	r0	NOUN
bracis-19038	559	47	)	)	PUNCT
bracis-19038	559	48	share	share	VERB
bracis-19038	559	49	this	this	DET
bracis-19038	559	50	paper	paper	NOUN
bracis-19038	559	51	anyone	anyone	PRON
bracis-19038	559	52	you	you	PRON
bracis-19038	559	53	share	share	VERB
bracis-19038	559	54	the	the	DET
bracis-19038	559	55	following	follow	VERB
bracis-19038	559	56	link	link	NOUN
bracis-19038	559	57	with	with	ADP
bracis-19038	559	58	will	will	AUX
bracis-19038	559	59	be	be	AUX
bracis-19038	559	60	able	able	ADJ
bracis-19038	559	61	to	to	PART
bracis-19038	559	62	read	read	VERB
bracis-19038	559	63	this	this	DET
bracis-19038	559	64	content	content	NOUN
bracis-19038	559	65	:	:	PUNCT
bracis-19038	559	66	get	get	VERB
bracis-19038	559	67	shareable	shareable	ADJ
bracis-19038	559	68	linksorry	linksorry	NOUN
bracis-19038	559	69	,	,	PUNCT
bracis-19038	559	70	a	a	DET
bracis-19038	559	71	shareable	shareable	ADJ
bracis-19038	559	72	link	link	NOUN
bracis-19038	559	73	is	be	AUX
bracis-19038	559	74	not	not	PART
bracis-19038	559	75	currently	currently	ADV
bracis-19038	559	76	available	available	ADJ
bracis-19038	559	77	for	for	ADP
bracis-19038	559	78	this	this	DET
bracis-19038	559	79	article	article	NOUN
bracis-19038	559	80	.	.	PUNCT
bracis-19038	560	1	copy	copy	VERB
bracis-19038	560	2	shareable	shareable	ADJ
bracis-19038	560	3	link	link	NOUN
bracis-19038	560	4	to	to	PART
bracis-19038	560	5	clipboard	clipboard	NOUN
bracis-19038	560	6	provided	provide	VERB
bracis-19038	560	7	by	by	ADP
bracis-19038	560	8	the	the	DET
bracis-19038	560	9	springer	springer	NOUN
bracis-19038	560	10	nature	nature	PROPN
bracis-19038	560	11	sharedit	sharedit	PROPN
bracis-19038	560	12	content	content	NOUN
bracis-19038	560	13	-	-	PUNCT
bracis-19038	560	14	sharing	share	VERB
bracis-19038	560	15	initiative	initiative	NOUN
bracis-19038	560	16	keywords	keyword	NOUN
bracis-19038	560	17	logic	logic	NOUN
bracis-19038	560	18	programming	programming	NOUN
bracis-19038	560	19	preferences	preference	NOUN
bracis-19038	560	20	semantics	semantic	NOUN
bracis-19038	560	21	publish	publish	VERB
bracis-19038	560	22	with	with	ADP
bracis-19038	560	23	us	us	PROPN
bracis-19038	560	24	policies	policy	NOUN
bracis-19038	560	25	and	and	CCONJ
bracis-19038	560	26	ethics	ethic	NOUN
bracis-19038	560	27	profiles	profile	NOUN
bracis-19038	560	28	renan	renan	PROPN
bracis-19038	560	29	cordeiro	cordeiro	PROPN
bracis-19038	560	30	view	view	PROPN
bracis-19038	560	31	author	author	NOUN
bracis-19038	560	32	profile	profile	NOUN
bracis-19038	560	33	search	search	NOUN
bracis-19038	560	34	search	search	NOUN
bracis-19038	560	35	by	by	ADP
bracis-19038	560	36	keyword	keyword	NOUN
bracis-19038	560	37	or	or	CCONJ
bracis-19038	560	38	author	author	NOUN
bracis-19038	560	39	search	search	NOUN
bracis-19038	560	40	navigation	navigation	NOUN
bracis-19038	560	41	find	find	VERB
bracis-19038	560	42	a	a	DET
bracis-19038	560	43	journal	journal	NOUN
bracis-19038	560	44	publish	publish	VERB
bracis-19038	560	45	with	with	ADP
bracis-19038	560	46	us	we	PRON
bracis-19038	560	47	track	track	VERB
bracis-19038	560	48	your	your	PRON
bracis-19038	560	49	research	research	NOUN
bracis-19038	560	50	discover	discover	VERB
bracis-19038	560	51	content	content	NOUN
bracis-19038	560	52	journals	journal	NOUN
bracis-19038	560	53	a	a	DET
bracis-19038	560	54	-	-	PUNCT
bracis-19038	560	55	z	z	NOUN
bracis-19038	560	56	books	book	NOUN
bracis-19038	560	57	a	a	DET
bracis-19038	560	58	-	-	PUNCT
bracis-19038	560	59	z	z	NOUN
bracis-19038	560	60	publish	publish	NOUN
bracis-19038	560	61	with	with	ADP
bracis-19038	560	62	us	us	PROPN
