id	sid	tid	token	lemma	pos
bracis-33646	1	1	a	a	DET
bracis-33646	1	2	topology	topology	NOUN
bracis-33646	1	3	-	-	PUNCT
bracis-33646	1	4	inspired	inspire	VERB
bracis-33646	1	5	approach	approach	NOUN
bracis-33646	1	6	to	to	ADP
bracis-33646	1	7	 	 	SPACE
bracis-33646	1	8	agm	agm	PROPN
bracis-33646	1	9	belief	belief	NOUN
bracis-33646	1	10	change	change	NOUN
bracis-33646	1	11	|	|	ADV
bracis-33646	1	12	springer	springer	NOUN
bracis-33646	1	13	nature	nature	NOUN
bracis-33646	1	14	link	link	PROPN
bracis-33646	1	15	(	(	PUNCT
bracis-33646	1	16	formerly	formerly	ADV
bracis-33646	1	17	springerlink	springerlink	NOUN
bracis-33646	1	18	)	)	PUNCT
bracis-33646	1	19	skip	skip	VERB
bracis-33646	1	20	to	to	ADP
bracis-33646	1	21	main	main	ADJ
bracis-33646	1	22	content	content	NOUN
bracis-33646	1	23	advertisement	advertisement	NOUN
bracis-33646	1	24	log	log	NOUN
bracis-33646	1	25	in	in	ADP
bracis-33646	1	26	menu	menu	NOUN
bracis-33646	1	27	find	find	VERB
bracis-33646	1	28	a	a	DET
bracis-33646	1	29	journal	journal	NOUN
bracis-33646	1	30	publish	publish	VERB
bracis-33646	1	31	with	with	ADP
bracis-33646	1	32	us	we	PRON
bracis-33646	1	33	track	track	VERB
bracis-33646	1	34	your	your	PRON
bracis-33646	1	35	research	research	NOUN
bracis-33646	1	36	search	search	NOUN
bracis-33646	1	37	cart	cart	NOUN
bracis-33646	1	38	home	home	NOUN
bracis-33646	1	39	intelligent	intelligent	ADJ
bracis-33646	1	40	systems	system	NOUN
bracis-33646	1	41	conference	conference	NOUN
bracis-33646	1	42	paper	paper	NOUN
bracis-33646	1	43	a	a	DET
bracis-33646	1	44	topology	topology	NOUN
bracis-33646	1	45	-	-	PUNCT
bracis-33646	1	46	inspired	inspire	VERB
bracis-33646	1	47	approach	approach	NOUN
bracis-33646	1	48	to	to	ADP
bracis-33646	1	49	 	 	SPACE
bracis-33646	1	50	agm	agm	PROPN
bracis-33646	1	51	belief	belief	NOUN
bracis-33646	1	52	change	change	NOUN
bracis-33646	1	53	conference	conference	NOUN
bracis-33646	1	54	paper	paper	NOUN
bracis-33646	1	55	first	first	ADV
bracis-33646	1	56	online	online	ADV
bracis-33646	1	57	:	:	PUNCT
bracis-33646	1	58	31	31	NUM
bracis-33646	1	59	january	january	NOUN
bracis-33646	1	60	2025	2025	NUM
bracis-33646	1	61	pp	pp	ADP
bracis-33646	1	62	3–17	3–17	PROPN
bracis-33646	1	63	cite	cite	VERB
bracis-33646	1	64	this	this	DET
bracis-33646	1	65	conference	conference	NOUN
bracis-33646	1	66	paper	paper	NOUN
bracis-33646	1	67	access	access	NOUN
bracis-33646	1	68	provided	provide	VERB
bracis-33646	1	69	by	by	ADP
bracis-33646	1	70	university	university	PROPN
bracis-33646	1	71	of	of	ADP
bracis-33646	1	72	notre	notre	PROPN
bracis-33646	1	73	dame	dame	PROPN
bracis-33646	1	74	hesburgh	hesburgh	PROPN
bracis-33646	1	75	library	library	PROPN
bracis-33646	1	76	download	download	PROPN
bracis-33646	1	77	book	book	NOUN
bracis-33646	1	78	pdf	pdf	PROPN
bracis-33646	1	79	download	download	NOUN
bracis-33646	1	80	book	book	NOUN
bracis-33646	1	81	epub	epub	PROPN
bracis-33646	1	82	intelligent	intelligent	ADJ
bracis-33646	1	83	systems	system	NOUN
bracis-33646	1	84	(	(	PUNCT
bracis-33646	1	85	bracis	bracis	NOUN
bracis-33646	1	86	2024	2024	NUM
bracis-33646	1	87	)	)	PUNCT
bracis-33646	1	88	a	a	DET
bracis-33646	1	89	topology	topology	NOUN
bracis-33646	1	90	-	-	PUNCT
bracis-33646	1	91	inspired	inspire	VERB
bracis-33646	1	92	approach	approach	NOUN
bracis-33646	1	93	to	to	ADP
bracis-33646	1	94	 	 	SPACE
bracis-33646	1	95	agm	agm	PROPN
bracis-33646	1	96	belief	belief	NOUN
bracis-33646	1	97	change	change	NOUN
bracis-33646	1	98	download	download	NOUN
bracis-33646	1	99	book	book	NOUN
bracis-33646	1	100	pdf	pdf	PROPN
bracis-33646	1	101	download	download	NOUN
bracis-33646	1	102	book	book	PROPN
bracis-33646	1	103	epub	epub	PROPN
bracis-33646	1	104	marlo	marlo	PROPN
bracis-33646	1	105	souza	souza	PROPN
bracis-33646	1	106	  	  	SPACE
bracis-33646	1	107	orcid	orcid	PROPN
bracis-33646	1	108	:	:	PUNCT
bracis-33646	1	109	orcid.org/0000-0002-5373-72719	orcid.org/0000-0002-5373-72719	NOUN
bracis-33646	1	110	  	  	SPACE
bracis-33646	1	111	part	part	NOUN
bracis-33646	1	112	of	of	ADP
bracis-33646	1	113	the	the	DET
bracis-33646	1	114	book	book	NOUN
bracis-33646	1	115	series	series	NOUN
bracis-33646	1	116	:	:	PUNCT
bracis-33646	1	117	lecture	lecture	NOUN
bracis-33646	1	118	notes	note	NOUN
bracis-33646	1	119	in	in	ADP
bracis-33646	1	120	computer	computer	NOUN
bracis-33646	1	121	science	science	NOUN
bracis-33646	1	122	(	(	PUNCT
bracis-33646	1	123	(	(	PUNCT
bracis-33646	1	124	lnai	lnai	ADJ
bracis-33646	1	125	,	,	PUNCT
bracis-33646	1	126	volume	volume	NOUN
bracis-33646	1	127	15415	15415	NUM
bracis-33646	1	128	)	)	PUNCT
bracis-33646	1	129	)	)	PUNCT
bracis-33646	1	130	included	include	VERB
bracis-33646	1	131	in	in	ADP
bracis-33646	1	132	the	the	DET
bracis-33646	1	133	following	follow	VERB
bracis-33646	1	134	conference	conference	NOUN
bracis-33646	1	135	series	series	NOUN
bracis-33646	1	136	:	:	PUNCT
bracis-33646	1	137	brazilian	brazilian	ADJ
bracis-33646	1	138	conference	conference	NOUN
bracis-33646	1	139	on	on	ADP
bracis-33646	1	140	intelligent	intelligent	ADJ
bracis-33646	1	141	systems	system	NOUN
bracis-33646	1	142	220	220	NUM
bracis-33646	1	143	accesses	access	NOUN
bracis-33646	1	144	abstract	abstract	PROPN
bracis-33646	1	145	agm	agm	PROPN
bracis-33646	1	146	’s	’s	PART
bracis-33646	1	147	belief	belief	NOUN
bracis-33646	1	148	revision	revision	NOUN
bracis-33646	1	149	is	be	AUX
bracis-33646	1	150	one	one	NUM
bracis-33646	1	151	of	of	ADP
bracis-33646	1	152	the	the	DET
bracis-33646	1	153	main	main	ADJ
bracis-33646	1	154	paradigms	paradigm	NOUN
bracis-33646	1	155	in	in	ADP
bracis-33646	1	156	the	the	DET
bracis-33646	1	157	study	study	NOUN
bracis-33646	1	158	of	of	ADP
bracis-33646	1	159	belief	belief	NOUN
bracis-33646	1	160	change	change	NOUN
bracis-33646	1	161	operations	operation	NOUN
bracis-33646	1	162	.	.	PUNCT
bracis-33646	2	1	despite	despite	SCONJ
bracis-33646	2	2	its	its	PRON
bracis-33646	2	3	popularity	popularity	NOUN
bracis-33646	2	4	,	,	PUNCT
bracis-33646	2	5	it	it	PRON
bracis-33646	2	6	is	be	AUX
bracis-33646	2	7	well	well	ADV
bracis-33646	2	8	recognised	recognise	VERB
bracis-33646	2	9	that	that	SCONJ
bracis-33646	2	10	agm	agm	PROPN
bracis-33646	2	11	’s	’s	PART
bracis-33646	2	12	work	work	NOUN
bracis-33646	2	13	relies	rely	VERB
bracis-33646	2	14	on	on	ADP
bracis-33646	2	15	a	a	DET
bracis-33646	2	16	strong	strong	ADJ
bracis-33646	2	17	idealisation	idealisation	NOUN
bracis-33646	2	18	of	of	ADP
bracis-33646	2	19	the	the	DET
bracis-33646	2	20	agent	agent	NOUN
bracis-33646	2	21	’s	’s	PART
bracis-33646	2	22	capabilities	capability	NOUN
bracis-33646	2	23	and	and	CCONJ
bracis-33646	2	24	on	on	ADP
bracis-33646	2	25	the	the	DET
bracis-33646	2	26	supporting	support	VERB
bracis-33646	2	27	logic	logic	NOUN
bracis-33646	2	28	.	.	PUNCT
bracis-33646	3	1	recent	recent	ADJ
bracis-33646	3	2	results	result	NOUN
bracis-33646	3	3	in	in	ADP
bracis-33646	3	4	the	the	DET
bracis-33646	3	5	literature	literature	NOUN
bracis-33646	3	6	have	have	AUX
bracis-33646	3	7	shed	shed	VERB
bracis-33646	3	8	light	light	NOUN
bracis-33646	3	9	on	on	ADP
bracis-33646	3	10	the	the	DET
bracis-33646	3	11	definability	definability	NOUN
bracis-33646	3	12	of	of	ADP
bracis-33646	3	13	agm	agm	PROPN
bracis-33646	3	14	-	-	PUNCT
bracis-33646	3	15	like	like	ADJ
bracis-33646	3	16	belief	belief	NOUN
bracis-33646	3	17	change	change	NOUN
bracis-33646	3	18	operations	operation	NOUN
bracis-33646	3	19	in	in	ADP
bracis-33646	3	20	general	general	ADJ
bracis-33646	3	21	logics	logic	NOUN
bracis-33646	3	22	,	,	PUNCT
bracis-33646	3	23	showing	show	VERB
bracis-33646	3	24	how	how	SCONJ
bracis-33646	3	25	the	the	DET
bracis-33646	3	26	properties	property	NOUN
bracis-33646	3	27	of	of	ADP
bracis-33646	3	28	a	a	DET
bracis-33646	3	29	logic	logic	NOUN
bracis-33646	3	30	can	can	AUX
bracis-33646	3	31	be	be	AUX
bracis-33646	3	32	leveraged	leverage	VERB
bracis-33646	3	33	to	to	PART
bracis-33646	3	34	construct	construct	VERB
bracis-33646	3	35	these	these	DET
bracis-33646	3	36	operations	operation	NOUN
bracis-33646	3	37	.	.	PUNCT
bracis-33646	4	1	exploring	explore	VERB
bracis-33646	4	2	well	well	ADV
bracis-33646	4	3	-	-	PUNCT
bracis-33646	4	4	known	know	VERB
bracis-33646	4	5	connections	connection	NOUN
bracis-33646	4	6	between	between	ADP
bracis-33646	4	7	logic	logic	NOUN
bracis-33646	4	8	,	,	PUNCT
bracis-33646	4	9	algebra	algebra	NOUN
bracis-33646	4	10	and	and	CCONJ
bracis-33646	4	11	topology	topology	NOUN
bracis-33646	4	12	,	,	PUNCT
bracis-33646	4	13	our	our	PRON
bracis-33646	4	14	work	work	NOUN
bracis-33646	4	15	explores	explore	VERB
bracis-33646	4	16	a	a	DET
bracis-33646	4	17	general	general	ADJ
bracis-33646	4	18	notion	notion	NOUN
bracis-33646	4	19	of	of	ADP
bracis-33646	4	20	belief	belief	NOUN
bracis-33646	4	21	change	change	NOUN
bracis-33646	4	22	contraction	contraction	NOUN
bracis-33646	4	23	,	,	PUNCT
bracis-33646	4	24	which	which	PRON
bracis-33646	4	25	can	can	AUX
bracis-33646	4	26	be	be	AUX
bracis-33646	4	27	connected	connect	VERB
bracis-33646	4	28	to	to	ADP
bracis-33646	4	29	well	well	ADV
bracis-33646	4	30	-	-	PUNCT
bracis-33646	4	31	studied	study	VERB
bracis-33646	4	32	operations	operation	NOUN
bracis-33646	4	33	in	in	ADP
bracis-33646	4	34	the	the	DET
bracis-33646	4	35	literature	literature	NOUN
bracis-33646	4	36	,	,	PUNCT
bracis-33646	4	37	such	such	ADJ
bracis-33646	4	38	as	as	ADP
bracis-33646	4	39	agm	agm	PROPN
bracis-33646	4	40	rational	rational	ADJ
bracis-33646	4	41	contractions	contraction	NOUN
bracis-33646	4	42	,	,	PUNCT
bracis-33646	4	43	partial	partial	ADJ
bracis-33646	4	44	meet	meet	NOUN
bracis-33646	4	45	contractions	contraction	NOUN
bracis-33646	4	46	,	,	PUNCT
bracis-33646	4	47	and	and	CCONJ
bracis-33646	4	48	multiple	multiple	ADJ
bracis-33646	4	49	contractions	contraction	NOUN
bracis-33646	4	50	,	,	PUNCT
bracis-33646	4	51	employing	employ	VERB
bracis-33646	4	52	the	the	DET
bracis-33646	4	53	framework	framework	NOUN
bracis-33646	4	54	of	of	ADP
bracis-33646	4	55	abstract	abstract	ADJ
bracis-33646	4	56	model	model	NOUN
bracis-33646	4	57	theory	theory	NOUN
bracis-33646	4	58	and	and	CCONJ
bracis-33646	4	59	topological	topological	ADJ
bracis-33646	4	60	semantics	semantic	NOUN
bracis-33646	4	61	.	.	PUNCT
bracis-33646	5	1	we	we	PRON
bracis-33646	5	2	show	show	VERB
bracis-33646	5	3	that	that	SCONJ
bracis-33646	5	4	agm	agm	PROPN
bracis-33646	5	5	rational	rational	ADJ
bracis-33646	5	6	contractions	contraction	NOUN
bracis-33646	5	7	can	can	AUX
bracis-33646	5	8	be	be	AUX
bracis-33646	5	9	characterised	characterise	VERB
bracis-33646	5	10	in	in	ADP
bracis-33646	5	11	our	our	PRON
bracis-33646	5	12	framework	framework	NOUN
bracis-33646	5	13	,	,	PUNCT
bracis-33646	5	14	and	and	CCONJ
bracis-33646	5	15	we	we	PRON
bracis-33646	5	16	can	can	AUX
bracis-33646	5	17	establish	establish	VERB
bracis-33646	5	18	connections	connection	NOUN
bracis-33646	5	19	to	to	ADP
bracis-33646	5	20	different	different	ADJ
bracis-33646	5	21	results	result	NOUN
bracis-33646	5	22	in	in	ADP
bracis-33646	5	23	the	the	DET
bracis-33646	5	24	literature	literature	NOUN
bracis-33646	5	25	.	.	PUNCT
bracis-33646	6	1	access	access	NOUN
bracis-33646	6	2	provided	provide	VERB
bracis-33646	6	3	by	by	ADP
bracis-33646	6	4	university	university	PROPN
bracis-33646	6	5	of	of	ADP
bracis-33646	6	6	notre	notre	PROPN
bracis-33646	6	7	dame	dame	PROPN
bracis-33646	6	8	hesburgh	hesburgh	PROPN
bracis-33646	6	9	library	library	PROPN
bracis-33646	6	10	.	.	PUNCT
bracis-33646	7	1	download	download	PROPN
bracis-33646	7	2	conference	conference	NOUN
bracis-33646	7	3	paper	paper	NOUN
bracis-33646	7	4	pdf	pdf	NOUN
bracis-33646	7	5	similar	similar	ADJ
bracis-33646	7	6	content	content	NOUN
bracis-33646	7	7	being	be	AUX
bracis-33646	7	8	viewed	view	VERB
bracis-33646	7	9	by	by	ADP
bracis-33646	7	10	others	other	NOUN
bracis-33646	7	11	on	on	ADP
bracis-33646	7	12	a	a	DET
bracis-33646	7	13	logico	logico	PROPN
bracis-33646	7	14	-	-	PUNCT
bracis-33646	7	15	algebraic	algebraic	ADJ
bracis-33646	7	16	approach	approach	NOUN
bracis-33646	7	17	to	to	ADP
bracis-33646	7	18	agm	agm	PROPN
bracis-33646	7	19	belief	belief	NOUN
bracis-33646	7	20	contraction	contraction	NOUN
bracis-33646	7	21	theory	theory	NOUN
bracis-33646	7	22	article	article	NOUN
bracis-33646	7	23	05	05	NUM
bracis-33646	8	1	january	january	PROPN
bracis-33646	8	2	2021	2021	NUM
bracis-33646	8	3	belief	belief	NOUN
bracis-33646	8	4	contraction	contraction	NOUN
bracis-33646	8	5	in	in	ADP
bracis-33646	8	6	the	the	DET
bracis-33646	8	7	context	context	NOUN
bracis-33646	8	8	of	of	ADP
bracis-33646	8	9	the	the	DET
bracis-33646	8	10	general	general	ADJ
bracis-33646	8	11	theory	theory	NOUN
bracis-33646	8	12	of	of	ADP
bracis-33646	8	13	rational	rational	ADJ
bracis-33646	8	14	choice	choice	NOUN
bracis-33646	8	15	chapter	chapter	NOUN
bracis-33646	8	16	©	©	PROPN
bracis-33646	8	17	2016	2016	NUM
bracis-33646	8	18	towards	towards	ADP
bracis-33646	8	19	a	a	DET
bracis-33646	8	20	theory	theory	NOUN
bracis-33646	8	21	of	of	ADP
bracis-33646	8	22	hyperintensional	hyperintensional	ADJ
bracis-33646	8	23	belief	belief	NOUN
bracis-33646	8	24	change	change	NOUN
bracis-33646	8	25	chapter	chapter	NOUN
bracis-33646	8	26	©	©	NOUN
bracis-33646	8	27	2020	2020	NUM
bracis-33646	8	28	1	1	NUM
bracis-33646	8	29	introduction	introduction	NOUN
bracis-33646	8	30	belief	belief	NOUN
bracis-33646	8	31	change	change	NOUN
bracis-33646	8	32	is	be	AUX
bracis-33646	8	33	the	the	DET
bracis-33646	8	34	area	area	NOUN
bracis-33646	8	35	that	that	PRON
bracis-33646	8	36	studies	study	VERB
bracis-33646	8	37	how	how	SCONJ
bracis-33646	8	38	doxastic	doxastic	ADJ
bracis-33646	8	39	agents	agent	NOUN
bracis-33646	8	40	change	change	VERB
bracis-33646	8	41	their	their	PRON
bracis-33646	8	42	minds	mind	NOUN
bracis-33646	8	43	after	after	ADP
bracis-33646	8	44	acquiring	acquire	VERB
bracis-33646	8	45	new	new	ADJ
bracis-33646	8	46	information	information	NOUN
bracis-33646	8	47	.	.	PUNCT
bracis-33646	9	1	one	one	NUM
bracis-33646	9	2	of	of	ADP
bracis-33646	9	3	the	the	DET
bracis-33646	9	4	most	most	ADV
bracis-33646	9	5	influential	influential	ADJ
bracis-33646	9	6	approaches	approach	NOUN
bracis-33646	9	7	in	in	ADP
bracis-33646	9	8	the	the	DET
bracis-33646	9	9	literature	literature	NOUN
bracis-33646	9	10	,	,	PUNCT
bracis-33646	9	11	namely	namely	ADV
bracis-33646	9	12	the	the	DET
bracis-33646	9	13	agm	agm	PROPN
bracis-33646	9	14	framework	framework	NOUN
bracis-33646	9	15	[	[	X
bracis-33646	9	16	1	1	NUM
bracis-33646	9	17	]	]	PUNCT
bracis-33646	9	18	,	,	PUNCT
bracis-33646	9	19	studies	study	NOUN
bracis-33646	9	20	rational	rational	ADJ
bracis-33646	9	21	constraints	constraint	NOUN
bracis-33646	9	22	,	,	PUNCT
bracis-33646	9	23	or	or	CCONJ
bracis-33646	9	24	postulates	postulate	NOUN
bracis-33646	9	25	,	,	PUNCT
bracis-33646	9	26	that	that	PRON
bracis-33646	9	27	characterise	characterise	VERB
bracis-33646	9	28	rational	rational	ADJ
bracis-33646	9	29	ways	way	NOUN
bracis-33646	9	30	of	of	ADP
bracis-33646	9	31	changing	change	VERB
bracis-33646	9	32	beliefs	belief	NOUN
bracis-33646	9	33	,	,	PUNCT
bracis-33646	9	34	given	give	VERB
bracis-33646	9	35	a	a	DET
bracis-33646	9	36	representation	representation	NOUN
bracis-33646	9	37	of	of	ADP
bracis-33646	9	38	one	one	NUM
bracis-33646	9	39	’s	’s	PART
bracis-33646	9	40	doxastic	doxastic	ADJ
bracis-33646	9	41	state	state	NOUN
bracis-33646	9	42	.	.	PUNCT
bracis-33646	10	1	while	while	SCONJ
bracis-33646	10	2	the	the	DET
bracis-33646	10	3	seminal	seminal	ADJ
bracis-33646	10	4	work	work	NOUN
bracis-33646	10	5	of	of	ADP
bracis-33646	10	6	agm	agm	PROPN
bracis-33646	10	7	focuses	focus	VERB
bracis-33646	10	8	on	on	ADP
bracis-33646	10	9	belief	belief	NOUN
bracis-33646	10	10	change	change	NOUN
bracis-33646	10	11	for	for	ADP
bracis-33646	10	12	classical	classical	ADJ
bracis-33646	10	13	logic	logic	NOUN
bracis-33646	10	14	,	,	PUNCT
bracis-33646	10	15	recently	recently	ADV
bracis-33646	10	16	,	,	PUNCT
bracis-33646	10	17	several	several	ADJ
bracis-33646	10	18	works	work	NOUN
bracis-33646	10	19	investigated	investigate	VERB
bracis-33646	10	20	its	its	PRON
bracis-33646	10	21	applications	application	NOUN
bracis-33646	10	22	to	to	ADP
bracis-33646	10	23	a	a	DET
bracis-33646	10	24	wide	wide	ADJ
bracis-33646	10	25	range	range	NOUN
bracis-33646	10	26	of	of	ADP
bracis-33646	10	27	non	non	ADJ
bracis-33646	10	28	-	-	ADJ
bracis-33646	10	29	classical	classical	ADJ
bracis-33646	10	30	logics	logic	NOUN
bracis-33646	10	31	of	of	ADP
bracis-33646	10	32	interest	interest	NOUN
bracis-33646	10	33	in	in	ADP
bracis-33646	10	34	artificial	artificial	ADJ
bracis-33646	10	35	intelligence	intelligence	NOUN
bracis-33646	10	36	[	[	X
bracis-33646	10	37	4	4	NUM
bracis-33646	10	38	,	,	PUNCT
bracis-33646	10	39	16	16	NUM
bracis-33646	10	40	]	]	PUNCT
bracis-33646	10	41	.	.	PUNCT
bracis-33646	11	1	investigating	investigate	VERB
bracis-33646	11	2	the	the	DET
bracis-33646	11	3	definability	definability	NOUN
bracis-33646	11	4	of	of	ADP
bracis-33646	11	5	agm	agm	PROPN
bracis-33646	11	6	belief	belief	NOUN
bracis-33646	11	7	change	change	NOUN
bracis-33646	11	8	operations	operation	NOUN
bracis-33646	11	9	on	on	ADP
bracis-33646	11	10	abstract	abstract	ADJ
bracis-33646	11	11	logics	logic	NOUN
bracis-33646	11	12	,	,	PUNCT
bracis-33646	11	13	flouris	flouris	PROPN
bracis-33646	11	14	 	 	SPACE
bracis-33646	12	1	[	[	X
bracis-33646	12	2	5	5	NUM
bracis-33646	12	3	]	]	PUNCT
bracis-33646	12	4	shows	show	VERB
bracis-33646	12	5	necessary	necessary	ADJ
bracis-33646	12	6	and	and	CCONJ
bracis-33646	12	7	sufficient	sufficient	ADJ
bracis-33646	12	8	conditions	condition	NOUN
bracis-33646	12	9	for	for	ADP
bracis-33646	12	10	a	a	DET
bracis-33646	12	11	logic	logic	NOUN
bracis-33646	12	12	to	to	PART
bracis-33646	12	13	allow	allow	VERB
bracis-33646	12	14	the	the	DET
bracis-33646	12	15	definition	definition	NOUN
bracis-33646	12	16	of	of	ADP
bracis-33646	12	17	these	these	DET
bracis-33646	12	18	operations	operation	NOUN
bracis-33646	12	19	and	and	CCONJ
bracis-33646	12	20	that	that	SCONJ
bracis-33646	12	21	several	several	ADJ
bracis-33646	12	22	logics	logic	NOUN
bracis-33646	12	23	did	do	AUX
bracis-33646	12	24	not	not	PART
bracis-33646	12	25	satisfy	satisfy	VERB
bracis-33646	12	26	these	these	DET
bracis-33646	12	27	requirements	requirement	NOUN
bracis-33646	12	28	.	.	PUNCT
bracis-33646	13	1	flouris	flouris	PROPN
bracis-33646	13	2	employs	employ	VERB
bracis-33646	13	3	machinery	machinery	NOUN
bracis-33646	13	4	from	from	ADP
bracis-33646	13	5	abstract	abstract	ADJ
bracis-33646	13	6	logics	logic	NOUN
bracis-33646	13	7	and	and	CCONJ
bracis-33646	13	8	topology	topology	NOUN
bracis-33646	13	9	to	to	PART
bracis-33646	13	10	prove	prove	VERB
bracis-33646	13	11	their	their	PRON
bracis-33646	13	12	results	result	NOUN
bracis-33646	13	13	.	.	PUNCT
bracis-33646	14	1	similarly	similarly	ADV
bracis-33646	14	2	,	,	PUNCT
bracis-33646	14	3	investigating	investigate	VERB
bracis-33646	14	4	model	model	ADJ
bracis-33646	14	5	-	-	PUNCT
bracis-33646	14	6	theoretic	theoretic	ADJ
bracis-33646	14	7	approaches	approach	NOUN
bracis-33646	14	8	to	to	PART
bracis-33646	14	9	define	define	VERB
bracis-33646	14	10	forms	form	NOUN
bracis-33646	14	11	of	of	ADP
bracis-33646	14	12	belief	belief	NOUN
bracis-33646	14	13	change	change	NOUN
bracis-33646	14	14	,	,	PUNCT
bracis-33646	14	15	souza	souza	PROPN
bracis-33646	14	16	and	and	CCONJ
bracis-33646	14	17	wasserman	wasserman	PROPN
bracis-33646	14	18	 	 	SPACE
bracis-33646	15	1	[	[	X
bracis-33646	15	2	18	18	NUM
bracis-33646	15	3	,	,	PUNCT
bracis-33646	15	4	p.13	p.13	AUX
bracis-33646	15	5	]	]	PUNCT
bracis-33646	15	6	point	point	NOUN
bracis-33646	15	7	out	out	ADP
bracis-33646	15	8	that	that	SCONJ
bracis-33646	15	9	“	"	PUNCT
bracis-33646	15	10	different	different	ADJ
bracis-33646	15	11	notions	notion	NOUN
bracis-33646	15	12	of	of	ADP
bracis-33646	15	13	minimality	minimality	NOUN
bracis-33646	15	14	arise	arise	VERB
bracis-33646	15	15	as	as	ADP
bracis-33646	15	16	the	the	DET
bracis-33646	15	17	reflection	reflection	NOUN
bracis-33646	15	18	of	of	ADP
bracis-33646	15	19	topological	topological	ADJ
bracis-33646	15	20	properties	property	NOUN
bracis-33646	15	21	of	of	ADP
bracis-33646	15	22	the	the	DET
bracis-33646	15	23	model	model	NOUN
bracis-33646	15	24	space	space	NOUN
bracis-33646	15	25	”	"	PUNCT
bracis-33646	15	26	,	,	PUNCT
bracis-33646	15	27	which	which	PRON
bracis-33646	15	28	indicates	indicate	VERB
bracis-33646	15	29	a	a	DET
bracis-33646	15	30	deeper	deep	ADJ
bracis-33646	15	31	connection	connection	NOUN
bracis-33646	15	32	between	between	ADP
bracis-33646	15	33	agm	agm	PROPN
bracis-33646	15	34	belief	belief	NOUN
bracis-33646	15	35	change	change	NOUN
bracis-33646	15	36	and	and	CCONJ
bracis-33646	15	37	the	the	DET
bracis-33646	15	38	characteristics	characteristic	NOUN
bracis-33646	15	39	of	of	ADP
bracis-33646	15	40	topological	topological	ADJ
bracis-33646	15	41	space	space	NOUN
bracis-33646	15	42	defined	define	VERB
bracis-33646	15	43	by	by	ADP
bracis-33646	15	44	the	the	DET
bracis-33646	15	45	logic	logic	NOUN
bracis-33646	15	46	.	.	PUNCT
bracis-33646	16	1	the	the	DET
bracis-33646	16	2	literature	literature	NOUN
bracis-33646	16	3	on	on	ADP
bracis-33646	16	4	abstract	abstract	ADJ
bracis-33646	16	5	logic	logic	NOUN
bracis-33646	16	6	and	and	CCONJ
bracis-33646	16	7	abstract	abstract	ADJ
bracis-33646	16	8	model	model	NOUN
bracis-33646	16	9	theory	theory	NOUN
bracis-33646	16	10	has	have	AUX
bracis-33646	16	11	long	long	ADV
bracis-33646	16	12	established	establish	VERB
bracis-33646	16	13	deep	deep	ADJ
bracis-33646	16	14	connections	connection	NOUN
bracis-33646	16	15	between	between	ADP
bracis-33646	16	16	properties	property	NOUN
bracis-33646	16	17	of	of	ADP
bracis-33646	16	18	a	a	DET
bracis-33646	16	19	logic	logic	NOUN
bracis-33646	16	20	and	and	CCONJ
bracis-33646	16	21	of	of	ADP
bracis-33646	16	22	the	the	DET
bracis-33646	16	23	topology	topology	NOUN
bracis-33646	16	24	of	of	ADP
bracis-33646	16	25	the	the	DET
bracis-33646	16	26	space	space	NOUN
bracis-33646	16	27	of	of	ADP
bracis-33646	16	28	models	model	NOUN
bracis-33646	16	29	that	that	PRON
bracis-33646	16	30	defines	define	VERB
bracis-33646	16	31	it	it	PRON
bracis-33646	16	32	[	[	X
bracis-33646	16	33	11	11	NUM
bracis-33646	16	34	,	,	PUNCT
bracis-33646	16	35	12	12	NUM
bracis-33646	16	36	,	,	PUNCT
bracis-33646	16	37	21	21	NUM
bracis-33646	16	38	]	]	PUNCT
bracis-33646	16	39	.	.	PUNCT
bracis-33646	17	1	surprisingly	surprisingly	ADV
bracis-33646	17	2	,	,	PUNCT
bracis-33646	17	3	although	although	SCONJ
bracis-33646	17	4	topological	topological	ADJ
bracis-33646	17	5	approaches	approach	NOUN
bracis-33646	17	6	to	to	ADP
bracis-33646	17	7	the	the	DET
bracis-33646	17	8	study	study	NOUN
bracis-33646	17	9	of	of	ADP
bracis-33646	17	10	formal	formal	ADJ
bracis-33646	17	11	epistemology	epistemology	NOUN
bracis-33646	17	12	and	and	CCONJ
bracis-33646	17	13	epistemic	epistemic	ADJ
bracis-33646	17	14	logic	logic	NOUN
bracis-33646	17	15	exist	exist	VERB
bracis-33646	17	16	in	in	ADP
bracis-33646	17	17	the	the	DET
bracis-33646	17	18	literature	literature	NOUN
bracis-33646	17	19	[	[	X
bracis-33646	17	20	2	2	NUM
bracis-33646	17	21	,	,	PUNCT
bracis-33646	17	22	3	3	NUM
bracis-33646	17	23	,	,	PUNCT
bracis-33646	17	24	10	10	NUM
bracis-33646	17	25	]	]	PUNCT
bracis-33646	17	26	,	,	PUNCT
bracis-33646	17	27	to	to	ADP
bracis-33646	17	28	our	our	PRON
bracis-33646	17	29	knowledge	knowledge	NOUN
bracis-33646	17	30	,	,	PUNCT
bracis-33646	17	31	very	very	ADV
bracis-33646	17	32	little	little	ADJ
bracis-33646	17	33	work	work	NOUN
bracis-33646	17	34	has	have	AUX
bracis-33646	17	35	been	be	AUX
bracis-33646	17	36	dedicated	dedicate	VERB
bracis-33646	17	37	to	to	ADP
bracis-33646	17	38	the	the	DET
bracis-33646	17	39	study	study	NOUN
bracis-33646	17	40	of	of	ADP
bracis-33646	17	41	topological	topological	ADJ
bracis-33646	17	42	aspects	aspect	NOUN
bracis-33646	17	43	of	of	ADP
bracis-33646	17	44	belief	belief	NOUN
bracis-33646	17	45	change	change	NOUN
bracis-33646	17	46	.	.	PUNCT
bracis-33646	18	1	in	in	ADP
bracis-33646	18	2	fact	fact	NOUN
bracis-33646	18	3	,	,	PUNCT
bracis-33646	18	4	to	to	ADP
bracis-33646	18	5	our	our	PRON
bracis-33646	18	6	knowledge	knowledge	NOUN
bracis-33646	18	7	,	,	PUNCT
bracis-33646	18	8	only	only	ADV
bracis-33646	18	9	the	the	DET
bracis-33646	18	10	work	work	NOUN
bracis-33646	18	11	of	of	ADP
bracis-33646	18	12	özgün	özgün	NOUN
bracis-33646	18	13	 	 	SPACE
bracis-33646	19	1	[	[	SYM
bracis-33646	19	2	13	13	NUM
bracis-33646	19	3	]	]	PUNCT
bracis-33646	19	4	explicitly	explicitly	ADV
bracis-33646	19	5	explores	explore	VERB
bracis-33646	19	6	topological	topological	ADJ
bracis-33646	19	7	models	model	NOUN
bracis-33646	19	8	to	to	PART
bracis-33646	19	9	study	study	VERB
bracis-33646	19	10	belief	belief	NOUN
bracis-33646	19	11	change	change	NOUN
bracis-33646	19	12	.	.	PUNCT
bracis-33646	20	1	topological	topological	ADJ
bracis-33646	20	2	notions	notion	NOUN
bracis-33646	20	3	,	,	PUNCT
bracis-33646	20	4	however	however	ADV
bracis-33646	20	5	,	,	PUNCT
bracis-33646	20	6	seem	seem	VERB
bracis-33646	20	7	to	to	PART
bracis-33646	20	8	infiltrate	infiltrate	VERB
bracis-33646	20	9	model	model	ADJ
bracis-33646	20	10	-	-	PUNCT
bracis-33646	20	11	theoretic	theoretic	ADJ
bracis-33646	20	12	approaches	approach	NOUN
bracis-33646	20	13	to	to	ADP
bracis-33646	20	14	belief	belief	NOUN
bracis-33646	20	15	change	change	NOUN
bracis-33646	20	16	,	,	PUNCT
bracis-33646	20	17	such	such	ADJ
bracis-33646	20	18	as	as	ADP
bracis-33646	20	19	that	that	PRON
bracis-33646	20	20	of	of	ADP
bracis-33646	20	21	peppas	peppa	NOUN
bracis-33646	20	22	 	 	SPACE
bracis-33646	21	1	[	[	X
bracis-33646	21	2	14	14	NUM
bracis-33646	21	3	]	]	PUNCT
bracis-33646	21	4	and	and	CCONJ
bracis-33646	21	5	of	of	ADP
bracis-33646	21	6	ribeiro	ribeiro	PROPN
bracis-33646	21	7	et	et	PROPN
bracis-33646	21	8	al	al	PROPN
bracis-33646	21	9	.	.	PUNCT
bracis-33646	21	10	 	 	SPACE
bracis-33646	22	1	[	[	X
bracis-33646	22	2	15	15	NUM
bracis-33646	22	3	]	]	PUNCT
bracis-33646	22	4	on	on	ADP
bracis-33646	22	5	the	the	DET
bracis-33646	22	6	generalisation	generalisation	NOUN
bracis-33646	22	7	of	of	ADP
bracis-33646	22	8	agm	agm	PROPN
bracis-33646	22	9	belief	belief	NOUN
bracis-33646	22	10	change	change	NOUN
bracis-33646	22	11	to	to	ADP
bracis-33646	22	12	other	other	ADJ
bracis-33646	22	13	logics	logic	NOUN
bracis-33646	22	14	than	than	ADP
bracis-33646	22	15	those	those	PRON
bracis-33646	22	16	considered	consider	VERB
bracis-33646	22	17	by	by	ADP
bracis-33646	22	18	the	the	DET
bracis-33646	22	19	original	original	ADJ
bracis-33646	22	20	authors	author	NOUN
bracis-33646	22	21	.	.	PUNCT
bracis-33646	23	1	in	in	ADP
bracis-33646	23	2	this	this	DET
bracis-33646	23	3	work	work	NOUN
bracis-33646	23	4	,	,	PUNCT
bracis-33646	23	5	we	we	PRON
bracis-33646	23	6	investigate	investigate	VERB
bracis-33646	23	7	a	a	DET
bracis-33646	23	8	general	general	ADJ
bracis-33646	23	9	notion	notion	NOUN
bracis-33646	23	10	of	of	ADP
bracis-33646	23	11	belief	belief	NOUN
bracis-33646	23	12	change	change	NOUN
bracis-33646	23	13	contraction	contraction	NOUN
bracis-33646	23	14	and	and	CCONJ
bracis-33646	23	15	the	the	DET
bracis-33646	23	16	definability	definability	NOUN
bracis-33646	23	17	of	of	ADP
bracis-33646	23	18	agm	agm	PROPN
bracis-33646	23	19	belief	belief	NOUN
bracis-33646	23	20	contraction	contraction	NOUN
bracis-33646	23	21	operators	operator	NOUN
bracis-33646	23	22	based	base	VERB
bracis-33646	23	23	on	on	ADP
bracis-33646	23	24	results	result	NOUN
bracis-33646	23	25	from	from	ADP
bracis-33646	23	26	abstract	abstract	ADJ
bracis-33646	23	27	model	model	NOUN
bracis-33646	23	28	theory	theory	NOUN
bracis-33646	23	29	and	and	CCONJ
bracis-33646	23	30	its	its	PRON
bracis-33646	23	31	connections	connection	NOUN
bracis-33646	23	32	to	to	ADP
bracis-33646	23	33	topology	topology	NOUN
bracis-33646	23	34	(	(	PUNCT
bracis-33646	23	35	theorems	theorem	NOUN
bracis-33646	23	36	 	 	SPACE
bracis-33646	23	37	1	1	NUM
bracis-33646	23	38	and	and	CCONJ
bracis-33646	23	39	2	2	NUM
bracis-33646	23	40	,	,	PUNCT
bracis-33646	23	41	and	and	CCONJ
bracis-33646	23	42	lemma	lemma	PROPN
bracis-33646	23	43	 	 	SPACE
bracis-33646	23	44	5	5	NUM
bracis-33646	23	45	)	)	PUNCT
bracis-33646	23	46	,	,	PUNCT
bracis-33646	23	47	generalising	generalise	VERB
bracis-33646	23	48	the	the	DET
bracis-33646	23	49	results	result	NOUN
bracis-33646	23	50	of	of	ADP
bracis-33646	23	51	ribeiro	ribeiro	PROPN
bracis-33646	23	52	et	et	PROPN
bracis-33646	23	53	al	al	PROPN
bracis-33646	23	54	.	.	PUNCT
bracis-33646	23	55	 	 	SPACE
bracis-33646	24	1	[	[	X
bracis-33646	24	2	15	15	NUM
bracis-33646	24	3	]	]	PUNCT
bracis-33646	24	4	on	on	ADP
bracis-33646	24	5	the	the	DET
bracis-33646	24	6	definability	definability	NOUN
bracis-33646	24	7	of	of	ADP
bracis-33646	24	8	agm	agm	PROPN
bracis-33646	24	9	contraction	contraction	PROPN
bracis-33646	24	10	for	for	ADP
bracis-33646	24	11	non	non	ADJ
bracis-33646	24	12	-	-	ADJ
bracis-33646	24	13	monotonic	monotonic	ADJ
bracis-33646	24	14	logics	logic	NOUN
bracis-33646	24	15	(	(	PUNCT
bracis-33646	24	16	proposition	proposition	NOUN
bracis-33646	24	17	 	 	SPACE
bracis-33646	24	18	6	6	NUM
bracis-33646	24	19	and	and	CCONJ
bracis-33646	24	20	corollary	corollary	ADJ
bracis-33646	24	21	 	 	SPACE
bracis-33646	24	22	2	2	NUM
bracis-33646	24	23	)	)	PUNCT
bracis-33646	24	24	.	.	PUNCT
bracis-33646	25	1	we	we	PRON
bracis-33646	25	2	employ	employ	VERB
bracis-33646	25	3	our	our	PRON