bracis-19038	560	63	journal	journal	PROPN
bracis-19038	560	64	finder	finder	PROPN
bracis-19038	560	65	publish	publish	VERB
bracis-19038	560	66	your	your	PRON
bracis-19038	560	67	research	research	NOUN
bracis-19038	560	68	language	language	NOUN
bracis-19038	560	69	editing	edit	VERB
bracis-19038	560	70	open	open	ADJ
bracis-19038	560	71	access	access	NOUN
bracis-19038	560	72	publishing	publishing	NOUN
bracis-19038	560	73	products	product	NOUN
bracis-19038	560	74	and	and	CCONJ
bracis-19038	560	75	services	service	NOUN
bracis-19038	560	76	our	our	PRON
bracis-19038	560	77	products	product	NOUN
bracis-19038	560	78	librarians	librarian	VERB
bracis-19038	560	79	societies	society	NOUN
bracis-19038	560	80	partners	partner	NOUN
bracis-19038	560	81	and	and	CCONJ
bracis-19038	560	82	advertisers	advertiser	NOUN
bracis-19038	560	83	our	our	PRON
bracis-19038	560	84	brands	brand	NOUN
bracis-19038	560	85	springer	springer	NOUN
bracis-19038	560	86	nature	nature	PROPN
bracis-19038	560	87	portfolio	portfolio	PROPN
bracis-19038	560	88	bmc	bmc	PROPN
bracis-19038	560	89	palgrave	palgrave	PROPN
bracis-19038	560	90	macmillan	macmillan	PROPN
bracis-19038	560	91	apress	apress	PROPN
bracis-19038	560	92	discover	discover	VERB
bracis-19038	560	93	your	your	PRON
bracis-19038	560	94	privacy	privacy	NOUN
bracis-19038	560	95	choices	choice	NOUN
bracis-19038	560	96	/	/	SYM
bracis-19038	560	97	manage	manage	NOUN
bracis-19038	560	98	cookies	cookie	NOUN
bracis-19038	560	99	your	your	PRON
bracis-19038	560	100	us	us	PROPN
bracis-19038	561	1	state	state	NOUN
bracis-19038	561	2	privacy	privacy	NOUN
bracis-19038	561	3	rights	right	NOUN
bracis-19038	561	4	accessibility	accessibility	NOUN
bracis-19038	561	5	statement	statement	NOUN
bracis-19038	561	6	terms	term	NOUN
bracis-19038	561	7	and	and	CCONJ
bracis-19038	561	8	conditions	condition	NOUN
bracis-19038	561	9	privacy	privacy	NOUN
bracis-19038	561	10	policy	policy	NOUN
bracis-19038	561	11	help	help	NOUN
bracis-19038	561	12	and	and	CCONJ
bracis-19038	561	13	support	support	VERB
bracis-19038	561	14	legal	legal	ADJ
bracis-19038	561	15	notice	notice	NOUN
bracis-19038	561	16	cancel	cancel	VERB
bracis-19038	561	17	contracts	contract	NOUN
bracis-19038	561	18	here	here	ADV
bracis-19038	561	19	129.74.145.123	129.74.145.123	NUM
bracis-19038	561	20	hesburgh	hesburgh	PROPN
bracis-19038	561	21	library	library	PROPN
bracis-19038	561	22	er	er	INTJ
bracis-19038	561	23	unit	unit	NOUN
bracis-19038	561	24	(	(	PUNCT
bracis-19038	561	25	3005732405	3005732405	NUM
bracis-19038	561	26	)	)	PUNCT
bracis-19038	561	27	northeast	northeast	ADJ
bracis-19038	561	28	research	research	NOUN
bracis-19038	561	29	libraries	library	NOUN
bracis-19038	561	30	(	(	PUNCT
bracis-19038	561	31	nerl	nerl	PROPN
bracis-19038	561	32	)	)	PUNCT
bracis-19038	561	33	(	(	PUNCT
bracis-19038	561	34	8200828607	8200828607	NUM
bracis-19038	561	35	)	)	PUNCT
bracis-19038	561	36	nerl	nerl	VERB
bracis-19038	561	37	ta	ta	X
bracis-19038	561	38	account	account	NOUN
bracis-19038	561	39	(	(	PUNCT
bracis-19038	561	40	3006206169	3006206169	NUM
bracis-19038	561	41	)	)	PUNCT
bracis-19038	561	42	university	university	NOUN
bracis-19038	561	43	of	of	ADP
bracis-19038	561	44	notre	notre	PROPN
bracis-19038	561	45	dame	dame	PROPN
bracis-19038	561	46	hesburgh	hesburgh	PROPN
bracis-19038	561	47	library	library	NOUN
bracis-19038	561	48	(	(	PUNCT
bracis-19038	561	49	3000184373	3000184373	NUM
bracis-19038	561	50	)	)	PUNCT
bracis-19038	562	1	©	©	ADP
bracis-19038	562	2	2025	2025	NUM
bracis-19038	562	3	springer	springer	NOUN
bracis-19038	562	4	nature	nature	NOUN