bracis-33646	25	4	characterisation	characterisation	NOUN
bracis-33646	25	5	to	to	PART
bracis-33646	25	6	show	show	VERB
bracis-33646	25	7	,	,	PUNCT
bracis-33646	25	8	in	in	ADP
bracis-33646	25	9	example	example	NOUN
bracis-33646	25	10	 	 	SPACE
bracis-33646	25	11	1	1	NUM
bracis-33646	25	12	,	,	PUNCT
bracis-33646	25	13	that	that	PRON
bracis-33646	25	14	propositional	propositional	ADJ
bracis-33646	25	15	intuitionistic	intuitionistic	ADJ
bracis-33646	25	16	logic	logic	NOUN
bracis-33646	25	17	is	be	AUX
bracis-33646	25	18	not	not	PART
bracis-33646	25	19	agm	agm	NOUN
bracis-33646	25	20	-	-	PUNCT
bracis-33646	25	21	compatible	compatible	ADJ
bracis-33646	25	22	.	.	PUNCT
bracis-33646	26	1	this	this	DET
bracis-33646	26	2	work	work	NOUN
bracis-33646	26	3	is	be	AUX
bracis-33646	26	4	structured	structure	VERB
bracis-33646	26	5	as	as	SCONJ
bracis-33646	26	6	follows	follow	VERB
bracis-33646	26	7	:	:	PUNCT
bracis-33646	26	8	in	in	ADP
bracis-33646	26	9	sect	sect	NOUN
bracis-33646	26	10	.	.	PUNCT
bracis-33646	26	11	 	 	SPACE
bracis-33646	27	1	2	2	NUM
bracis-33646	27	2	we	we	PRON
bracis-33646	27	3	present	present	VERB
bracis-33646	27	4	preliminary	preliminary	ADJ
bracis-33646	27	5	notions	notion	NOUN
bracis-33646	27	6	related	relate	VERB
bracis-33646	27	7	to	to	ADP
bracis-33646	27	8	abstract	abstract	ADJ
bracis-33646	27	9	logic	logic	NOUN
bracis-33646	27	10	and	and	CCONJ
bracis-33646	27	11	belief	belief	NOUN
bracis-33646	27	12	change	change	NOUN
bracis-33646	27	13	,	,	PUNCT
bracis-33646	27	14	which	which	PRON
bracis-33646	27	15	will	will	AUX
bracis-33646	27	16	be	be	AUX
bracis-33646	27	17	the	the	DET
bracis-33646	27	18	base	base	NOUN
bracis-33646	27	19	of	of	ADP
bracis-33646	27	20	our	our	PRON
bracis-33646	27	21	work	work	NOUN
bracis-33646	27	22	;	;	PUNCT
bracis-33646	27	23	in	in	ADP
bracis-33646	27	24	sect	sect	NOUN
bracis-33646	27	25	.	.	PUNCT
bracis-33646	27	26	 	 	SPACE
bracis-33646	28	1	3	3	NUM
bracis-33646	28	2	,	,	PUNCT
bracis-33646	28	3	we	we	PRON
bracis-33646	28	4	develop	develop	VERB
bracis-33646	28	5	the	the	DET
bracis-33646	28	6	semantic	semantic	ADJ
bracis-33646	28	7	framework	framework	NOUN
bracis-33646	28	8	employed	employ	VERB
bracis-33646	28	9	in	in	ADP
bracis-33646	28	10	this	this	DET
bracis-33646	28	11	work	work	NOUN
bracis-33646	28	12	,	,	PUNCT
bracis-33646	28	13	investigating	investigate	VERB
bracis-33646	28	14	the	the	DET
bracis-33646	28	15	connections	connection	NOUN
bracis-33646	28	16	between	between	ADP
bracis-33646	28	17	logic	logic	NOUN
bracis-33646	28	18	,	,	PUNCT
bracis-33646	28	19	abstract	abstract	ADJ
bracis-33646	28	20	model	model	NOUN
bracis-33646	28	21	theory	theory	NOUN
bracis-33646	28	22	and	and	CCONJ
bracis-33646	28	23	topology	topology	NOUN
bracis-33646	28	24	;	;	PUNCT
bracis-33646	28	25	in	in	ADP
bracis-33646	28	26	sect	sect	NOUN
bracis-33646	28	27	.	.	PUNCT
bracis-33646	28	28	 	 	SPACE
bracis-33646	29	1	4	4	NUM
bracis-33646	29	2	,	,	PUNCT
bracis-33646	29	3	we	we	PRON
bracis-33646	29	4	employ	employ	VERB
bracis-33646	29	5	the	the	DET
bracis-33646	29	6	investigated	investigate	VERB
bracis-33646	29	7	framework	framework	NOUN
bracis-33646	29	8	to	to	PART
bracis-33646	29	9	define	define	VERB
bracis-33646	29	10	belief	belief	NOUN
bracis-33646	29	11	change	change	NOUN
bracis-33646	29	12	operations	operation	NOUN
bracis-33646	29	13	,	,	PUNCT
bracis-33646	29	14	and	and	CCONJ
bracis-33646	29	15	study	study	VERB
bracis-33646	29	16	their	their	PRON
bracis-33646	29	17	properties	property	NOUN
bracis-33646	29	18	;	;	PUNCT
bracis-33646	29	19	in	in	ADP
bracis-33646	29	20	sect	sect	NOUN
bracis-33646	29	21	.	.	PUNCT
bracis-33646	29	22	 	 	SPACE
bracis-33646	30	1	5	5	NUM
bracis-33646	30	2	,	,	PUNCT
bracis-33646	30	3	we	we	PRON
bracis-33646	30	4	discuss	discuss	VERB
bracis-33646	30	5	the	the	DET
bracis-33646	30	6	related	related	ADJ
bracis-33646	30	7	work	work	NOUN
bracis-33646	30	8	.	.	PUNCT
bracis-33646	31	1	finally	finally	ADV
bracis-33646	31	2	,	,	PUNCT
bracis-33646	31	3	we	we	PRON
bracis-33646	31	4	present	present	VERB
bracis-33646	31	5	some	some	DET
bracis-33646	31	6	final	final	ADJ
bracis-33646	31	7	considerations	consideration	NOUN
bracis-33646	31	8	on	on	ADP
bracis-33646	31	9	the	the	DET
bracis-33646	31	10	significance	significance	NOUN
bracis-33646	31	11	of	of	ADP
bracis-33646	31	12	our	our	PRON
bracis-33646	31	13	results	result	NOUN
bracis-33646	31	14	and	and	CCONJ
bracis-33646	31	15	pathways	pathway	NOUN
bracis-33646	31	16	for	for	ADP
bracis-33646	31	17	future	future	ADJ
bracis-33646	31	18	research	research	NOUN
bracis-33646	31	19	.	.	PUNCT
bracis-33646	32	1	2	2	NUM
bracis-33646	32	2	preliminaries	preliminary	NOUN
bracis-33646	32	3	in	in	ADP
bracis-33646	32	4	this	this	DET
bracis-33646	32	5	work	work	NOUN
bracis-33646	32	6	,	,	PUNCT
bracis-33646	32	7	we	we	PRON
bracis-33646	32	8	employ	employ	VERB
bracis-33646	32	9	the	the	DET
bracis-33646	32	10	tools	tool	NOUN
bracis-33646	32	11	from	from	ADP
bracis-33646	32	12	abstract	abstract	ADJ
bracis-33646	32	13	logic	logic	NOUN
bracis-33646	32	14	and	and	CCONJ
bracis-33646	32	15	abstract	abstract	ADJ
bracis-33646	32	16	model	model	NOUN
bracis-33646	32	17	theory	theory	NOUN
bracis-33646	32	18	to	to	PART
bracis-33646	32	19	study	study	VERB
bracis-33646	32	20	classes	class	NOUN
bracis-33646	32	21	of	of	ADP
bracis-33646	32	22	belief	belief	NOUN
bracis-33646	32	23	change	change	NOUN
bracis-33646	32	24	operations	operation	NOUN
bracis-33646	32	25	and	and	CCONJ
bracis-33646	32	26	their	their	PRON
bracis-33646	32	27	definability	definability	NOUN
bracis-33646	32	28	in	in	ADP
bracis-33646	32	29	non	non	ADJ
bracis-33646	32	30	-	-	ADJ
bracis-33646	32	31	classical	classical	ADJ
bracis-33646	32	32	logics	logic	NOUN
bracis-33646	32	33	.	.	PUNCT
bracis-33646	33	1	we	we	PRON
bracis-33646	33	2	will	will	AUX
bracis-33646	33	3	call	call	VERB
bracis-33646	33	4	a	a	DET
bracis-33646	33	5	logic	logic	NOUN
bracis-33646	33	6	any	any	DET
bracis-33646	33	7	pair	pair	NOUN
bracis-33646	33	8	\(\mathcal	\(\mathcal	ADJ
bracis-33646	33	9	{	{	PUNCT
bracis-33646	33	10	l	l	NOUN
bracis-33646	33	11	}	}	PUNCT
bracis-33646	33	12	=	=	PUNCT
bracis-33646	33	13	\langle	\langle	PROPN
bracis-33646	33	14	l	l	NOUN
bracis-33646	33	15	,	,	PUNCT
bracis-33646	33	16	cn	cn	VERB
bracis-33646	33	17	\rangle	\rangle	PROPN
bracis-33646	33	18	\	\	PROPN
bracis-33646	33	19	)	)	PUNCT
bracis-33646	33	20	,	,	PUNCT
bracis-33646	33	21	where	where	SCONJ
bracis-33646	33	22	l	l	NOUN
bracis-33646	33	23	is	be	AUX
bracis-33646	33	24	a	a	DET
bracis-33646	33	25	non	non	ADJ
bracis-33646	33	26	-	-	ADJ
bracis-33646	33	27	empty	empty	ADJ
bracis-33646	33	28	set	set	NOUN
bracis-33646	33	29	,	,	PUNCT
bracis-33646	33	30	called	call	VERB
bracis-33646	33	31	the	the	DET
bracis-33646	33	32	logical	logical	ADJ
bracis-33646	33	33	language	language	NOUN
bracis-33646	33	34	,	,	PUNCT
bracis-33646	33	35	and	and	CCONJ
bracis-33646	33	36	\(cn:2^l\rightarrow	\(cn:2^l\rightarrow	VERB
bracis-33646	33	37	2^l\	2^l\	NUM
bracis-33646	33	38	)	)	PUNCT
bracis-33646	33	39	is	be	AUX
bracis-33646	33	40	a	a	DET
bracis-33646	33	41	function	function	NOUN
bracis-33646	33	42	called	call	VERB
bracis-33646	33	43	a	a	DET
bracis-33646	33	44	consequence	consequence	NOUN
bracis-33646	33	45	operator	operator	NOUN
bracis-33646	33	46	satisfying	satisfy	VERB
bracis-33646	33	47	the	the	DET
bracis-33646	33	48	following	follow	VERB
bracis-33646	33	49	propertiesfootnote	propertiesfootnote	NOUN
bracis-33646	33	50	1	1	NUM
bracis-33646	33	51	:	:	PUNCT
bracis-33646	33	52	inclusion	inclusion	NOUN
bracis-33646	33	53	:	:	PUNCT
bracis-33646	33	54	\(a	\(a	PROPN
bracis-33646	33	55	\subseteq	\subseteq	PROPN
bracis-33646	33	56	cn(a)\	cn(a)\	NOUN
bracis-33646	33	57	)	)	PUNCT
bracis-33646	33	58	.	.	PUNCT
bracis-33646	34	1	idempotence	idempotence	NOUN
bracis-33646	34	2	:	:	PUNCT
bracis-33646	34	3	\(cn(a	\(cn(a	PROPN
bracis-33646	34	4	)	)	PUNCT
bracis-33646	34	5	=	=	SYM
bracis-33646	34	6	cn(cn(a))\	cn(cn(a))\	PROPN
bracis-33646	34	7	)	)	PUNCT
bracis-33646	34	8	.	.	PUNCT
bracis-33646	35	1	monotonicity	monotonicity	NOUN
bracis-33646	35	2	:	:	PUNCT
bracis-33646	35	3	if	if	SCONJ
bracis-33646	35	4	\(a\subseteq	\(a\subseteq	PROPN
bracis-33646	35	5	a'\	a'\	PROPN
bracis-33646	35	6	)	)	PUNCT
bracis-33646	35	7	then	then	ADV
bracis-33646	35	8	\(cn(a	\(cn(a	PROPN
bracis-33646	35	9	)	)	PUNCT
bracis-33646	35	10	\subseteq	\subseteq	PROPN
bracis-33646	35	11	cn(a')\	cn(a')\	PROPN
bracis-33646	35	12	)	)	PUNCT
bracis-33646	35	13	.	.	PUNCT
bracis-33646	36	1	given	give	VERB
bracis-33646	36	2	a	a	DET
bracis-33646	36	3	logic	logic	NOUN
bracis-33646	36	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	36	5	{	{	PUNCT
bracis-33646	36	6	l	l	NOUN
bracis-33646	36	7	}	}	PUNCT
bracis-33646	36	8	=	=	PUNCT
bracis-33646	36	9	\langle	\langle	PROPN
bracis-33646	36	10	l	l	NOUN
bracis-33646	36	11	,	,	PUNCT
bracis-33646	36	12	cn\rangle	cn\rangle	NOUN
bracis-33646	36	13	\	\	NOUN
bracis-33646	36	14	)	)	PUNCT
bracis-33646	36	15	,	,	PUNCT
bracis-33646	36	16	we	we	PRON
bracis-33646	36	17	will	will	AUX
bracis-33646	36	18	employ	employ	VERB
bracis-33646	36	19	the	the	DET
bracis-33646	36	20	notation	notation	NOUN
bracis-33646	36	21	\(th_\mathcal	\(th_\mathcal	NOUN
bracis-33646	36	22	{	{	PUNCT
bracis-33646	36	23	l}\	l}\	PROPN
bracis-33646	36	24	)	)	PUNCT
bracis-33646	36	25	to	to	PART
bracis-33646	36	26	describe	describe	VERB
bracis-33646	36	27	the	the	DET
bracis-33646	36	28	set	set	NOUN
bracis-33646	36	29	of	of	ADP
bracis-33646	36	30	all	all	DET
bracis-33646	36	31	theories	theory	NOUN
bracis-33646	36	32	of	of	ADP
bracis-33646	36	33	\(\mathcal	\(\mathcal	ADJ
bracis-33646	36	34	{	{	PUNCT
bracis-33646	36	35	l}\	l}\	PROPN
bracis-33646	36	36	)	)	PUNCT
bracis-33646	36	37	,	,	PUNCT
bracis-33646	36	38	i.e.	i.e.	X
bracis-33646	36	39	\(th_\mathcal	\(th_\mathcal	ADJ
bracis-33646	36	40	{	{	PUNCT
bracis-33646	36	41	l}=	l}=	PROPN
bracis-33646	36	42	\{a\subseteq	\{a\subseteq	PROPN
bracis-33646	36	43	l~|~	l~|~	ADJ
bracis-33646	36	44	cn(a	cn(a	NOUN
bracis-33646	36	45	)	)	PUNCT
bracis-33646	36	46	=	=	SYM
bracis-33646	36	47	a\}\	a\}\	NOUN
bracis-33646	36	48	)	)	PUNCT
bracis-33646	36	49	.	.	PUNCT
bracis-33646	37	1	furthermore	furthermore	ADV
bracis-33646	37	2	,	,	PUNCT
bracis-33646	37	3	we	we	PRON
bracis-33646	37	4	say	say	VERB
bracis-33646	37	5	a	a	DET
bracis-33646	37	6	logic	logic	NOUN
bracis-33646	37	7	is	be	AUX
bracis-33646	37	8	compact	compact	ADJ
bracis-33646	37	9	if	if	SCONJ
bracis-33646	37	10	,	,	PUNCT
bracis-33646	37	11	for	for	ADP
bracis-33646	37	12	any	any	DET
bracis-33646	37	13	\(a	\(a	NOUN
bracis-33646	37	14	\subseteq	\subseteq	PROPN
bracis-33646	37	15	l\	l\	NOUN
bracis-33646	37	16	)	)	PUNCT
bracis-33646	37	17	and	and	CCONJ
bracis-33646	37	18	\(\varphi	\(\varphi	ADJ
bracis-33646	37	19	\in	\in	PROPN
bracis-33646	37	20	l\	l\	PROPN
bracis-33646	37	21	)	)	PUNCT
bracis-33646	37	22	,	,	PUNCT
bracis-33646	37	23	it	it	PRON
bracis-33646	37	24	holds	hold	VERB
bracis-33646	37	25	that	that	SCONJ
bracis-33646	37	26	if	if	SCONJ
bracis-33646	37	27	\(\varphi	\(\varphi	ADJ
bracis-33646	37	28	\in	\in	PROPN
bracis-33646	37	29	cn(a)\	cn(a)\	NOUN
bracis-33646	37	30	)	)	PUNCT
bracis-33646	37	31	,	,	PUNCT
bracis-33646	37	32	then	then	ADV
bracis-33646	37	33	there	there	PRON
bracis-33646	37	34	is	be	VERB
bracis-33646	37	35	some	some	DET
bracis-33646	37	36	finite	finite	NOUN
bracis-33646	37	37	\(a'\subseteq	\(a'\subseteq	PROPN
bracis-33646	37	38	a\	a\	NOUN
bracis-33646	37	39	)	)	PUNCT
bracis-33646	37	40	s.t	s.t	PROPN
bracis-33646	37	41	.	.	PROPN
bracis-33646	37	42	\(\varphi	\(\varphi	PROPN
bracis-33646	37	43	\in	\in	PROPN
bracis-33646	37	44	cn(a')\	cn(a')\	NOUN
bracis-33646	37	45	)	)	PUNCT
bracis-33646	37	46	.	.	PUNCT
bracis-33646	38	1	given	give	VERB
bracis-33646	38	2	a	a	DET
bracis-33646	38	3	logic	logic	NOUN
bracis-33646	38	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	38	5	{	{	PUNCT
bracis-33646	38	6	l}\	l}\	PROPN
bracis-33646	38	7	)	)	PUNCT
bracis-33646	38	8	as	as	ADP
bracis-33646	38	9	above	above	ADV
bracis-33646	38	10	,	,	PUNCT
bracis-33646	38	11	we	we	PRON
bracis-33646	38	12	call	call	VERB
bracis-33646	38	13	a	a	DET
bracis-33646	38	14	belief	belief	NOUN
bracis-33646	38	15	change	change	NOUN
bracis-33646	38	16	operation	operation	NOUN
bracis-33646	38	17	any	any	DET
bracis-33646	38	18	function	function	NOUN
bracis-33646	38	19	\(\star	\(\star	NOUN
bracis-33646	38	20	:	:	PUNCT
bracis-33646	38	21	2^l	2^l	NUM
bracis-33646	38	22	\times	\time	NOUN
bracis-33646	38	23	l	l	NOUN
bracis-33646	38	24	\rightarrow	\rightarrow	PROPN
bracis-33646	38	25	2^l\	2^l\	NUM
bracis-33646	38	26	)	)	PUNCT
bracis-33646	38	27	,	,	PUNCT
bracis-33646	38	28	which	which	PRON
bracis-33646	38	29	maps	map	VERB
bracis-33646	38	30	pairs	pair	NOUN
bracis-33646	38	31	of	of	ADP
bracis-33646	38	32	sets	set	NOUN
bracis-33646	38	33	of	of	ADP
bracis-33646	38	34	sentences	sentence	NOUN
bracis-33646	38	35	and	and	CCONJ
bracis-33646	38	36	a	a	DET
bracis-33646	38	37	sentence	sentence	NOUN
bracis-33646	38	38	,	,	PUNCT
bracis-33646	38	39	called	call	VERB
bracis-33646	38	40	a	a	DET
bracis-33646	38	41	set	set	NOUN
bracis-33646	38	42	of	of	ADP
bracis-33646	38	43	beliefs	belief	NOUN
bracis-33646	38	44	and	and	CCONJ
bracis-33646	38	45	a	a	DET
bracis-33646	38	46	piece	piece	NOUN
bracis-33646	38	47	of	of	ADP
bracis-33646	38	48	input	input	NOUN
bracis-33646	38	49	information	information	NOUN
bracis-33646	38	50	,	,	PUNCT
bracis-33646	38	51	to	to	ADP
bracis-33646	38	52	a	a	DET
bracis-33646	38	53	set	set	NOUN
bracis-33646	38	54	of	of	ADP
bracis-33646	38	55	sentences	sentence	NOUN
bracis-33646	38	56	,	,	PUNCT
bracis-33646	38	57	the	the	DET
bracis-33646	38	58	resulting	result	VERB
bracis-33646	38	59	beliefs	belief	NOUN
bracis-33646	38	60	.	.	PUNCT
bracis-33646	39	1	agm	agm	PROPN
bracis-33646	39	2	 	 	SPACE
bracis-33646	39	3	[	[	X
bracis-33646	39	4	1	1	X
bracis-33646	39	5	]	]	PUNCT
bracis-33646	39	6	investigate	investigate	VERB
bracis-33646	39	7	three	three	NUM
bracis-33646	39	8	basic	basic	ADJ
bracis-33646	39	9	belief	belief	NOUN
bracis-33646	39	10	change	change	NOUN
bracis-33646	39	11	operations	operation	NOUN
bracis-33646	39	12	:	:	PUNCT
bracis-33646	39	13	expansions	expansion	NOUN
bracis-33646	39	14	,	,	PUNCT
bracis-33646	39	15	contractions	contraction	NOUN
bracis-33646	39	16	and	and	CCONJ
bracis-33646	39	17	revisions	revision	NOUN
bracis-33646	39	18	.	.	PUNCT
bracis-33646	40	1	belief	belief	NOUN
bracis-33646	40	2	expansion	expansion	NOUN
bracis-33646	40	3	blindly	blindly	ADV
bracis-33646	40	4	integrates	integrate	VERB
bracis-33646	40	5	a	a	DET
bracis-33646	40	6	new	new	ADJ
bracis-33646	40	7	piece	piece	NOUN
bracis-33646	40	8	of	of	ADP
bracis-33646	40	9	information	information	NOUN
bracis-33646	40	10	into	into	ADP
bracis-33646	40	11	the	the	DET
bracis-33646	40	12	agent	agent	NOUN
bracis-33646	40	13	’s	’s	PART
bracis-33646	40	14	beliefs	belief	NOUN
bracis-33646	40	15	.	.	PUNCT
bracis-33646	41	1	belief	belief	NOUN
bracis-33646	41	2	contraction	contraction	NOUN
bracis-33646	41	3	removes	remove	VERB
bracis-33646	41	4	a	a	DET
bracis-33646	41	5	currently	currently	ADV
bracis-33646	41	6	held	hold	VERB
bracis-33646	41	7	belief	belief	NOUN
bracis-33646	41	8	from	from	ADP
bracis-33646	41	9	the	the	DET
bracis-33646	41	10	agent	agent	NOUN
bracis-33646	41	11	’s	’s	PART
bracis-33646	41	12	set	set	NOUN
bracis-33646	41	13	of	of	ADP
bracis-33646	41	14	beliefs	belief	NOUN
bracis-33646	41	15	with	with	ADP
bracis-33646	41	16	minimal	minimal	ADJ
bracis-33646	41	17	alterations	alteration	NOUN
bracis-33646	41	18	.	.	PUNCT
bracis-33646	42	1	finally	finally	ADV
bracis-33646	42	2	,	,	PUNCT
bracis-33646	42	3	belief	belief	NOUN
bracis-33646	42	4	revision	revision	NOUN
bracis-33646	42	5	is	be	AUX
bracis-33646	42	6	the	the	DET
bracis-33646	42	7	operation	operation	NOUN
bracis-33646	42	8	of	of	ADP
bracis-33646	42	9	integrating	integrate	VERB
bracis-33646	42	10	new	new	ADJ
bracis-33646	42	11	information	information	NOUN
bracis-33646	42	12	into	into	ADP
bracis-33646	42	13	an	an	DET
bracis-33646	42	14	agent	agent	NOUN
bracis-33646	42	15	’s	’s	PART
bracis-33646	42	16	beliefs	belief	NOUN
bracis-33646	42	17	while	while	SCONJ
bracis-33646	42	18	maintaining	maintain	VERB
bracis-33646	42	19	consistency	consistency	NOUN
bracis-33646	42	20	.	.	PUNCT
bracis-33646	43	1	among	among	ADP
bracis-33646	43	2	these	these	DET
bracis-33646	43	3	basic	basic	ADJ
bracis-33646	43	4	operations	operation	NOUN
bracis-33646	43	5	,	,	PUNCT
bracis-33646	43	6	only	only	ADV
bracis-33646	43	7	expansion	expansion	NOUN
bracis-33646	43	8	can	can	AUX
bracis-33646	43	9	be	be	AUX
bracis-33646	43	10	univocally	univocally	ADV
bracis-33646	43	11	defined	define	VERB
bracis-33646	43	12	.	.	PUNCT
bracis-33646	44	1	the	the	DET
bracis-33646	44	2	other	other	ADJ
bracis-33646	44	3	two	two	NUM
bracis-33646	44	4	are	be	AUX
bracis-33646	44	5	characterised	characterise	VERB
bracis-33646	44	6	by	by	ADP
bracis-33646	44	7	a	a	DET
bracis-33646	44	8	set	set	NOUN
bracis-33646	44	9	of	of	ADP
bracis-33646	44	10	postulates	postulate	NOUN
bracis-33646	44	11	,	,	PUNCT
bracis-33646	44	12	which	which	PRON
bracis-33646	44	13	define	define	VERB
bracis-33646	44	14	a	a	DET
bracis-33646	44	15	class	class	NOUN
bracis-33646	44	16	of	of	ADP
bracis-33646	44	17	suitable	suitable	ADJ
bracis-33646	44	18	change	change	NOUN
bracis-33646	44	19	operators	operator	NOUN
bracis-33646	44	20	representing	represent	VERB
bracis-33646	44	21	different	different	ADJ
bracis-33646	44	22	rational	rational	ADJ
bracis-33646	44	23	ways	way	NOUN
bracis-33646	44	24	in	in	ADP
bracis-33646	44	25	which	which	PRON
bracis-33646	44	26	an	an	DET
bracis-33646	44	27	agent	agent	NOUN
bracis-33646	44	28	can	can	AUX
bracis-33646	44	29	change	change	VERB
bracis-33646	44	30	their	their	PRON
bracis-33646	44	31	beliefs	belief	NOUN
bracis-33646	44	32	.	.	PUNCT
bracis-33646	45	1	given	give	VERB
bracis-33646	45	2	a	a	DET
bracis-33646	45	3	closed	closed	ADJ
bracis-33646	45	4	set	set	NOUN
bracis-33646	45	5	of	of	ADP
bracis-33646	45	6	beliefsfootnote	beliefsfootnote	NOUN
bracis-33646	45	7	2	2	NUM
bracis-33646	45	8	,	,	PUNCT
bracis-33646	45	9	i.e.	i.e.	X
bracis-33646	45	10	\(k\subseteq	\(k\subseteq	PROPN
bracis-33646	45	11	l\	l\	PROPN
bracis-33646	45	12	)	)	PUNCT
bracis-33646	45	13	s.t	s.t	PROPN
bracis-33646	45	14	.	.	PUNCT
bracis-33646	45	15	\(k	\(k	NOUN
bracis-33646	45	16	=	=	SYM
bracis-33646	45	17	cn(k)\	cn(k)\	NOUN
bracis-33646	45	18	)	)	PUNCT
bracis-33646	45	19	,	,	PUNCT
bracis-33646	45	20	we	we	PRON
bracis-33646	45	21	say	say	VERB
bracis-33646	45	22	a	a	DET
bracis-33646	45	23	belief	belief	NOUN
bracis-33646	45	24	change	change	NOUN
bracis-33646	45	25	operation	operation	NOUN
bracis-33646	45	26	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	45	27	)	)	PUNCT
bracis-33646	45	28	is	be	AUX
bracis-33646	45	29	an	an	DET
bracis-33646	45	30	agm	agm	PROPN
bracis-33646	45	31	rational	rational	ADJ
bracis-33646	45	32	contraction	contraction	NOUN
bracis-33646	45	33	on	on	ADP
bracis-33646	45	34	k	k	PROPN
bracis-33646	45	35	if	if	SCONJ
bracis-33646	45	36	for	for	ADP
bracis-33646	45	37	any	any	DET
bracis-33646	45	38	\(\varphi	\(\varphi	ADJ
bracis-33646	45	39	,	,	PUNCT
bracis-33646	45	40	\psi	\psi	PROPN
bracis-33646	45	41	\in	\in	PROPN
bracis-33646	45	42	l\	l\	PROPN
bracis-33646	45	43	)	)	PUNCT
bracis-33646	45	44	,	,	PUNCT
bracis-33646	45	45	it	it	PRON
bracis-33646	45	46	satisfies	satisfy	VERB
bracis-33646	45	47	:	:	PUNCT
bracis-33646	45	48	(	(	PUNCT
bracis-33646	45	49	closure	closure	NOUN
bracis-33646	45	50	)	)	PUNCT
bracis-33646	45	51	\(k\dot{-}\varphi	\(k\dot{-}\varphi	PROPN
bracis-33646	45	52	=	=	SYM
bracis-33646	45	53	cn(k\dot{-}\varphi	cn(k\dot{-}\varphi	ADJ
bracis-33646	45	54	)	)	PUNCT
bracis-33646	45	55	\	\	NOUN
bracis-33646	45	56	)	)	PUNCT
bracis-33646	45	57	(	(	PUNCT
bracis-33646	45	58	success	success	NOUN
bracis-33646	45	59	)	)	PUNCT
bracis-33646	45	60	if	if	SCONJ
bracis-33646	45	61	\(\varphi	\(\varphi	ADJ
bracis-33646	45	62	\not	\not	ADV
bracis-33646	45	63	\in	\in	ADJ
bracis-33646	45	64	cn(\emptyset	cn(\emptyset	NOUN
bracis-33646	45	65	)	)	PUNCT
bracis-33646	45	66	\	\	NOUN
bracis-33646	45	67	)	)	PUNCT
bracis-33646	46	1	then	then	ADV
bracis-33646	46	2	\(\varphi	\(\varphi	X
bracis-33646	46	3	\notin	\notin	ADP
bracis-33646	46	4	k	k	PROPN
bracis-33646	46	5	\dot{-}\varphi	\dot{-}\varphi	PROPN
bracis-33646	46	6	\	\	PROPN
bracis-33646	46	7	)	)	PUNCT
bracis-33646	46	8	(	(	PUNCT
bracis-33646	46	9	inclusion	inclusion	NOUN
bracis-33646	46	10	)	)	PUNCT
bracis-33646	46	11	\(k\dot{-}\varphi	\(k\dot{-}\varphi	PROPN
bracis-33646	46	12	\subseteq	\subseteq	PROPN
bracis-33646	46	13	k\	k\	PROPN
bracis-33646	46	14	)	)	PUNCT
bracis-33646	46	15	(	(	PUNCT
bracis-33646	46	16	vacuity	vacuity	PROPN
bracis-33646	46	17	)	)	PUNCT
bracis-33646	46	18	if	if	SCONJ
bracis-33646	46	19	\(\varphi	\(\varphi	ADJ
bracis-33646	46	20	\not	\not	ADV
bracis-33646	46	21	\in	\in	PROPN
bracis-33646	46	22	k\	k\	NOUN
bracis-33646	46	23	)	)	PUNCT
bracis-33646	46	24	then	then	ADV
bracis-33646	46	25	\(k\dot{-}\varphi	\(k\dot{-}\varphi	PROPN
bracis-33646	46	26	=	=	SYM
bracis-33646	46	27	k\	k\	NOUN
bracis-33646	46	28	)	)	PUNCT
bracis-33646	46	29	(	(	PUNCT
bracis-33646	46	30	recovery	recovery	NOUN
bracis-33646	46	31	)	)	PUNCT
bracis-33646	46	32	\(k	\(k	NOUN
bracis-33646	46	33	\subseteq	\subseteq	PROPN
bracis-33646	46	34	cn(k\dot{-}\varphi	cn(k\dot{-}\varphi	VERB
bracis-33646	46	35	\cup	\cup	ADP
bracis-33646	46	36	\{\varphi	\{\varphi	NUM
bracis-33646	46	37	\})\	\})\	NOUN
bracis-33646	46	38	)	)	PUNCT
bracis-33646	46	39	(	(	PUNCT
bracis-33646	46	40	extensionality	extensionality	NOUN
bracis-33646	46	41	)	)	PUNCT
bracis-33646	46	42	if	if	SCONJ
bracis-33646	46	43	\(cn(\varphi	\(cn(\varphi	NOUN
bracis-33646	46	44	)	)	PUNCT
bracis-33646	46	45	=	=	SYM
bracis-33646	46	46	cn(\psi	cn(\psi	PROPN
bracis-33646	46	47	)	)	PUNCT
bracis-33646	46	48	\	\	PROPN
bracis-33646	46	49	)	)	PUNCT
bracis-33646	46	50	then	then	ADV
bracis-33646	46	51	\(k\dot{-}\varphi	\(k\dot{-}\varphi	VERB
bracis-33646	46	52	=	=	X
bracis-33646	46	53	k\dot{-}\psi	k\dot{-}\psi	NOUN
bracis-33646	46	54	\	\	NOUN
bracis-33646	46	55	)	)	PUNCT
bracis-33646	46	56	to	to	PART
bracis-33646	46	57	characterise	characterise	VERB
bracis-33646	46	58	their	their	PRON
bracis-33646	46	59	rational	rational	ADJ
bracis-33646	46	60	contractions	contraction	NOUN
bracis-33646	46	61	,	,	PUNCT
bracis-33646	46	62	agm	agm	PROPN
bracis-33646	46	63	propose	propose	VERB
bracis-33646	46	64	the	the	DET
bracis-33646	46	65	notion	notion	NOUN
bracis-33646	46	66	of	of	ADP
bracis-33646	46	67	partial	partial	ADJ
bracis-33646	46	68	meet	meet	NOUN
bracis-33646	46	69	belief	belief	NOUN
bracis-33646	46	70	contraction	contraction	NOUN
bracis-33646	46	71	,	,	PUNCT
bracis-33646	46	72	an	an	DET
bracis-33646	46	73	operation	operation	NOUN
bracis-33646	46	74	that	that	PRON
bracis-33646	46	75	preserves	preserve	VERB
bracis-33646	46	76	a	a	DET
bracis-33646	46	77	maximal	maximal	ADJ
bracis-33646	46	78	amount	amount	NOUN
bracis-33646	46	79	of	of	ADP
bracis-33646	46	80	“	"	PUNCT
bracis-33646	46	81	safe	safe	ADJ
bracis-33646	46	82	”	"	PUNCT
bracis-33646	46	83	information	information	NOUN
bracis-33646	46	84	from	from	ADP
bracis-33646	46	85	the	the	DET
bracis-33646	46	86	agent	agent	NOUN
bracis-33646	46	87	’s	’s	PART
bracis-33646	46	88	beliefs	belief	NOUN
bracis-33646	46	89	,	,	PUNCT
bracis-33646	46	90	i.e.	i.e.	X
bracis-33646	46	91	,	,	PUNCT
bracis-33646	46	92	information	information	NOUN
bracis-33646	46	93	that	that	PRON
bracis-33646	46	94	can	can	AUX
bracis-33646	46	95	not	not	PART
bracis-33646	46	96	be	be	AUX
bracis-33646	46	97	used	use	VERB
bracis-33646	46	98	to	to	PART
bracis-33646	46	99	derive	derive	VERB
bracis-33646	46	100	what	what	PRON
bracis-33646	46	101	the	the	DET
bracis-33646	46	102	agent	agent	NOUN
bracis-33646	46	103	has	have	AUX
bracis-33646	46	104	ceased	cease	VERB
bracis-33646	46	105	to	to	PART
bracis-33646	46	106	believe	believe	VERB
bracis-33646	46	107	.	.	PUNCT
bracis-33646	47	1	definition	definition	NOUN
bracis-33646	47	2	1	1	NUM
bracis-33646	47	3	let	let	VERB
bracis-33646	47	4	\(b\subseteq	\(b\subseteq	PROPN
bracis-33646	47	5	l\	l\	PROPN
bracis-33646	47	6	)	)	PUNCT
bracis-33646	47	7	be	be	AUX
bracis-33646	47	8	a	a	DET
bracis-33646	47	9	set	set	NOUN
bracis-33646	47	10	of	of	ADP
bracis-33646	47	11	formulas	formula	NOUN
bracis-33646	47	12	and	and	CCONJ
bracis-33646	47	13	\(\varphi	\(\varphi	ADJ
bracis-33646	47	14	\in	\in	PROPN
bracis-33646	47	15	l\	l\	PROPN
bracis-33646	47	16	)	)	PUNCT
bracis-33646	47	17	be	be	AUX
bracis-33646	47	18	a	a	DET
bracis-33646	47	19	formula	formula	NOUN
bracis-33646	47	20	of	of	ADP
bracis-33646	47	21	l	l	NOUN
bracis-33646	47	22	,	,	PUNCT
bracis-33646	47	23	the	the	DET
bracis-33646	47	24	remainder	remainder	NOUN
bracis-33646	47	25	set	set	VERB
bracis-33646	47	26	\(b\bot	\(b\bot	ADV
bracis-33646	47	27	_	_	PUNCT
bracis-33646	47	28	\mathcal	\mathcal	ADJ
bracis-33646	47	29	{	{	PUNCT
bracis-33646	47	30	l	l	NOUN
bracis-33646	47	31	}	}	PUNCT
bracis-33646	47	32	\varphi	\varphi	PROPN
bracis-33646	47	33	\	\	NOUN
bracis-33646	47	34	)	)	PUNCT
bracis-33646	47	35	is	be	AUX
bracis-33646	47	36	the	the	DET
bracis-33646	47	37	set	set	NOUN
bracis-33646	47	38	of	of	ADP
bracis-33646	47	39	sets	set	NOUN
bracis-33646	47	40	\(b'\	\(b'\	NOUN
bracis-33646	47	41	)	)	PUNCT
bracis-33646	48	1	satisfying	satisfy	VERB
bracis-33646	48	2	:	:	PUNCT
bracis-33646	48	3	\(b'\subseteq	\(b'\subseteq	NUM
bracis-33646	48	4	b\	b\	NOUN
bracis-33646	48	5	)	)	PUNCT
bracis-33646	48	6	\(\varphi	\(\varphi	ADJ
bracis-33646	48	7	\not	\not	ADV
bracis-33646	48	8	\in	\in	PROPN
bracis-33646	48	9	cn(b')\	cn(b')\	NOUN
bracis-33646	48	10	)	)	PUNCT
bracis-33646	48	11	\(b'\subset	\(b'\subset	VERB
bracis-33646	48	12	b''\subseteq	b''\subseteq	ADJ
bracis-33646	48	13	b\	b\	NOUN
bracis-33646	48	14	)	)	PUNCT
bracis-33646	48	15	implies	imply	VERB
bracis-33646	48	16	\(\varphi	\(\varphi	ADJ
bracis-33646	48	17	\in	\in	ADJ
bracis-33646	48	18	cn(b'')\	cn(b'')\	NOUN
bracis-33646	48	19	)	)	PUNCT
bracis-33646	48	20	.	.	PUNCT
bracis-33646	49	1	a	a	DET
bracis-33646	49	2	partial	partial	ADJ
bracis-33646	49	3	meet	meet	NOUN
bracis-33646	49	4	contraction	contraction	NOUN
bracis-33646	49	5	\(\dot{-}\	\(\dot{-}\	PROPN
bracis-33646	49	6	)	)	PUNCT
bracis-33646	49	7	is	be	AUX
bracis-33646	49	8	an	an	DET
bracis-33646	49	9	operation	operation	NOUN
bracis-33646	49	10	for	for	ADP
bracis-33646	49	11	which	which	PRON
bracis-33646	49	12	there	there	PRON
bracis-33646	49	13	is	be	VERB
bracis-33646	49	14	a	a	DET
bracis-33646	49	15	selection	selection	NOUN
bracis-33646	49	16	function	function	NOUN
bracis-33646	49	17	\(\gamma	\(\gamma	PUNCT
bracis-33646	49	18	\	\	NOUN
bracis-33646	49	19	)	)	PUNCT
bracis-33646	49	20	,	,	PUNCT
bracis-33646	49	21	that	that	PRON
bracis-33646	49	22	characterises	characterise	VERB
bracis-33646	49	23	this	this	DET
bracis-33646	49	24	operation	operation	NOUN
bracis-33646	49	25	.	.	PUNCT
bracis-33646	50	1	by	by	ADP
bracis-33646	50	2	selection	selection	NOUN
bracis-33646	50	3	function	function	NOUN
bracis-33646	50	4	,	,	PUNCT
bracis-33646	50	5	we	we	PRON
bracis-33646	50	6	mean	mean	VERB
bracis-33646	50	7	that	that	SCONJ
bracis-33646	50	8	the	the	DET
bracis-33646	50	9	function	function	NOUN
bracis-33646	50	10	\(\gamma	\(\gamma	X
bracis-33646	50	11	\	\	NOUN
bracis-33646	50	12	)	)	PUNCT
bracis-33646	50	13	satisfies	satisfie	NOUN
bracis-33646	50	14	(	(	PUNCT
bracis-33646	50	15	i	i	NOUN
bracis-33646	50	16	)	)	PUNCT
bracis-33646	50	17	\(\emptyset	\(\emptyset	NOUN
bracis-33646	51	1	\ne	\ne	PROPN
bracis-33646	51	2	\gamma	\gamma	PROPN
bracis-33646	51	3	(	(	PUNCT
bracis-33646	51	4	b\bot	b\bot	PROPN
bracis-33646	51	5	_	_	PUNCT
bracis-33646	51	6	\mathcal	\mathcal	ADJ
bracis-33646	51	7	{	{	PUNCT
bracis-33646	51	8	l	l	NOUN
bracis-33646	51	9	}	}	PUNCT
bracis-33646	51	10	\varphi	\varphi	PROPN
bracis-33646	51	11	)	)	PUNCT
bracis-33646	51	12	\subseteq	\subseteq	PROPN
bracis-33646	51	13	b\bot	b\bot	PROPN
bracis-33646	52	1	_	_	PUNCT
bracis-33646	52	2	\mathcal	\mathcal	ADJ
bracis-33646	52	3	{	{	PUNCT
bracis-33646	52	4	l	l	NOUN
bracis-33646	52	5	}	}	PUNCT
bracis-33646	52	6	\varphi	\varphi	PROPN
bracis-33646	52	7	\	\	NOUN
bracis-33646	52	8	)	)	PUNCT
bracis-33646	52	9	if	if	SCONJ
bracis-33646	52	10	\(b\bot	\(b\bot	ADV
bracis-33646	52	11	_	_	PUNCT
bracis-33646	52	12	\mathcal	\mathcal	ADJ
bracis-33646	52	13	{	{	PUNCT
bracis-33646	52	14	l	l	NOUN
bracis-33646	52	15	}	}	PUNCT
bracis-33646	52	16	\varphi	\varphi	PROPN
bracis-33646	52	17	\ne	\ne	PROPN
bracis-33646	52	18	\emptyset	\emptyset	VERB
bracis-33646	52	19	\	\	NOUN
bracis-33646	52	20	)	)	PUNCT
bracis-33646	52	21	and	and	CCONJ
bracis-33646	52	22	(	(	PUNCT
bracis-33646	52	23	ii	ii	NOUN
bracis-33646	52	24	)	)	PUNCT
bracis-33646	52	25	\(\gamma	\(\gamma	X
bracis-33646	53	1	(	(	PUNCT
bracis-33646	53	2	b\bot	b\bot	NOUN
bracis-33646	53	3	_	_	PUNCT
bracis-33646	53	4	\mathcal	\mathcal	ADJ
bracis-33646	53	5	{	{	PUNCT
bracis-33646	53	6	l	l	NOUN
bracis-33646	53	7	}	}	PUNCT
bracis-33646	53	8	\varphi	\varphi	PROPN
bracis-33646	53	9	)	)	PUNCT
bracis-33646	53	10	=	=	SYM
bracis-33646	53	11	\{b\}\	\{b\}\	NOUN
bracis-33646	53	12	)	)	PUNCT
bracis-33646	53	13	otherwise	otherwise	ADV
bracis-33646	53	14	.	.	PUNCT
bracis-33646	54	1	definition	definition	NOUN
bracis-33646	54	2	2	2	NUM
bracis-33646	54	3	we	we	PRON
bracis-33646	54	4	say	say	VERB
bracis-33646	54	5	a	a	DET
bracis-33646	54	6	belief	belief	NOUN
bracis-33646	54	7	base	base	NOUN
bracis-33646	54	8	change	change	NOUN
bracis-33646	54	9	operator	operator	NOUN
bracis-33646	54	10	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	54	11	)	)	PUNCT
bracis-33646	54	12	is	be	AUX
bracis-33646	54	13	a	a	DET
bracis-33646	54	14	partial	partial	ADJ
bracis-33646	54	15	meet	meet	NOUN
bracis-33646	54	16	contraction	contraction	NOUN
bracis-33646	54	17	on	on	ADP
bracis-33646	54	18	a	a	DET
bracis-33646	54	19	set	set	ADJ
bracis-33646	54	20	\(b	\(b	NOUN
bracis-33646	54	21	\subseteq	\subseteq	PROPN
bracis-33646	54	22	l\	l\	NOUN
bracis-33646	54	23	)	)	PUNCT
bracis-33646	54	24	if	if	SCONJ
bracis-33646	54	25	there	there	PRON
bracis-33646	54	26	is	be	VERB
bracis-33646	54	27	a	a	DET
bracis-33646	54	28	selection	selection	NOUN
bracis-33646	54	29	function	function	NOUN
bracis-33646	54	30	\(\gamma	\(\gamma	PUNCT
bracis-33646	54	31	\	\	NOUN
bracis-33646	54	32	)	)	PUNCT
bracis-33646	54	33	,	,	PUNCT
bracis-33646	54	34	s.t	s.t	PROPN
bracis-33646	54	35	.	.	PROPN
bracis-33646	54	36	for	for	ADP
bracis-33646	54	37	any	any	DET
bracis-33646	54	38	\(\varphi	\(\varphi	ADJ
bracis-33646	54	39	\	\	ADJ
bracis-33646	54	40	)	)	PUNCT
bracis-33646	54	41	$	$	SYM
bracis-33646	54	42	$	$	SYM
bracis-33646	54	43	b\dot{-}\varphi	b\dot{-}\varphi	ADV
bracis-33646	55	1	=	=	SYM
bracis-33646	55	2	\bigcap	\bigcap	ADP
bracis-33646	55	3	\gamma	\gamma	PROPN
bracis-33646	55	4	(	(	PUNCT
bracis-33646	55	5	b\bot	b\bot	NOUN
bracis-33646	55	6	_	_	PUNCT
bracis-33646	55	7	\mathcal	\mathcal	ADJ
bracis-33646	55	8	{	{	PUNCT
bracis-33646	55	9	l	l	NOUN
bracis-33646	55	10	}	}	PUNCT
bracis-33646	55	11	\varphi	\varphi	PROPN
bracis-33646	55	12	)	)	PUNCT
bracis-33646	55	13	.$$	.$$	PUNCT
bracis-33646	56	1	the	the	DET
bracis-33646	56	2	authors	author	NOUN
bracis-33646	56	3	show	show	VERB
bracis-33646	56	4	that	that	SCONJ
bracis-33646	56	5	for	for	ADP
bracis-33646	56	6	any	any	DET
bracis-33646	56	7	compact	compact	ADJ
bracis-33646	56	8	logic	logic	NOUN
bracis-33646	56	9	closed	close	VERB
bracis-33646	56	10	by	by	ADP
bracis-33646	56	11	classical	classical	ADJ
bracis-33646	56	12	disjunction	disjunction	NOUN
bracis-33646	56	13	and	and	CCONJ
bracis-33646	56	14	negation	negation	NOUN
bracis-33646	56	15	,	,	PUNCT
bracis-33646	56	16	a	a	DET
bracis-33646	56	17	rational	rational	ADJ
bracis-33646	56	18	contraction	contraction	NOUN
bracis-33646	56	19	on	on	ADP
bracis-33646	56	20	a	a	DET
bracis-33646	56	21	closed	closed	ADJ
bracis-33646	56	22	set	set	NOUN
bracis-33646	56	23	k	k	PROPN
bracis-33646	56	24	is	be	AUX
bracis-33646	56	25	a	a	DET
bracis-33646	56	26	partial	partial	ADJ
bracis-33646	56	27	meet	meet	NOUN
bracis-33646	56	28	contraction	contraction	NOUN
bracis-33646	56	29	on	on	ADP
bracis-33646	56	30	k	k	PROPN
bracis-33646	56	31	and	and	CCONJ
bracis-33646	56	32	vice	vice	ADV
bracis-33646	56	33	versa	versa	ADV
bracis-33646	56	34	.	.	PUNCT
bracis-33646	57	1	this	this	DET
bracis-33646	57	2	equivalence	equivalence	NOUN
bracis-33646	57	3	,	,	PUNCT
bracis-33646	57	4	however	however	ADV
bracis-33646	57	5	,	,	PUNCT
bracis-33646	57	6	does	do	AUX
bracis-33646	57	7	not	not	PART
bracis-33646	57	8	hold	hold	VERB
bracis-33646	57	9	in	in	ADP
bracis-33646	57	10	general	general	ADJ
bracis-33646	57	11	for	for	ADP
bracis-33646	57	12	any	any	DET
bracis-33646	57	13	abstract	abstract	ADJ
bracis-33646	57	14	logic	logic	NOUN
bracis-33646	57	15	[	[	X
bracis-33646	57	16	17	17	NUM
bracis-33646	57	17	]	]	PUNCT
bracis-33646	57	18	.	.	PUNCT
bracis-33646	58	1	on	on	ADP
bracis-33646	58	2	the	the	DET
bracis-33646	58	3	other	other	ADJ
bracis-33646	58	4	hand	hand	NOUN
bracis-33646	58	5	,	,	PUNCT
bracis-33646	58	6	flouris	flouris	PROPN
bracis-33646	58	7	 	 	SPACE
bracis-33646	59	1	[	[	X
bracis-33646	59	2	5	5	NUM
bracis-33646	59	3	]	]	PUNCT
bracis-33646	59	4	studied	study	VERB
bracis-33646	59	5	the	the	DET
bracis-33646	59	6	definability	definability	NOUN
bracis-33646	59	7	of	of	ADP
bracis-33646	59	8	rational	rational	ADJ
bracis-33646	59	9	contraction	contraction	NOUN
bracis-33646	59	10	operations	operation	NOUN
bracis-33646	59	11	,	,	PUNCT
bracis-33646	59	12	i.e.	i.e.	X
bracis-33646	59	13	operations	operation	NOUN
bracis-33646	59	14	satisfying	satisfy	VERB
bracis-33646	59	15	the	the	DET
bracis-33646	59	16	original	original	ADJ
bracis-33646	59	17	agm	agm	PROPN
bracis-33646	59	18	postulates	postulate	NOUN
bracis-33646	59	19	,	,	PUNCT
bracis-33646	59	20	in	in	ADP
bracis-33646	59	21	tarskian	tarskian	NOUN
bracis-33646	59	22	logics	logic	NOUN
bracis-33646	59	23	,	,	PUNCT
bracis-33646	59	24	obtaining	obtain	VERB
bracis-33646	59	25	sufficient	sufficient	ADJ
bracis-33646	59	26	and	and	CCONJ
bracis-33646	59	27	necessary	necessary	ADJ
bracis-33646	59	28	conditions	condition	NOUN
bracis-33646	59	29	for	for	ADP
bracis-33646	59	30	such	such	ADJ
bracis-33646	59	31	definability	definability	NOUN
bracis-33646	59	32	.	.	PUNCT
bracis-33646	60	1	similarly	similarly	ADV
bracis-33646	60	2	,	,	PUNCT
bracis-33646	60	3	hansson	hansson	PROPN
bracis-33646	60	4	and	and	CCONJ
bracis-33646	60	5	wassermann	wassermann	PROPN
bracis-33646	60	6	 	 	SPACE
bracis-33646	60	7	[	[	X
bracis-33646	60	8	9	9	NUM
bracis-33646	60	9	]	]	PUNCT
bracis-33646	60	10	showed	show	VERB
bracis-33646	60	11	that	that	SCONJ
bracis-33646	60	12	partial	partial	ADJ
bracis-33646	60	13	meet	meet	NOUN
bracis-33646	60	14	contractions	contraction	NOUN
bracis-33646	60	15	are	be	AUX
bracis-33646	60	16	definable	definable	ADJ
bracis-33646	60	17	in	in	ADP
bracis-33646	60	18	any	any	DET
bracis-33646	60	19	monotonic	monotonic	ADJ
bracis-33646	60	20	and	and	CCONJ
bracis-33646	60	21	compact	compact	ADJ
bracis-33646	60	22	(	(	PUNCT
bracis-33646	60	23	not	not	PART
bracis-33646	60	24	necessarily	necessarily	ADV
bracis-33646	60	25	taskian	taskian	ADJ
bracis-33646	60	26	)	)	PUNCT
bracis-33646	60	27	logic	logic	NOUN
bracis-33646	60	28	.	.	PUNCT
bracis-33646	61	1	in	in	ADP
bracis-33646	61	2	this	this	DET
bracis-33646	61	3	work	work	NOUN
bracis-33646	61	4	,	,	PUNCT
bracis-33646	61	5	we	we	PRON
bracis-33646	61	6	will	will	AUX
bracis-33646	61	7	focus	focus	VERB
bracis-33646	61	8	on	on	ADP
bracis-33646	61	9	agm	agm	PROPN
bracis-33646	61	10	rational	rational	ADJ
bracis-33646	61	11	contractions	contraction	NOUN
bracis-33646	61	12	;	;	PUNCT
bracis-33646	61	13	as	as	ADP
bracis-33646	61	14	such	such	ADJ
bracis-33646	61	15	,	,	PUNCT
bracis-33646	61	16	in	in	ADP
bracis-33646	61	17	the	the	DET
bracis-33646	61	18	following	following	NOUN
bracis-33646	61	19	,	,	PUNCT
bracis-33646	61	20	we	we	PRON
bracis-33646	61	21	will	will	AUX
bracis-33646	61	22	discuss	discuss	VERB
bracis-33646	61	23	only	only	ADV
bracis-33646	61	24	flouris	flouris	ADJ
bracis-33646	61	25	’	'	PUNCT
bracis-33646	61	26	characterisation	characterisation	NOUN
bracis-33646	61	27	.	.	PUNCT
bracis-33646	62	1	definition	definition	NOUN
bracis-33646	62	2	3	3	NUM
bracis-33646	62	3	let	let	VERB
bracis-33646	62	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	62	5	{	{	PUNCT
bracis-33646	62	6	l}=\langle	l}=\langle	ADJ
bracis-33646	62	7	l	l	NOUN
bracis-33646	62	8	,	,	PUNCT
bracis-33646	62	9	cn\rangle	cn\rangle	NOUN
bracis-33646	62	10	\	\	NOUN
bracis-33646	62	11	)	)	PUNCT
bracis-33646	62	12	be	be	AUX
bracis-33646	62	13	a	a	DET
bracis-33646	62	14	logic	logic	NOUN
bracis-33646	62	15	,	,	PUNCT
bracis-33646	62	16	a	a	DET
bracis-33646	62	17	set	set	ADJ
bracis-33646	62	18	\(b\subseteq	\(b\subseteq	NOUN
bracis-33646	62	19	l\	l\	PROPN
bracis-33646	62	20	)	)	PUNCT
bracis-33646	62	21	is	be	AUX
bracis-33646	62	22	said	say	VERB
bracis-33646	62	23	to	to	PART
bracis-33646	62	24	be	be	AUX
bracis-33646	62	25	decomposable	decomposable	ADJ
bracis-33646	62	26	in	in	ADP
bracis-33646	62	27	\(\mathcal	\(\mathcal	ADJ
bracis-33646	62	28	{	{	PUNCT
bracis-33646	62	29	l}\	l}\	PROPN
bracis-33646	62	30	)	)	PUNCT
bracis-33646	62	31	,	,	PUNCT
bracis-33646	62	32	if	if	SCONJ
bracis-33646	62	33	for	for	ADP
bracis-33646	62	34	any	any	DET
bracis-33646	62	35	\(\varphi	\(\varphi	ADJ
bracis-33646	62	36	\in	\in	ADJ
bracis-33646	62	37	l\	l\	PROPN
bracis-33646	62	38	)	)	PUNCT
bracis-33646	62	39	,	,	PUNCT
bracis-33646	62	40	with	with	ADP
bracis-33646	62	41	\(cn(\emptyset	\(cn(\emptyset	NOUN
bracis-33646	62	42	)	)	PUNCT
bracis-33646	63	1	\subset	\subset	ADP
bracis-33646	63	2	cn(\varphi	cn(\varphi	PROPN
bracis-33646	63	3	)	)	PUNCT
bracis-33646	63	4	\subseteq	\subseteq	PROPN
bracis-33646	63	5	cn(b)\	cn(b)\	NUM
bracis-33646	63	6	)	)	PUNCT
bracis-33646	63	7	,	,	PUNCT
bracis-33646	63	8	the	the	DET
bracis-33646	63	9	set	set	NOUN
bracis-33646	63	10	$	$	SYM
bracis-33646	63	11	$	$	SYM
bracis-33646	63	12	\varphi	\varphi	PROPN
bracis-33646	63	13	^-(b	^-(b	NUM
bracis-33646	63	14	)	)	PUNCT
bracis-33646	63	15	=	=	PUNCT
bracis-33646	63	16	\{b	\{b	PROPN
bracis-33646	63	17	'	'	PART
bracis-33646	63	18	\subseteq	\subseteq	PROPN
bracis-33646	63	19	b~|	b~|	PROPN
bracis-33646	63	20	\varphi	\varphi	PROPN
bracis-33646	63	21	\not	\not	ADV
bracis-33646	63	22	\in	\in	VERB
bracis-33646	63	23	cn(b	cn(b	NOUN
bracis-33646	63	24	'	'	PART
bracis-33646	63	25	)	)	PUNCT
bracis-33646	63	26	~\text	~\text	NOUN
bracis-33646	63	27	{	{	PUNCT
bracis-33646	63	28	and	and	CCONJ
bracis-33646	63	29	}	}	PUNCT
bracis-33646	63	30	~	~	PUNCT
bracis-33646	63	31	cn(b)=cn(b'\cup	cn(b)=cn(b'\cup	VERB
bracis-33646	63	32	\{\varphi	\{\varphi	ADJ
bracis-33646	63	33	\})\}$$	\})\}$$	PROPN
bracis-33646	63	34	is	be	AUX
bracis-33646	63	35	not	not	PART
bracis-33646	63	36	empty	empty	ADJ
bracis-33646	63	37	.	.	PUNCT
bracis-33646	64	1	a	a	DET
bracis-33646	64	2	logic	logic	NOUN
bracis-33646	64	3	is	be	AUX
bracis-33646	64	4	said	say	VERB
bracis-33646	64	5	to	to	PART
bracis-33646	64	6	be	be	AUX
bracis-33646	64	7	decomposable	decomposable	ADJ
bracis-33646	64	8	if	if	SCONJ
bracis-33646	64	9	every	every	DET
bracis-33646	64	10	\(b\subseteq	\(b\subseteq	ADJ
bracis-33646	64	11	l\	l\	NOUN
bracis-33646	64	12	)	)	PUNCT
bracis-33646	64	13	is	be	AUX
bracis-33646	64	14	decomposable	decomposable	ADJ
bracis-33646	64	15	.	.	PUNCT
bracis-33646	65	1	flouris	flouris	PROPN
bracis-33646	65	2	 	 	SPACE
bracis-33646	66	1	[	[	X
bracis-33646	66	2	5	5	NUM
bracis-33646	66	3	]	]	PUNCT
bracis-33646	66	4	show	show	VERB
bracis-33646	66	5	that	that	SCONJ
bracis-33646	66	6	decomposability	decomposability	NOUN
bracis-33646	66	7	is	be	AUX
bracis-33646	66	8	a	a	DET
bracis-33646	66	9	necessary	necessary	ADJ
bracis-33646	66	10	and	and	CCONJ
bracis-33646	66	11	sufficient	sufficient	ADJ
bracis-33646	66	12	condition	condition	NOUN
bracis-33646	66	13	for	for	ADP
bracis-33646	66	14	the	the	DET
bracis-33646	66	15	definability	definability	NOUN
bracis-33646	66	16	of	of	ADP
bracis-33646	66	17	agm	agm	PROPN
bracis-33646	66	18	contraction	contraction	NOUN
bracis-33646	66	19	operations	operation	NOUN
bracis-33646	66	20	.	.	PUNCT
bracis-33646	67	1	proposition	proposition	NOUN
bracis-33646	67	2	1	1	NUM
bracis-33646	67	3	(	(	PUNCT
bracis-33646	67	4	adapted	adapt	VERB
bracis-33646	67	5	from	from	ADP
bracis-33646	67	6	[	[	X
bracis-33646	67	7	5	5	NUM
bracis-33646	67	8	]	]	PUNCT
bracis-33646	67	9	)	)	PUNCT
bracis-33646	67	10	.	.	PUNCT
bracis-33646	68	1	let	let	VERB
bracis-33646	68	2	\(\mathcal	\(\mathcal	ADJ
bracis-33646	68	3	{	{	PUNCT
bracis-33646	68	4	l}=\langle	l}=\langle	ADJ
bracis-33646	68	5	l	l	NOUN
bracis-33646	68	6	,	,	PUNCT
bracis-33646	68	7	cn\rangle	cn\rangle	NOUN
bracis-33646	68	8	\	\	NOUN
bracis-33646	68	9	)	)	PUNCT
bracis-33646	68	10	be	be	AUX
bracis-33646	68	11	a	a	DET
bracis-33646	68	12	logic	logic	NOUN
bracis-33646	68	13	,	,	PUNCT
bracis-33646	68	14	\(k\subseteq	\(k\subseteq	PROPN
bracis-33646	68	15	l\	l\	PROPN
bracis-33646	68	16	)	)	PUNCT
bracis-33646	68	17	be	be	AUX
bracis-33646	68	18	a	a	DET
bracis-33646	68	19	closed	closed	ADJ
bracis-33646	68	20	set	set	NOUN
bracis-33646	68	21	of	of	ADP
bracis-33646	68	22	formulas	formula	NOUN
bracis-33646	68	23	,	,	PUNCT
bracis-33646	68	24	which	which	PRON
bracis-33646	68	25	is	be	AUX
bracis-33646	68	26	decomposable	decomposable	ADJ
bracis-33646	68	27	in	in	ADP
bracis-33646	68	28	\(\mathcal	\(\mathcal	ADJ
bracis-33646	68	29	{	{	PUNCT
bracis-33646	68	30	l}\	l}\	PROPN
bracis-33646	68	31	)	)	PUNCT
bracis-33646	68	32	,	,	PUNCT
bracis-33646	68	33	and	and	CCONJ
bracis-33646	68	34	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	68	35	)	)	PUNCT
bracis-33646	68	36	be	be	VERB
bracis-33646	68	37	a	a	DET
bracis-33646	68	38	belief	belief	NOUN
bracis-33646	68	39	change	change	NOUN
bracis-33646	68	40	operation	operation	NOUN
bracis-33646	68	41	,	,	PUNCT
bracis-33646	68	42	then	then	ADV
bracis-33646	68	43	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	68	44	)	)	PUNCT
bracis-33646	68	45	is	be	AUX
bracis-33646	68	46	a	a	DET
bracis-33646	68	47	rational	rational	ADJ
bracis-33646	68	48	contraction	contraction	NOUN
bracis-33646	68	49	on	on	ADP
bracis-33646	68	50	k	k	PROPN
bracis-33646	68	51	iff	iff	PROPN
bracis-33646	68	52	for	for	ADP
bracis-33646	68	53	any	any	DET
bracis-33646	68	54	\(\varphi	\(\varphi	ADJ
bracis-33646	68	55	\in	\in	NOUN
bracis-33646	68	56	l\	l\	PROPN
bracis-33646	68	57	)	)	PUNCT
bracis-33646	68	58	it	it	PRON
bracis-33646	68	59	holds	hold	VERB
bracis-33646	68	60	that	that	SCONJ
bracis-33646	68	61	(	(	PUNCT
bracis-33646	68	62	i	i	NOUN
bracis-33646	68	63	)	)	PUNCT
bracis-33646	68	64	\(k\dot{-}\varphi	\(k\dot{-}\varphi	NOUN
bracis-33646	68	65	=	=	SYM
bracis-33646	68	66	cn(k')\	cn(k')\	NOUN
bracis-33646	68	67	)	)	PUNCT
bracis-33646	68	68	for	for	ADP
bracis-33646	68	69	some	some	DET
bracis-33646	68	70	\(k	\(k	NOUN
bracis-33646	68	71	'	'	PART
bracis-33646	68	72	\in	\in	PROPN
bracis-33646	68	73	\varphi	\varphi	PROPN
bracis-33646	68	74	^-(k)\	^-(k)\	NUM
bracis-33646	68	75	)	)	PUNCT
bracis-33646	68	76	,	,	PUNCT
bracis-33646	68	77	if	if	SCONJ
bracis-33646	68	78	\(cn(\emptyset	\(cn(\emptyset	VERB
bracis-33646	68	79	)	)	PUNCT
bracis-33646	69	1	\subset	\subset	ADP
bracis-33646	69	2	cn(\varphi	cn(\varphi	PROPN
bracis-33646	69	3	)	)	PUNCT
bracis-33646	69	4	\subseteq	\subseteq	PROPN
bracis-33646	69	5	cn(k)\	cn(k)\	NOUN
bracis-33646	69	6	)	)	PUNCT
bracis-33646	69	7	,	,	PUNCT
bracis-33646	69	8	and	and	CCONJ
bracis-33646	69	9	(	(	PUNCT
bracis-33646	69	10	ii	ii	NOUN
bracis-33646	69	11	)	)	PUNCT
bracis-33646	69	12	\(k\dot{-}\varphi	\(k\dot{-}\varphi	PROPN
bracis-33646	69	13	=	=	SYM
bracis-33646	69	14	k\	k\	NOUN
bracis-33646	69	15	)	)	PUNCT
bracis-33646	69	16	,	,	PUNCT
bracis-33646	69	17	otherwise	otherwise	ADV
bracis-33646	69	18	.	.	PUNCT
bracis-33646	70	1	our	our	PRON
bracis-33646	70	2	aim	aim	NOUN
bracis-33646	70	3	in	in	ADP
bracis-33646	70	4	this	this	DET
bracis-33646	70	5	work	work	NOUN
bracis-33646	70	6	is	be	AUX
bracis-33646	70	7	to	to	PART
bracis-33646	70	8	study	study	VERB
bracis-33646	70	9	a	a	DET
bracis-33646	70	10	general	general	ADJ
bracis-33646	70	11	notion	notion	NOUN
bracis-33646	70	12	of	of	ADP
bracis-33646	70	13	belief	belief	NOUN
bracis-33646	70	14	change	change	NOUN
bracis-33646	70	15	that	that	PRON
bracis-33646	70	16	subsumes	subsume	VERB
bracis-33646	70	17	different	different	ADJ
bracis-33646	70	18	notions	notion	NOUN
bracis-33646	70	19	,	,	PUNCT
bracis-33646	70	20	such	such	ADJ
bracis-33646	70	21	as	as	ADP
bracis-33646	70	22	partial	partial	ADJ
bracis-33646	70	23	meet	meet	NOUN
bracis-33646	70	24	and	and	CCONJ
bracis-33646	70	25	rational	rational	ADJ
bracis-33646	70	26	contraction	contraction	NOUN
bracis-33646	70	27	,	,	PUNCT
bracis-33646	70	28	in	in	ADP
bracis-33646	70	29	a	a	DET
bracis-33646	70	30	single	single	ADJ
bracis-33646	70	31	semantic	semantic	ADJ
bracis-33646	70	32	framework	framework	NOUN
bracis-33646	70	33	and	and	CCONJ
bracis-33646	70	34	characterise	characterise	VERB
bracis-33646	70	35	them	they	PRON
bracis-33646	70	36	.	.	PUNCT
bracis-33646	71	1	here	here	ADV
bracis-33646	71	2	,	,	PUNCT
bracis-33646	71	3	we	we	PRON
bracis-33646	71	4	will	will	AUX
bracis-33646	71	5	focus	focus	VERB
bracis-33646	71	6	on	on	ADP
bracis-33646	71	7	characterising	characterise	VERB
bracis-33646	71	8	rational	rational	ADJ
bracis-33646	71	9	contractions	contraction	NOUN
bracis-33646	71	10	and	and	CCONJ
bracis-33646	71	11	using	use	VERB
bracis-33646	71	12	our	our	PRON
bracis-33646	71	13	framework	framework	NOUN
bracis-33646	71	14	to	to	PART
bracis-33646	71	15	study	study	VERB
bracis-33646	71	16	how	how	SCONJ
bracis-33646	71	17	the	the	DET
bracis-33646	71	18	topological	topological	ADJ
bracis-33646	71	19	properties	property	NOUN
bracis-33646	71	20	of	of	ADP
bracis-33646	71	21	the	the	DET
bracis-33646	71	22	interpretation	interpretation	NOUN
bracis-33646	71	23	space	space	NOUN
bracis-33646	71	24	of	of	ADP
bracis-33646	71	25	the	the	DET
bracis-33646	71	26	logic	logic	NOUN
bracis-33646	71	27	allow	allow	VERB
bracis-33646	71	28	the	the	DET
bracis-33646	71	29	construction	construction	NOUN
bracis-33646	71	30	of	of	ADP
bracis-33646	71	31	rational	rational	ADJ
bracis-33646	71	32	contractions	contraction	NOUN
bracis-33646	71	33	.	.	PUNCT
bracis-33646	72	1	in	in	ADP
bracis-33646	72	2	doing	do	VERB
bracis-33646	72	3	so	so	ADV
bracis-33646	72	4	,	,	PUNCT
bracis-33646	72	5	we	we	PRON
bracis-33646	72	6	generalise	generalise	VERB
bracis-33646	72	7	ribeiro	ribeiro	PROPN
bracis-33646	72	8	et	et	PROPN
bracis-33646	72	9	al	al	PROPN
bracis-33646	72	10	.	.	PROPN
bracis-33646	72	11	’s	’s	PART
bracis-33646	72	12	results	result	NOUN
bracis-33646	72	13	on	on	ADP
bracis-33646	72	14	the	the	DET
bracis-33646	72	15	characterisation	characterisation	NOUN
bracis-33646	72	16	of	of	ADP
bracis-33646	72	17	rational	rational	ADJ
bracis-33646	72	18	contractions	contraction	NOUN
bracis-33646	72	19	for	for	ADP
bracis-33646	72	20	non	non	ADJ
bracis-33646	72	21	-	-	ADJ
bracis-33646	72	22	compact	compact	ADJ
bracis-33646	72	23	logics	logic	NOUN
bracis-33646	72	24	.	.	PUNCT
bracis-33646	73	1	3	3	NUM
bracis-33646	73	2	logics	logic	NOUN
bracis-33646	73	3	,	,	PUNCT
bracis-33646	73	4	abstract	abstract	ADJ
bracis-33646	73	5	model	model	NOUN
bracis-33646	73	6	theories	theory	NOUN
bracis-33646	73	7	,	,	PUNCT
bracis-33646	73	8	and	and	CCONJ
bracis-33646	73	9	 	 	SPACE
bracis-33646	73	10	topological	topological	ADJ
bracis-33646	73	11	spaces	space	NOUN
bracis-33646	73	12	the	the	DET
bracis-33646	73	13	deep	deep	ADJ
bracis-33646	73	14	connection	connection	NOUN
bracis-33646	73	15	between	between	ADP
bracis-33646	73	16	logic	logic	NOUN
bracis-33646	73	17	,	,	PUNCT
bracis-33646	73	18	algebra	algebra	NOUN
bracis-33646	73	19	,	,	PUNCT
bracis-33646	73	20	and	and	CCONJ
bracis-33646	73	21	topology	topology	NOUN
bracis-33646	73	22	is	be	AUX
bracis-33646	73	23	well	well	ADV
bracis-33646	73	24	-	-	PUNCT
bracis-33646	73	25	known	know	VERB
bracis-33646	73	26	since	since	ADV
bracis-33646	73	27	,	,	PUNCT
bracis-33646	73	28	at	at	ADP
bracis-33646	73	29	least	least	ADJ
bracis-33646	73	30	,	,	PUNCT
bracis-33646	73	31	the	the	DET
bracis-33646	73	32	works	work	NOUN
bracis-33646	73	33	of	of	ADP
bracis-33646	73	34	stone	stone	NOUN
bracis-33646	73	35	 	 	SPACE
bracis-33646	74	1	[	[	X
bracis-33646	74	2	20	20	NUM
bracis-33646	74	3	]	]	PUNCT
bracis-33646	74	4	.	.	PUNCT
bracis-33646	75	1	this	this	DET
bracis-33646	75	2	connection	connection	NOUN
bracis-33646	75	3	has	have	AUX
bracis-33646	75	4	given	give	VERB
bracis-33646	75	5	rise	rise	NOUN
bracis-33646	75	6	to	to	ADP
bracis-33646	75	7	fruitful	fruitful	ADJ
bracis-33646	75	8	research	research	NOUN
bracis-33646	75	9	in	in	ADP
bracis-33646	75	10	areas	area	NOUN
bracis-33646	75	11	such	such	ADJ
bracis-33646	75	12	as	as	ADP
bracis-33646	75	13	algebraic	algebraic	ADJ
bracis-33646	75	14	logic	logic	NOUN
bracis-33646	75	15	,	,	PUNCT
bracis-33646	75	16	abstract	abstract	ADJ
bracis-33646	75	17	model	model	NOUN
bracis-33646	75	18	theory	theory	NOUN
bracis-33646	75	19	,	,	PUNCT
bracis-33646	75	20	among	among	ADP
bracis-33646	75	21	others	other	NOUN
bracis-33646	75	22	.	.	PUNCT
bracis-33646	76	1	here	here	ADV
bracis-33646	76	2	,	,	PUNCT
bracis-33646	76	3	we	we	PRON
bracis-33646	76	4	will	will	AUX
bracis-33646	76	5	briefly	briefly	ADV
bracis-33646	76	6	explore	explore	VERB
bracis-33646	76	7	some	some	DET
bracis-33646	76	8	connections	connection	NOUN
bracis-33646	76	9	between	between	ADP
bracis-33646	76	10	logic	logic	NOUN
bracis-33646	76	11	and	and	CCONJ
bracis-33646	76	12	topology	topology	NOUN
bracis-33646	76	13	by	by	ADP
bracis-33646	76	14	means	mean	NOUN
bracis-33646	76	15	of	of	ADP
bracis-33646	76	16	an	an	DET
bracis-33646	76	17	abstract	abstract	ADJ
bracis-33646	76	18	model	model	ADJ
bracis-33646	76	19	-	-	PUNCT
bracis-33646	76	20	theoretic	theoretic	ADJ
bracis-33646	76	21	approach	approach	NOUN
bracis-33646	76	22	,	,	PUNCT
bracis-33646	76	23	which	which	PRON
bracis-33646	76	24	will	will	AUX
bracis-33646	76	25	inform	inform	VERB
bracis-33646	76	26	our	our	PRON
bracis-33646	76	27	results	result	NOUN
bracis-33646	76	28	in	in	ADP
bracis-33646	76	29	sect	sect	NOUN
bracis-33646	76	30	.	.	PUNCT
bracis-33646	76	31	 	 	SPACE
bracis-33646	77	1	4	4	X
bracis-33646	77	2	.	.	PUNCT
bracis-33646	78	1	the	the	DET
bracis-33646	78	2	reasoning	reasoning	NOUN
bracis-33646	78	3	for	for	ADP
bracis-33646	78	4	focusing	focus	VERB
bracis-33646	78	5	on	on	ADP
bracis-33646	78	6	a	a	DET
bracis-33646	78	7	model	model	ADJ
bracis-33646	78	8	-	-	PUNCT
bracis-33646	78	9	theoretic	theoretic	ADJ
bracis-33646	78	10	approach	approach	NOUN
bracis-33646	78	11	for	for	ADP
bracis-33646	78	12	belief	belief	NOUN
bracis-33646	78	13	change	change	NOUN
bracis-33646	78	14	is	be	AUX
bracis-33646	78	15	not	not	PART
bracis-33646	78	16	only	only	ADV
bracis-33646	78	17	based	base	VERB
bracis-33646	78	18	on	on	ADP
bracis-33646	78	19	the	the	DET
bracis-33646	78	20	fact	fact	NOUN
bracis-33646	78	21	that	that	SCONJ
bracis-33646	78	22	this	this	DET
bracis-33646	78	23	approach	approach	NOUN
bracis-33646	78	24	,	,	PUNCT
bracis-33646	78	25	in	in	ADP
bracis-33646	78	26	our	our	PRON
bracis-33646	78	27	opinion	opinion	NOUN
bracis-33646	78	28	,	,	PUNCT
bracis-33646	78	29	provides	provide	VERB
bracis-33646	78	30	an	an	DET
bracis-33646	78	31	interesting	interesting	ADJ
bracis-33646	78	32	framework	framework	NOUN
bracis-33646	78	33	with	with	ADP
bracis-33646	78	34	which	which	PRON
bracis-33646	78	35	we	we	PRON
bracis-33646	78	36	can	can	AUX
bracis-33646	78	37	connect	connect	VERB
bracis-33646	78	38	and	and	CCONJ
bracis-33646	78	39	contrast	contrast	VERB
bracis-33646	78	40	the	the	DET
bracis-33646	78	41	fundamental	fundamental	ADJ
bracis-33646	78	42	assumptions	assumption	NOUN
bracis-33646	78	43	of	of	ADP
bracis-33646	78	44	our	our	PRON
bracis-33646	78	45	theory	theory	NOUN
bracis-33646	78	46	with	with	ADP
bracis-33646	78	47	those	those	PRON
bracis-33646	78	48	of	of	ADP
bracis-33646	78	49	related	related	ADJ
bracis-33646	78	50	fields	field	NOUN
bracis-33646	78	51	,	,	PUNCT
bracis-33646	78	52	such	such	ADJ
bracis-33646	78	53	as	as	ADP
bracis-33646	78	54	epistemic	epistemic	ADJ
bracis-33646	78	55	logic	logic	NOUN
bracis-33646	78	56	,	,	PUNCT
bracis-33646	78	57	conditional	conditional	ADJ
bracis-33646	78	58	logic	logic	NOUN
bracis-33646	78	59	and	and	CCONJ
bracis-33646	78	60	non	non	ADJ
bracis-33646	78	61	-	-	ADJ
bracis-33646	78	62	monotonic	monotonic	ADJ
bracis-33646	78	63	logics	logic	NOUN
bracis-33646	78	64	,	,	PUNCT
bracis-33646	78	65	but	but	CCONJ
bracis-33646	78	66	also	also	ADV
bracis-33646	78	67	a	a	DET
bracis-33646	78	68	semantic	semantic	ADJ
bracis-33646	78	69	approach	approach	NOUN
bracis-33646	78	70	helps	help	VERB
bracis-33646	78	71	us	we	PRON
bracis-33646	78	72	abstract	abstract	ADJ
bracis-33646	78	73	from	from	ADP
bracis-33646	78	74	concrete	concrete	ADJ
bracis-33646	78	75	realisations	realisation	NOUN
bracis-33646	78	76	of	of	ADP
bracis-33646	78	77	these	these	DET
bracis-33646	78	78	operations	operation	NOUN
bracis-33646	78	79	for	for	ADP
bracis-33646	78	80	particular	particular	ADJ
bracis-33646	78	81	logics	logic	NOUN
bracis-33646	78	82	,	,	PUNCT
bracis-33646	78	83	based	base	VERB
bracis-33646	78	84	on	on	ADP
bracis-33646	78	85	notions	notion	NOUN
bracis-33646	78	86	such	such	ADJ
bracis-33646	78	87	as	as	ADP
bracis-33646	78	88	remainder	remainder	NOUN
bracis-33646	78	89	sets	set	NOUN
bracis-33646	78	90	,	,	PUNCT
bracis-33646	78	91	sets	set	NOUN
bracis-33646	78	92	of	of	ADP
bracis-33646	78	93	complements	complement	NOUN
bracis-33646	78	94	,	,	PUNCT
bracis-33646	78	95	etc	etc	X
bracis-33646	78	96	.	.	X
bracis-33646	78	97	,	,	PUNCT
bracis-33646	78	98	to	to	ADP
bracis-33646	78	99	a	a	DET
bracis-33646	78	100	general	general	ADJ
bracis-33646	78	101	understanding	understanding	NOUN
bracis-33646	78	102	of	of	ADP
bracis-33646	78	103	agm	agm	PROPN
bracis-33646	78	104	belief	belief	NOUN
bracis-33646	78	105	change	change	NOUN
bracis-33646	78	106	as	as	ADP
bracis-33646	78	107	a	a	DET
bracis-33646	78	108	phenomenon	phenomenon	NOUN
bracis-33646	78	109	.	.	PUNCT
bracis-33646	79	1	as	as	ADP
bracis-33646	79	2	such	such	ADJ
bracis-33646	79	3	,	,	PUNCT
bracis-33646	79	4	given	give	VERB
bracis-33646	79	5	a	a	DET
bracis-33646	79	6	logical	logical	ADJ
bracis-33646	79	7	language	language	NOUN
bracis-33646	79	8	l	l	NOUN
bracis-33646	79	9	,	,	PUNCT
bracis-33646	79	10	we	we	PRON
bracis-33646	79	11	will	will	AUX
bracis-33646	79	12	employ	employ	VERB
bracis-33646	79	13	the	the	DET
bracis-33646	79	14	notion	notion	NOUN
bracis-33646	79	15	of	of	ADP
bracis-33646	79	16	an	an	DET
bracis-33646	79	17	abstract	abstract	ADJ
bracis-33646	79	18	model	model	NOUN
bracis-33646	79	19	theory	theory	NOUN
bracis-33646	79	20	to	to	PART
bracis-33646	79	21	prescribe	prescribe	VERB
bracis-33646	79	22	how	how	SCONJ
bracis-33646	79	23	these	these	DET
bracis-33646	79	24	formulas	formula	NOUN
bracis-33646	79	25	can	can	AUX
bracis-33646	79	26	be	be	AUX
bracis-33646	79	27	interpreted	interpret	VERB
bracis-33646	79	28	.	.	PUNCT
bracis-33646	80	1	this	this	DET
bracis-33646	80	2	notion	notion	NOUN
bracis-33646	80	3	will	will	AUX
bracis-33646	80	4	then	then	ADV
bracis-33646	80	5	be	be	AUX
bracis-33646	80	6	used	use	VERB
bracis-33646	80	7	to	to	PART
bracis-33646	80	8	formally	formally	ADV
bracis-33646	80	9	define	define	VERB
bracis-33646	80	10	an	an	DET
bracis-33646	80	11	abstract	abstract	ADJ
bracis-33646	80	12	logic	logic	NOUN
bracis-33646	80	13	a	a	DET
bracis-33646	80	14	more	more	ADV
bracis-33646	80	15	common	common	ADJ
bracis-33646	80	16	terminology	terminology	NOUN
bracis-33646	80	17	to	to	ADP
bracis-33646	80	18	those	those	PRON
bracis-33646	80	19	working	work	VERB
bracis-33646	80	20	on	on	ADP
bracis-33646	80	21	agm	agm	PROPN
bracis-33646	80	22	-	-	PUNCT
bracis-33646	80	23	based	base	VERB
bracis-33646	80	24	belief	belief	NOUN
bracis-33646	80	25	change	change	NOUN
bracis-33646	80	26	,	,	PUNCT
bracis-33646	80	27	and	and	CCONJ
bracis-33646	80	28	with	with	ADP
bracis-33646	80	29	which	which	PRON
bracis-33646	80	30	we	we	PRON
bracis-33646	80	31	can	can	AUX
bracis-33646	80	32	establish	establish	VERB
bracis-33646	80	33	connections	connection	NOUN
bracis-33646	80	34	between	between	ADP
bracis-33646	80	35	our	our	PRON
bracis-33646	80	36	results	result	NOUN
bracis-33646	80	37	and	and	CCONJ
bracis-33646	80	38	those	those	PRON
bracis-33646	80	39	in	in	ADP
bracis-33646	80	40	the	the	DET
bracis-33646	80	41	literature	literature	NOUN
bracis-33646	80	42	.	.	PUNCT
bracis-33646	81	1	definition	definition	NOUN
bracis-33646	81	2	4	4	NUM
bracis-33646	81	3	let	let	VERB
bracis-33646	81	4	l	l	NOUN
bracis-33646	81	5	be	be	AUX
bracis-33646	81	6	a	a	DET
bracis-33646	81	7	logical	logical	ADJ
bracis-33646	81	8	language	language	NOUN
bracis-33646	81	9	,	,	PUNCT
bracis-33646	81	10	we	we	PRON
bracis-33646	81	11	call	call	VERB
bracis-33646	81	12	a	a	DET
bracis-33646	81	13	tuple	tuple	NOUN
bracis-33646	81	14	\(\mathcal	\(\mathcal	ADJ
bracis-33646	81	15	{	{	PUNCT
bracis-33646	81	16	m	m	NOUN
bracis-33646	81	17	}	}	PUNCT
bracis-33646	81	18	=	=	PUNCT
bracis-33646	81	19	\langle	\langle	PROPN
bracis-33646	81	20	m	m	PROPN
bracis-33646	81	21	,	,	PUNCT
bracis-33646	81	22	l	l	PROPN
bracis-33646	81	23	,	,	PUNCT
bracis-33646	81	24	\vdash	\vdash	VERB
bracis-33646	81	25	\rangle	\rangle	NOUN
bracis-33646	81	26	\	\	NOUN
bracis-33646	81	27	)	)	PUNCT
bracis-33646	81	28	an	an	DET
bracis-33646	81	29	abstract	abstract	ADJ
bracis-33646	81	30	model	model	NOUN
bracis-33646	81	31	theory	theory	NOUN
bracis-33646	81	32	(	(	PUNCT
bracis-33646	81	33	amt	amt	PROPN
bracis-33646	81	34	)	)	PUNCT
bracis-33646	81	35	if	if	SCONJ
bracis-33646	81	36	m	m	NOUN
bracis-33646	81	37	is	be	AUX
bracis-33646	81	38	a	a	DET
bracis-33646	81	39	non	non	ADJ
bracis-33646	81	40	-	-	ADJ
bracis-33646	81	41	empty	empty	ADJ
bracis-33646	81	42	set	set	NOUN
bracis-33646	81	43	of	of	ADP
bracis-33646	81	44	models	model	NOUN
bracis-33646	81	45	or	or	CCONJ
bracis-33646	81	46	interpretations	interpretation	NOUN
bracis-33646	81	47	;	;	PUNCT
bracis-33646	81	48	l	l	NOUN
bracis-33646	81	49	is	be	AUX
bracis-33646	81	50	a	a	DET
bracis-33646	81	51	non	non	ADJ
bracis-33646	81	52	-	-	ADJ
bracis-33646	81	53	empty	empty	ADJ
bracis-33646	81	54	set	set	NOUN
bracis-33646	81	55	of	of	ADP
bracis-33646	81	56	formulas	formula	NOUN
bracis-33646	81	57	called	call	VERB
bracis-33646	81	58	a	a	DET
bracis-33646	81	59	logical	logical	ADJ
bracis-33646	81	60	language	language	NOUN
bracis-33646	81	61	;	;	PUNCT
bracis-33646	81	62	\(\vdash	\(\vdash	NOUN
bracis-33646	81	63	:	:	PUNCT
bracis-33646	81	64	m	m	VERB
bracis-33646	81	65	\mapsto	\mapsto	PROPN
bracis-33646	81	66	2^l\	2^l\	NUM
bracis-33646	81	67	)	)	PUNCT
bracis-33646	81	68	is	be	AUX
bracis-33646	81	69	a	a	DET
bracis-33646	81	70	satisfaction	satisfaction	NOUN
bracis-33646	81	71	function	function	NOUN
bracis-33646	81	72	.	.	PUNCT
bracis-33646	82	1	given	give	VERB
bracis-33646	82	2	a	a	DET
bracis-33646	82	3	model	model	NOUN
bracis-33646	82	4	\(w\in	\(w\in	PUNCT
bracis-33646	82	5	m\	m\	NOUN
bracis-33646	82	6	)	)	PUNCT
bracis-33646	82	7	and	and	CCONJ
bracis-33646	82	8	a	a	DET
bracis-33646	82	9	formula	formula	NOUN
bracis-33646	82	10	\(\varphi	\(\varphi	CCONJ
bracis-33646	82	11	\in	\in	PROPN
bracis-33646	82	12	l\	l\	PROPN
bracis-33646	82	13	)	)	PUNCT
bracis-33646	82	14	,	,	PUNCT
bracis-33646	82	15	we	we	PRON
bracis-33646	82	16	say	say	VERB
bracis-33646	82	17	w	w	NOUN
bracis-33646	82	18	satisfies	satisfie	NOUN
bracis-33646	82	19	\(\varphi	\(\varphi	ADJ
bracis-33646	82	20	\	\	NOUN
bracis-33646	82	21	)	)	PUNCT
bracis-33646	82	22	,	,	PUNCT
bracis-33646	82	23	denoted	denote	VERB
bracis-33646	82	24	\(w\vdash	\(w\vdash	NOUN
bracis-33646	82	25	\varphi	\varphi	PROPN
bracis-33646	82	26	\	\	NOUN
bracis-33646	82	27	)	)	PUNCT
bracis-33646	82	28	,	,	PUNCT
bracis-33646	82	29	if	if	SCONJ
bracis-33646	82	30	\(\varphi	\(\varphi	PUNCT
bracis-33646	82	31	\in	\in	ADJ
bracis-33646	82	32	\vdash	\vdash	PROPN
bracis-33646	82	33	(	(	PUNCT
bracis-33646	82	34	w)\	w)\	NUM
bracis-33646	82	35	)	)	PUNCT
bracis-33646	82	36	.	.	PUNCT
bracis-33646	83	1	similarly	similarly	ADV
bracis-33646	83	2	,	,	PUNCT
bracis-33646	83	3	for	for	ADP
bracis-33646	83	4	a	a	DET
bracis-33646	83	5	set	set	NOUN
bracis-33646	83	6	\(\vargamma	\(\vargamma	NOUN
bracis-33646	83	7	\subseteq	\subseteq	PROPN
bracis-33646	83	8	l\	l\	NOUN
bracis-33646	83	9	)	)	PUNCT
bracis-33646	83	10	,	,	PUNCT
bracis-33646	83	11	\(w\vdash	\(w\vdash	VERB
bracis-33646	83	12	\vargamma	\vargamma	PROPN
bracis-33646	83	13	\	\	NOUN
bracis-33646	83	14	)	)	PUNCT
bracis-33646	83	15	if	if	SCONJ
bracis-33646	83	16	\(w\vdash	\(w\vdash	VERB
bracis-33646	83	17	\varphi	\varphi	ADP
bracis-33646	83	18	\	\	NOUN
bracis-33646	83	19	)	)	PUNCT
bracis-33646	83	20	for	for	ADP
bracis-33646	83	21	all	all	DET
bracis-33646	83	22	\(\varphi	\(\varphi	ADJ
bracis-33646	83	23	\in	\in	PROPN
bracis-33646	83	24	\vargamma	\vargamma	NOUN
bracis-33646	83	25	\	\	PROPN
bracis-33646	83	26	)	)	PUNCT
bracis-33646	83	27	.	.	PUNCT
bracis-33646	84	1	given	give	VERB
bracis-33646	84	2	a	a	DET
bracis-33646	84	3	set	set	NOUN
bracis-33646	84	4	of	of	ADP
bracis-33646	84	5	interpretations	interpretation	NOUN
bracis-33646	84	6	\(x\subseteq	\(x\subseteq	ADV
bracis-33646	84	7	m\	m\	NOUN
bracis-33646	84	8	)	)	PUNCT
bracis-33646	84	9	for	for	ADP
bracis-33646	84	10	some	some	DET
bracis-33646	84	11	abstract	abstract	ADJ
bracis-33646	84	12	model	model	NOUN
bracis-33646	84	13	theory	theory	NOUN
bracis-33646	84	14	,	,	PUNCT
bracis-33646	84	15	we	we	PRON
bracis-33646	84	16	will	will	AUX
bracis-33646	84	17	often	often	ADV
bracis-33646	84	18	employ	employ	VERB
bracis-33646	84	19	the	the	DET
bracis-33646	84	20	notation	notation	NOUN
bracis-33646	84	21	th(x	th(x	PUNCT
bracis-33646	84	22	)	)	PUNCT
bracis-33646	84	23	for	for	ADP
bracis-33646	84	24	the	the	DET
bracis-33646	84	25	set	set	NOUN
bracis-33646	84	26	of	of	ADP
bracis-33646	84	27	all	all	DET
bracis-33646	84	28	formulas	formula	NOUN
bracis-33646	84	29	satisfied	satisfy	VERB
bracis-33646	84	30	by	by	ADP
bracis-33646	84	31	the	the	DET
bracis-33646	84	32	interpretations	interpretation	NOUN
bracis-33646	84	33	of	of	ADP
bracis-33646	84	34	x	x	PRON
bracis-33646	84	35	also	also	ADV
bracis-33646	84	36	referred	refer	VERB
bracis-33646	84	37	to	to	ADP
bracis-33646	84	38	as	as	SCONJ
bracis-33646	84	39	the	the	DET
bracis-33646	84	40	‘	'	PUNCT
bracis-33646	84	41	theory	theory	NOUN
bracis-33646	84	42	of	of	ADP
bracis-33646	84	43	x.	x.	NOUN
bracis-33646	84	44	’	'	PUNCT
bracis-33646	84	45	if	if	SCONJ
bracis-33646	84	46	\(w\in	\(w\in	PUNCT
bracis-33646	84	47	m\	m\	NOUN
bracis-33646	84	48	)	)	PUNCT
bracis-33646	84	49	,	,	PUNCT
bracis-33646	84	50	we	we	PRON
bracis-33646	84	51	will	will	AUX
bracis-33646	84	52	denote	denote	VERB
bracis-33646	84	53	\(th(\{w\})\	\(th(\{w\})\	NOUN
bracis-33646	84	54	)	)	PUNCT
bracis-33646	84	55	by	by	ADP
bracis-33646	84	56	th(w	th(w	NOUN
bracis-33646	84	57	)	)	PUNCT
bracis-33646	84	58	.	.	PUNCT
bracis-33646	85	1	we	we	PRON
bracis-33646	85	2	also	also	ADV
bracis-33646	85	3	define	define	VERB
bracis-33646	85	4	,	,	PUNCT
bracis-33646	85	5	as	as	ADP
bracis-33646	85	6	usual	usual	ADJ
bracis-33646	85	7	,	,	PUNCT
bracis-33646	85	8	\(\llbracket	\(\llbracket	NOUN
bracis-33646	85	9	\vargamma	\vargamma	NOUN
bracis-33646	85	10	\rrbracket	\rrbracket	ADJ
bracis-33646	85	11	\	\	NOUN
bracis-33646	85	12	)	)	PUNCT
bracis-33646	85	13	as	as	SCONJ
bracis-33646	85	14	the	the	DET
bracis-33646	85	15	set	set	NOUN
bracis-33646	85	16	of	of	ADP
bracis-33646	85	17	all	all	DET
bracis-33646	85	18	interpretations	interpretation	NOUN
bracis-33646	85	19	satisfying	satisfy	VERB
bracis-33646	85	20	it	it	PRON
bracis-33646	85	21	.	.	PUNCT
bracis-33646	86	1	in	in	ADP
bracis-33646	86	2	the	the	DET
bracis-33646	86	3	following	following	NOUN
bracis-33646	86	4	,	,	PUNCT
bracis-33646	86	5	given	give	VERB
bracis-33646	86	6	a	a	DET
bracis-33646	86	7	set	set	NOUN
bracis-33646	86	8	of	of	ADP
bracis-33646	86	9	interpretations	interpretation	NOUN
bracis-33646	86	10	x	x	SYM
bracis-33646	86	11	,	,	PUNCT
bracis-33646	86	12	we	we	PRON
bracis-33646	86	13	will	will	AUX
bracis-33646	86	14	usually	usually	ADV
bracis-33646	86	15	denote	denote	VERB
bracis-33646	86	16	the	the	DET
bracis-33646	86	17	complement	complement	NOUN
bracis-33646	86	18	of	of	ADP
bracis-33646	86	19	x	x	X
bracis-33646	86	20	,	,	PUNCT
bracis-33646	86	21	i.e.	i.e.	X
bracis-33646	86	22	\(m\setminus	\(m\setminus	ADP
bracis-33646	86	23	x\	x\	NOUN
bracis-33646	86	24	)	)	PUNCT
bracis-33646	86	25	,	,	PUNCT
bracis-33646	86	26	by	by	ADP
bracis-33646	86	27	\(\overline{x}\	\(\overline{x}\	NOUN
bracis-33646	86	28	)	)	PUNCT
bracis-33646	86	29	.	.	PUNCT
bracis-33646	87	1	definition	definition	NOUN
bracis-33646	87	2	5	5	NUM
bracis-33646	87	3	let	let	VERB
bracis-33646	87	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	87	5	{	{	PUNCT
bracis-33646	87	6	l	l	NOUN
bracis-33646	87	7	}	}	PUNCT
bracis-33646	87	8	=	=	PUNCT
bracis-33646	87	9	\langle	\langle	PROPN
bracis-33646	87	10	l	l	NOUN
bracis-33646	87	11	,	,	PUNCT
bracis-33646	87	12	cn\rangle	cn\rangle	NOUN
bracis-33646	87	13	\	\	NOUN
bracis-33646	87	14	)	)	PUNCT
bracis-33646	87	15	be	be	AUX
bracis-33646	87	16	a	a	DET
bracis-33646	87	17	logic	logic	NOUN
bracis-33646	87	18	and	and	CCONJ
bracis-33646	87	19	\(\mathcal	\(\mathcal	ADJ
bracis-33646	87	20	{	{	PUNCT
bracis-33646	87	21	m	m	NOUN
bracis-33646	87	22	}	}	PUNCT
bracis-33646	87	23	=	=	PUNCT
bracis-33646	87	24	\langle	\langle	PROPN
bracis-33646	87	25	m	m	PROPN
bracis-33646	87	26	,	,	PUNCT
bracis-33646	87	27	l	l	PROPN
bracis-33646	87	28	,	,	PUNCT
bracis-33646	87	29	\vdash	\vdash	VERB
bracis-33646	87	30	\rangle	\rangle	NOUN
bracis-33646	87	31	\	\	NOUN
bracis-33646	87	32	)	)	PUNCT
bracis-33646	87	33	be	be	AUX
bracis-33646	87	34	an	an	DET
bracis-33646	87	35	abstract	abstract	ADJ
bracis-33646	87	36	model	model	NOUN
bracis-33646	87	37	theory	theory	NOUN
bracis-33646	87	38	.	.	PUNCT
bracis-33646	88	1	we	we	PRON
bracis-33646	88	2	say	say	VERB
bracis-33646	88	3	the	the	DET
bracis-33646	88	4	logic	logic	NOUN
bracis-33646	88	5	\(\mathcal	\(\mathcal	ADJ
bracis-33646	88	6	{	{	PUNCT
bracis-33646	88	7	l}\	l}\	PROPN
bracis-33646	88	8	)	)	PUNCT
bracis-33646	88	9	is	be	AUX
bracis-33646	88	10	induced	induce	VERB
bracis-33646	88	11	by	by	ADP
bracis-33646	88	12	\(\mathcal	\(\mathcal	ADJ
bracis-33646	88	13	{	{	PUNCT
bracis-33646	88	14	m}\	m}\	PROPN
bracis-33646	88	15	)	)	PUNCT
bracis-33646	88	16	if	if	SCONJ
bracis-33646	88	17	for	for	ADP
bracis-33646	88	18	any	any	DET
bracis-33646	88	19	\(\vargamma	\(\vargamma	NOUN
bracis-33646	88	20	\subseteq	\subseteq	PROPN
bracis-33646	88	21	l\	l\	PROPN
bracis-33646	88	22	)	)	PUNCT
bracis-33646	88	23	,	,	PUNCT
bracis-33646	88	24	it	it	PRON
bracis-33646	88	25	holds	hold	VERB
bracis-33646	88	26	that	that	SCONJ
bracis-33646	88	27	\(cn(\vargamma	\(cn(\vargamma	PROPN
bracis-33646	88	28	)	)	PUNCT
bracis-33646	89	1	=	=	SYM
bracis-33646	89	2	\{\psi	\{\psi	NOUN
bracis-33646	89	3	\in	\in	PROPN
bracis-33646	89	4	l~|~	l~|~	PROPN
bracis-33646	89	5	\text	\text	NOUN
bracis-33646	89	6	{	{	PUNCT
bracis-33646	89	7	for	for	ADP
bracis-33646	89	8	}	}	PUNCT
bracis-33646	89	9	\text	\text	NOUN
bracis-33646	89	10	{	{	PUNCT
bracis-33646	89	11	all	all	PRON
bracis-33646	89	12	}	}	PUNCT
bracis-33646	89	13	~w\in	~w\in	PUNCT
bracis-33646	89	14	m~\text	m~\text	PROPN
bracis-33646	89	15	{	{	PUNCT
bracis-33646	89	16	s.t	s.t	PROPN
bracis-33646	89	17	.	.	PROPN
bracis-33646	89	18	}	}	PUNCT
bracis-33646	89	19	~w\vdash	~w\vdash	NUM
bracis-33646	89	20	\vargamma	\vargamma	NOUN
bracis-33646	89	21	,	,	PUNCT
bracis-33646	89	22	w\vdash	w\vdash	VERB
bracis-33646	89	23	\psi	\psi	PROPN
bracis-33646	89	24	\}\	\}\	NOUN
bracis-33646	89	25	)	)	PUNCT
bracis-33646	89	26	.	.	PUNCT
bracis-33646	90	1	we	we	PRON
bracis-33646	90	2	will	will	AUX
bracis-33646	90	3	often	often	ADV
bracis-33646	90	4	denote	denote	VERB
bracis-33646	90	5	by	by	ADP
bracis-33646	90	6	\(\mathcal	\(\mathcal	ADJ
bracis-33646	90	7	{	{	PUNCT
bracis-33646	90	8	m	m	NOUN
bracis-33646	90	9	}	}	PUNCT
bracis-33646	90	10	=	=	SYM
bracis-33646	90	11	mod(\mathcal	mod(\mathcal	ADJ
bracis-33646	90	12	{	{	PUNCT
bracis-33646	90	13	l})\	l})\	X
bracis-33646	90	14	)	)	PUNCT
bracis-33646	90	15	the	the	DET
bracis-33646	90	16	fact	fact	NOUN
bracis-33646	90	17	that	that	SCONJ
bracis-33646	90	18	the	the	DET
bracis-33646	90	19	model	model	NOUN
bracis-33646	90	20	theory	theory	NOUN
bracis-33646	90	21	\(\mathcal	\(\mathcal	ADJ
bracis-33646	90	22	{	{	PUNCT
bracis-33646	90	23	m}\	m}\	PROPN
bracis-33646	90	24	)	)	PUNCT
bracis-33646	90	25	induces	induce	VERB
bracis-33646	90	26	the	the	DET
bracis-33646	90	27	logic	logic	NOUN
bracis-33646	90	28	\(\mathcal	\(\mathcal	ADJ
bracis-33646	90	29	{	{	PUNCT
bracis-33646	90	30	l}\	l}\	PROPN
bracis-33646	90	31	)	)	PUNCT
bracis-33646	90	32	.	.	PUNCT
bracis-33646	91	1	notice	notice	VERB
bracis-33646	91	2	that	that	SCONJ
bracis-33646	91	3	in	in	ADP
bracis-33646	91	4	definition	definition	NOUN
bracis-33646	91	5	 	 	SPACE
bracis-33646	91	6	5	5	NUM
bracis-33646	91	7	,	,	PUNCT
bracis-33646	91	8	since	since	SCONJ
bracis-33646	91	9	we	we	PRON
bracis-33646	91	10	establish	establish	VERB
bracis-33646	91	11	that	that	SCONJ
bracis-33646	91	12	\(\varphi	\(\varphi	ADJ
bracis-33646	91	13	\in	\in	PROPN
bracis-33646	91	14	cn(\vargamma	cn(\vargamma	PROPN
bracis-33646	91	15	)	)	PUNCT
bracis-33646	91	16	\	\	NOUN
bracis-33646	91	17	)	)	PUNCT
bracis-33646	92	1	iff	iff	PROPN
bracis-33646	92	2	\(\llbracket	\(\llbracket	NOUN
bracis-33646	92	3	\vargamma	\vargamma	PROPN
bracis-33646	92	4	\rrbracket	\rrbracket	VERB
bracis-33646	92	5	\subseteq	\subseteq	PROPN
bracis-33646	92	6	\llbracket	\llbracket	PROPN
bracis-33646	92	7	\varphi	\varphi	AUX
bracis-33646	92	8	\rrbracket	\rrbracket	VERB
bracis-33646	92	9	\	\	NOUN
bracis-33646	92	10	)	)	PUNCT
bracis-33646	92	11	,	,	PUNCT
bracis-33646	92	12	it	it	PRON
bracis-33646	92	13	is	be	AUX
bracis-33646	92	14	easy	easy	ADJ
bracis-33646	92	15	to	to	PART
bracis-33646	92	16	see	see	VERB
bracis-33646	92	17	that	that	SCONJ
bracis-33646	92	18	any	any	DET
bracis-33646	92	19	logic	logic	NOUN
bracis-33646	92	20	induced	induce	VERB
bracis-33646	92	21	by	by	ADP
bracis-33646	92	22	some	some	DET
bracis-33646	92	23	amt	amt	PROPN
bracis-33646	92	24	trivially	trivially	ADV
bracis-33646	92	25	satisfies	satisfy	VERB
bracis-33646	92	26	inclusion	inclusion	NOUN
bracis-33646	92	27	,	,	PUNCT
bracis-33646	92	28	monotonicity	monotonicity	NOUN
bracis-33646	92	29	and	and	CCONJ
bracis-33646	92	30	idempotency	idempotency	NOUN
bracis-33646	92	31	,	,	PUNCT
bracis-33646	92	32	i.e.	i.e.	X
bracis-33646	92	33	,	,	PUNCT
bracis-33646	92	34	it	it	PRON
bracis-33646	92	35	is	be	AUX
bracis-33646	92	36	tarskian	tarskian	NOUN
bracis-33646	92	37	.	.	PUNCT
bracis-33646	93	1	lemma	lemma	PROPN
bracis-33646	93	2	1	1	NUM
bracis-33646	93	3	let	let	VERB
bracis-33646	93	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	93	5	{	{	PUNCT
bracis-33646	93	6	m	m	NOUN
bracis-33646	93	7	}	}	PUNCT
bracis-33646	93	8	=	=	PUNCT
bracis-33646	93	9	\langle	\langle	PROPN
bracis-33646	93	10	m	m	PROPN
bracis-33646	93	11	,	,	PUNCT
bracis-33646	93	12	l	l	PROPN
bracis-33646	93	13	,	,	PUNCT
bracis-33646	93	14	\vdash	\vdash	VERB
bracis-33646	93	15	\rangle	\rangle	NOUN
bracis-33646	93	16	\	\	NOUN
bracis-33646	93	17	)	)	PUNCT
bracis-33646	93	18	be	be	AUX
bracis-33646	93	19	an	an	DET
bracis-33646	93	20	amt	amt	PROPN
bracis-33646	93	21	,	,	PUNCT
bracis-33646	93	22	it	it	PRON
bracis-33646	93	23	induces	induce	VERB
bracis-33646	93	24	a	a	DET
bracis-33646	93	25	tarskian	tarskian	ADJ
bracis-33646	93	26	logic	logic	NOUN
bracis-33646	93	27	\(\mathcal	\(\mathcal	ADJ
bracis-33646	93	28	{	{	PUNCT
bracis-33646	93	29	l}\	l}\	PROPN
bracis-33646	93	30	)	)	PUNCT
bracis-33646	93	31	.	.	PUNCT
bracis-33646	94	1	more	more	ADV
bracis-33646	94	2	yet	yet	ADV
bracis-33646	94	3	,	,	PUNCT
bracis-33646	94	4	given	give	VERB
bracis-33646	94	5	that	that	SCONJ
bracis-33646	94	6	any	any	DET
bracis-33646	94	7	logic	logic	NOUN
bracis-33646	94	8	defines	define	VERB
bracis-33646	94	9	a	a	DET
bracis-33646	94	10	lattice	lattice	NOUN
bracis-33646	94	11	of	of	ADP
bracis-33646	94	12	its	its	PRON
bracis-33646	94	13	theories	theory	NOUN
bracis-33646	94	14	,	,	PUNCT
bracis-33646	94	15	we	we	PRON
bracis-33646	94	16	can	can	AUX
bracis-33646	94	17	use	use	VERB
bracis-33646	94	18	that	that	DET
bracis-33646	94	19	structure	structure	NOUN
bracis-33646	94	20	as	as	ADP
bracis-33646	94	21	a	a	DET
bracis-33646	94	22	domain	domain	NOUN
bracis-33646	94	23	of	of	ADP
bracis-33646	94	24	interpretation	interpretation	NOUN
bracis-33646	94	25	of	of	ADP
bracis-33646	94	26	the	the	DET
bracis-33646	94	27	formulas	formula	NOUN
bracis-33646	94	28	.	.	PUNCT
bracis-33646	95	1	as	as	ADP
bracis-33646	95	2	such	such	ADJ
bracis-33646	95	3	,	,	PUNCT
bracis-33646	95	4	all	all	DET
bracis-33646	95	5	tarskian	tarskian	NOUN
bracis-33646	95	6	logics	logic	NOUN
bracis-33646	95	7	are	be	AUX
bracis-33646	95	8	induced	induce	VERB
bracis-33646	95	9	by	by	ADP
bracis-33646	95	10	some	some	DET
bracis-33646	95	11	amt	amt	PROPN
bracis-33646	95	12	.	.	PUNCT
bracis-33646	96	1	proposition	proposition	NOUN
bracis-33646	96	2	2	2	NUM
bracis-33646	96	3	any	any	DET
bracis-33646	96	4	tarskian	tarskian	ADJ
bracis-33646	96	5	logic	logic	NOUN
bracis-33646	96	6	\(\mathcal	\(\mathcal	ADJ
bracis-33646	96	7	{	{	PUNCT
bracis-33646	96	8	l}\	l}\	PROPN
bracis-33646	96	9	)	)	PUNCT
bracis-33646	96	10	is	be	AUX
bracis-33646	96	11	induced	induce	VERB
bracis-33646	96	12	by	by	ADP
bracis-33646	96	13	some	some	DET
bracis-33646	96	14	abstract	abstract	ADJ
bracis-33646	96	15	model	model	NOUN
bracis-33646	96	16	theory	theory	NOUN
bracis-33646	96	17	\(\mathcal	\(\mathcal	ADJ
bracis-33646	96	18	{	{	PUNCT
bracis-33646	96	19	m}\	m}\	PROPN
bracis-33646	96	20	)	)	PUNCT
bracis-33646	96	21	proof	proof	NOUN
bracis-33646	96	22	let	let	VERB
bracis-33646	96	23	\(\mathcal	\(\mathcal	ADJ
bracis-33646	96	24	{	{	PUNCT
bracis-33646	96	25	l	l	NOUN
bracis-33646	96	26	}	}	PUNCT
bracis-33646	96	27	=	=	PUNCT
bracis-33646	96	28	\langle	\langle	PROPN
bracis-33646	96	29	l	l	NOUN
bracis-33646	96	30	,	,	PUNCT
bracis-33646	96	31	cn\rangle	cn\rangle	NOUN
bracis-33646	96	32	\	\	PROPN
bracis-33646	96	33	)	)	PUNCT
bracis-33646	96	34	,	,	PUNCT
bracis-33646	96	35	recall	recall	VERB
bracis-33646	96	36	that	that	SCONJ
bracis-33646	96	37	the	the	DET
bracis-33646	96	38	set	set	NOUN
bracis-33646	96	39	of	of	ADP
bracis-33646	96	40	all	all	DET
bracis-33646	96	41	theories	theory	NOUN
bracis-33646	96	42	is	be	AUX
bracis-33646	96	43	defined	define	VERB
bracis-33646	96	44	as	as	ADP
bracis-33646	96	45	\(th_\mathcal	\(th_\mathcal	ADJ
bracis-33646	96	46	{	{	PUNCT
bracis-33646	96	47	l	l	NOUN
bracis-33646	96	48	}	}	PUNCT
bracis-33646	96	49	=	=	SYM
bracis-33646	96	50	\{\vargamma	\{\vargamma	PROPN
bracis-33646	96	51	\subseteq	\subseteq	PROPN
bracis-33646	96	52	l~|~	l~|~	PROPN
bracis-33646	96	53	cn(\vargamma	cn(\vargamma	PROPN
bracis-33646	96	54	)	)	PUNCT
bracis-33646	97	1	=	=	SYM
bracis-33646	97	2	\vargamma	\vargamma	VERB
bracis-33646	97	3	\}\	\}\	NOUN
bracis-33646	97	4	)	)	PUNCT
bracis-33646	97	5	.	.	PUNCT
bracis-33646	98	1	let	let	VERB
bracis-33646	98	2	us	we	PRON
bracis-33646	98	3	define	define	VERB
bracis-33646	98	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	98	5	{	{	PUNCT
bracis-33646	98	6	m	m	NOUN
bracis-33646	98	7	}	}	PUNCT
bracis-33646	98	8	=	=	PUNCT
bracis-33646	98	9	\langle	\langle	PRON
bracis-33646	98	10	th_\mathcal	th_\mathcal	ADJ
bracis-33646	98	11	{	{	PUNCT
bracis-33646	98	12	l	l	NOUN
bracis-33646	98	13	}	}	PUNCT
bracis-33646	98	14	,	,	PUNCT
bracis-33646	98	15	\vdash	\vdash	VERB
bracis-33646	98	16	\rangle	\rangle	NOUN
bracis-33646	98	17	\	\	NOUN
bracis-33646	98	18	)	)	PUNCT
bracis-33646	98	19	s.t	s.t	PROPN
bracis-33646	98	20	.	.	PUNCT
bracis-33646	98	21	\(\vargamma	\(\vargamma	PROPN
bracis-33646	98	22	\vdash	\vdash	PROPN
bracis-33646	98	23	\varphi	\varphi	PROPN
bracis-33646	98	24	\	\	NOUN
bracis-33646	98	25	)	)	PUNCT
bracis-33646	99	1	iff	iff	PROPN
bracis-33646	99	2	\(\varphi	\(\varphi	PROPN
bracis-33646	99	3	\in	\in	PROPN
bracis-33646	99	4	\vargamma	\vargamma	PROPN
bracis-33646	99	5	\	\	PROPN
bracis-33646	99	6	)	)	PUNCT
bracis-33646	99	7	.	.	PUNCT
bracis-33646	100	1	well	well	INTJ
bracis-33646	100	2	,	,	PUNCT
bracis-33646	100	3	let	let	VERB
bracis-33646	100	4	\(\vargamma	\(\vargamma	PROPN
bracis-33646	100	5	\subseteq	\subseteq	PROPN
bracis-33646	100	6	l\	l\	PROPN
bracis-33646	100	7	)	)	PUNCT
bracis-33646	100	8	be	be	AUX
bracis-33646	100	9	a	a	DET
bracis-33646	100	10	set	set	NOUN
bracis-33646	100	11	of	of	ADP
bracis-33646	100	12	\(\mathcal	\(\mathcal	ADJ
bracis-33646	100	13	{	{	PUNCT
bracis-33646	100	14	l}\)-formulas	l}\)-formula	NOUN
bracis-33646	100	15	.	.	X
bracis-33646	101	1	take	take	VERB
bracis-33646	101	2	\(\psi	\(\psi	ADJ
bracis-33646	101	3	\in	\in	PROPN
bracis-33646	101	4	cn(\vargamma	cn(\vargamma	PROPN
bracis-33646	101	5	)	)	PUNCT
bracis-33646	101	6	\	\	PROPN
bracis-33646	101	7	)	)	PUNCT
bracis-33646	101	8	,	,	PUNCT
bracis-33646	101	9	then	then	ADV
bracis-33646	101	10	for	for	ADP
bracis-33646	101	11	any	any	DET
bracis-33646	101	12	\(\vargamma	\(\vargamma	NOUN
bracis-33646	101	13	'	'	PUNCT
bracis-33646	101	14	\in	\in	PROPN
bracis-33646	101	15	th_\mathcal	th_\mathcal	ADJ
bracis-33646	101	16	{	{	PUNCT
bracis-33646	101	17	l}\	l}\	PROPN
bracis-33646	101	18	)	)	PUNCT
bracis-33646	101	19	,	,	PUNCT
bracis-33646	101	20	if	if	SCONJ
bracis-33646	101	21	\(\vargamma	\(\vargamma	PROPN
bracis-33646	101	22	'	'	PUNCT
bracis-33646	101	23	\vdash	\vdash	NOUN
bracis-33646	101	24	\vargamma	\vargamma	PROPN
bracis-33646	101	25	\	\	PROPN
bracis-33646	101	26	)	)	PUNCT
bracis-33646	101	27	,	,	PUNCT
bracis-33646	101	28	then	then	ADV
bracis-33646	101	29	\(\vargamma	\(\vargamma	PROPN
bracis-33646	101	30	\subseteq	\subseteq	PROPN
bracis-33646	101	31	\vargamma	\vargamma	PROPN
bracis-33646	101	32	'	'	PUNCT
bracis-33646	101	33	\	\	NOUN
bracis-33646	101	34	)	)	PUNCT
bracis-33646	102	1	and	and	CCONJ
bracis-33646	102	2	,	,	PUNCT
bracis-33646	102	3	since	since	SCONJ
bracis-33646	102	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	102	5	{	{	PUNCT
bracis-33646	102	6	l}\	l}\	PROPN
bracis-33646	102	7	)	)	PUNCT
bracis-33646	102	8	is	be	AUX
bracis-33646	102	9	tarskian	tarskian	NOUN
bracis-33646	102	10	,	,	PUNCT
bracis-33646	102	11	\(\vargamma	\(\vargamma	PROPN
bracis-33646	102	12	'	'	PUNCT
bracis-33646	102	13	\vdash	\vdash	NOUN
bracis-33646	102	14	\psi	\psi	PROPN
bracis-33646	102	15	\	\	NOUN
bracis-33646	102	16	)	)	PUNCT
bracis-33646	102	17	.	.	PUNCT
bracis-33646	103	1	now	now	ADV
bracis-33646	103	2	,	,	PUNCT
bracis-33646	103	3	take	take	VERB
bracis-33646	103	4	\(\psi	\(\psi	ADJ
bracis-33646	103	5	\in	\in	PROPN
bracis-33646	103	6	l\	l\	PROPN
bracis-33646	103	7	)	)	PUNCT
bracis-33646	103	8	s.t	s.t	PROPN
bracis-33646	103	9	.	.	PROPN
bracis-33646	103	10	for	for	ADP
bracis-33646	103	11	any	any	DET
bracis-33646	103	12	\(\vargamma	\(\vargamma	NOUN
bracis-33646	103	13	'	'	PUNCT
bracis-33646	103	14	\in	\in	ADJ
bracis-33646	103	15	th_\mathcal	th_\mathcal	ADJ
bracis-33646	103	16	{	{	PUNCT
bracis-33646	103	17	l}\	l}\	PROPN
bracis-33646	103	18	)	)	PUNCT
bracis-33646	103	19	with	with	ADP
bracis-33646	103	20	\(\vargamma	\(\vargamma	PROPN
bracis-33646	103	21	'	'	PUNCT
bracis-33646	103	22	\vdash	\vdash	NOUN
bracis-33646	103	23	\vargamma	\vargamma	PROPN
bracis-33646	103	24	\	\	NOUN
bracis-33646	103	25	)	)	PUNCT
bracis-33646	103	26	,	,	PUNCT
bracis-33646	103	27	it	it	PRON
bracis-33646	103	28	holds	hold	VERB
bracis-33646	103	29	that	that	SCONJ
bracis-33646	103	30	\(\vargamma	\(\vargamma	PRON
bracis-33646	103	31	'	'	PUNCT
bracis-33646	103	32	\vdash	\vdash	NOUN
bracis-33646	103	33	\psi	\psi	PROPN
bracis-33646	103	34	\	\	NOUN
bracis-33646	103	35	)	)	PUNCT
bracis-33646	103	36	.	.	PUNCT
bracis-33646	104	1	since	since	SCONJ
bracis-33646	104	2	\(\mathcal	\(\mathcal	ADJ
bracis-33646	104	3	{	{	PUNCT
bracis-33646	104	4	l}\	l}\	PROPN
bracis-33646	104	5	)	)	PUNCT
bracis-33646	104	6	is	be	AUX
bracis-33646	104	7	tarskian	tarskian	NOUN
bracis-33646	104	8	,	,	PUNCT
bracis-33646	104	9	\(\psi	\(\psi	ADP
bracis-33646	104	10	\in	\in	PROPN
bracis-33646	104	11	\vargamma	\vargamma	PROPN
bracis-33646	104	12	'	'	PUNCT
bracis-33646	104	13	\	\	NOUN
bracis-33646	104	14	)	)	PUNCT
bracis-33646	104	15	.	.	PUNCT
bracis-33646	105	1	as	as	ADP
bracis-33646	105	2	\(cn(\vargamma	\(cn(\vargamma	X
bracis-33646	105	3	)	)	PUNCT
bracis-33646	105	4	\in	\in	PROPN
bracis-33646	105	5	th_\mathcal	th_\mathcal	PROPN
bracis-33646	105	6	{	{	PUNCT
bracis-33646	105	7	l}\	l}\	PROPN
bracis-33646	105	8	)	)	PUNCT
bracis-33646	105	9	,	,	PUNCT
bracis-33646	105	10	then	then	ADV
bracis-33646	105	11	\(\psi	\(\psi	ADP
bracis-33646	105	12	\in	\in	PROPN
bracis-33646	105	13	cn(\vargamma	cn(\vargamma	PROPN
bracis-33646	105	14	)	)	PUNCT
bracis-33646	105	15	\	\	PROPN
bracis-33646	105	16	)	)	PUNCT
bracis-33646	105	17	,	,	PUNCT
bracis-33646	105	18	as	as	ADV
bracis-33646	105	19	well	well	ADV
bracis-33646	105	20	.	.	PUNCT
bracis-33646	106	1	thus	thus	ADV
bracis-33646	106	2	\(cn(\vargamma	\(cn(\vargamma	X
bracis-33646	106	3	)	)	PUNCT
bracis-33646	107	1	=	=	SYM
bracis-33646	107	2	\{\psi	\{\psi	NOUN
bracis-33646	107	3	\in	\in	PROPN
bracis-33646	107	4	l~|~	l~|~	PROPN
bracis-33646	107	5	\text	\text	NOUN
bracis-33646	107	6	{	{	PUNCT
bracis-33646	107	7	for	for	ADP
bracis-33646	107	8	}	}	PUNCT
bracis-33646	107	9	\text	\text	NOUN
bracis-33646	107	10	{	{	PUNCT
bracis-33646	107	11	all	all	PRON
bracis-33646	107	12	}	}	PUNCT
bracis-33646	107	13	~w\in	~w\in	PUNCT
bracis-33646	107	14	m~\text	m~\text	PROPN
bracis-33646	107	15	{	{	PUNCT
bracis-33646	107	16	s.t	s.t	PROPN
bracis-33646	107	17	.	.	PROPN
bracis-33646	107	18	}	}	PUNCT
bracis-33646	107	19	~w\vdash	~w\vdash	NUM
bracis-33646	107	20	\vargamma	\vargamma	PROPN
bracis-33646	107	21	~\text	~\text	PROPN
bracis-33646	107	22	{	{	PUNCT
bracis-33646	107	23	implies	imply	VERB
bracis-33646	107	24	}	}	PUNCT
bracis-33646	107	25	~	~	PUNCT
bracis-33646	107	26	w\vdash	w\vdash	NOUN
bracis-33646	107	27	\psi	\psi	PROPN
bracis-33646	107	28	\}.\	\}.\	NUM
bracis-33646	107	29	)	)	PUNCT
bracis-33646	107	30	   	   	SPACE
bracis-33646	107	31	\(\square	\(\square	VERB
bracis-33646	107	32	\	\	NOUN
bracis-33646	107	33	)	)	PUNCT
bracis-33646	108	1	next	next	ADV
bracis-33646	108	2	,	,	PUNCT
bracis-33646	108	3	we	we	PRON
bracis-33646	108	4	introduce	introduce	VERB
bracis-33646	108	5	an	an	DET
bracis-33646	108	6	important	important	ADJ
bracis-33646	108	7	concept	concept	NOUN
bracis-33646	108	8	to	to	ADP
bracis-33646	108	9	our	our	PRON
bracis-33646	108	10	theory	theory	NOUN
bracis-33646	108	11	,	,	PUNCT
bracis-33646	108	12	which	which	PRON
bracis-33646	108	13	will	will	AUX
bracis-33646	108	14	be	be	AUX
bracis-33646	108	15	used	use	VERB
bracis-33646	108	16	to	to	PART
bracis-33646	108	17	characterise	characterise	VERB
bracis-33646	108	18	agm	agm	PROPN
bracis-33646	108	19	rational	rational	ADJ
bracis-33646	108	20	contractions	contraction	NOUN
bracis-33646	108	21	in	in	ADP
bracis-33646	108	22	our	our	PRON
bracis-33646	108	23	framework	framework	NOUN
bracis-33646	108	24	.	.	PUNCT
bracis-33646	109	1	definition	definition	NOUN
bracis-33646	109	2	6	6	NUM
bracis-33646	109	3	let	let	VERB
bracis-33646	109	4	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	109	5	{	{	PUNCT
bracis-33646	109	6	l	l	NOUN
bracis-33646	109	7	}	}	PUNCT
bracis-33646	109	8	)	)	PUNCT
bracis-33646	110	1	=	=	PUNCT
bracis-33646	110	2	\mathcal	\mathcal	ADJ
bracis-33646	110	3	{	{	PUNCT
bracis-33646	110	4	m	m	NOUN
bracis-33646	110	5	}	}	PUNCT
bracis-33646	110	6	=	=	PUNCT
bracis-33646	110	7	\langle	\langle	PROPN
bracis-33646	110	8	m	m	PRON
bracis-33646	110	9	,	,	PUNCT
bracis-33646	110	10	\vdash	\vdash	VERB
bracis-33646	110	11	\rangle	\rangle	NOUN
bracis-33646	110	12	\	\	NOUN
bracis-33646	110	13	)	)	PUNCT
bracis-33646	110	14	be	be	AUX
bracis-33646	110	15	an	an	DET
bracis-33646	110	16	abstract	abstract	ADJ
bracis-33646	110	17	model	model	NOUN
bracis-33646	110	18	theory	theory	NOUN
bracis-33646	110	19	,	,	PUNCT
bracis-33646	110	20	we	we	PRON
bracis-33646	110	21	say	say	VERB
bracis-33646	110	22	a	a	DET
bracis-33646	110	23	set	set	NOUN
bracis-33646	110	24	of	of	ADP
bracis-33646	110	25	interpretations	interpretation	NOUN
bracis-33646	110	26	\(o	\(o	PROPN
bracis-33646	110	27	\subseteq	\subseteq	PROPN
bracis-33646	110	28	m\	m\	NOUN
bracis-33646	110	29	)	)	PUNCT
bracis-33646	110	30	is	be	AUX
bracis-33646	110	31	a	a	DET
bracis-33646	110	32	basic	basic	ADJ
bracis-33646	110	33	open	open	ADJ
bracis-33646	110	34	set	set	NOUN
bracis-33646	110	35	(	(	PUNCT
bracis-33646	110	36	b.o.s	b.o.s	PROPN
bracis-33646	110	37	.	.	PUNCT
bracis-33646	110	38	)	)	PUNCT
bracis-33646	110	39	of	of	ADP
bracis-33646	110	40	\(\mathcal	\(\mathcal	ADJ
bracis-33646	110	41	{	{	PUNCT
bracis-33646	110	42	m}\	m}\	PROPN
bracis-33646	110	43	)	)	PUNCT
bracis-33646	110	44	if	if	SCONJ
bracis-33646	110	45	\(\llbracket	\(\llbracket	NOUN
bracis-33646	110	46	th	th	X
bracis-33646	110	47	(	(	PUNCT
bracis-33646	110	48	o	o	NOUN
bracis-33646	110	49	)	)	PUNCT
bracis-33646	110	50	\rrbracket	\rrbracket	NOUN
bracis-33646	110	51	=	=	SYM
bracis-33646	110	52	o\	o\	NOUN
bracis-33646	110	53	)	)	PUNCT
bracis-33646	110	54	.	.	PUNCT
bracis-33646	111	1	we	we	PRON
bracis-33646	111	2	denote	denote	VERB
bracis-33646	111	3	by	by	ADP
bracis-33646	111	4	\(bo_{\mathcal	\(bo_{\mathcal	PROPN
bracis-33646	111	5	{	{	PUNCT
bracis-33646	111	6	m}}\	m}}\	PROPN
bracis-33646	111	7	)	)	PUNCT
bracis-33646	111	8	the	the	DET
bracis-33646	111	9	set	set	NOUN
bracis-33646	111	10	of	of	ADP
bracis-33646	111	11	all	all	DET
bracis-33646	111	12	b.o.s	b.o.s	PROPN
bracis-33646	111	13	.	.	PROPN
bracis-33646	111	14	’s	’s	PART
bracis-33646	112	1	of	of	ADP
bracis-33646	112	2	\(\mathcal	\(\mathcal	ADJ
bracis-33646	112	3	{	{	PUNCT
bracis-33646	112	4	m}\	m}\	PROPN
bracis-33646	112	5	)	)	PUNCT
bracis-33646	112	6	.	.	PUNCT
bracis-33646	113	1	a	a	DET
bracis-33646	113	2	similar	similar	ADJ
bracis-33646	113	3	notion	notion	NOUN
bracis-33646	113	4	to	to	ADP
bracis-33646	113	5	our	our	PRON
bracis-33646	113	6	basic	basic	ADJ
bracis-33646	113	7	open	open	ADJ
bracis-33646	113	8	sets	set	NOUN
bracis-33646	113	9	appears	appear	VERB
bracis-33646	113	10	in	in	ADP
bracis-33646	113	11	the	the	DET
bracis-33646	113	12	work	work	NOUN
bracis-33646	113	13	of	of	ADP
bracis-33646	113	14	ribeiro	ribeiro	PROPN
bracis-33646	113	15	[	[	X
bracis-33646	113	16	15	15	NUM
bracis-33646	113	17	]	]	PUNCT
bracis-33646	113	18	as	as	ADP
bracis-33646	113	19	complete	complete	ADJ
bracis-33646	113	20	interpretation	interpretation	NOUN
bracis-33646	113	21	sets	set	NOUN
bracis-33646	113	22	and	and	CCONJ
bracis-33646	113	23	plays	play	VERB
bracis-33646	113	24	a	a	DET
bracis-33646	113	25	similar	similar	ADJ
bracis-33646	113	26	role	role	NOUN
bracis-33646	113	27	in	in	ADP
bracis-33646	113	28	the	the	DET
bracis-33646	113	29	semantic	semantic	ADJ
bracis-33646	113	30	machinery	machinery	NOUN
bracis-33646	113	31	we	we	PRON
bracis-33646	113	32	will	will	AUX
bracis-33646	113	33	employ	employ	VERB
bracis-33646	113	34	in	in	ADP
bracis-33646	113	35	this	this	DET
bracis-33646	113	36	work	work	NOUN
bracis-33646	113	37	.	.	PUNCT
bracis-33646	114	1	notice	notice	VERB
bracis-33646	114	2	that	that	SCONJ
bracis-33646	114	3	the	the	DET
bracis-33646	114	4	b.o.s	b.o.s	PROPN
bracis-33646	114	5	.	.	PROPN
bracis-33646	114	6	’s	’s	PART
bracis-33646	114	7	are	be	AUX
bracis-33646	114	8	exactly	exactly	ADV
bracis-33646	114	9	those	those	DET
bracis-33646	114	10	sets	set	NOUN
bracis-33646	114	11	which	which	PRON
bracis-33646	114	12	are	be	AUX
bracis-33646	114	13	the	the	DET
bracis-33646	114	14	interpretation	interpretation	NOUN
bracis-33646	114	15	of	of	ADP
bracis-33646	114	16	a	a	DET
bracis-33646	114	17	theory	theory	NOUN
bracis-33646	114	18	.	.	PUNCT
bracis-33646	115	1	lemma	lemma	PROPN
bracis-33646	115	2	2	2	NUM
bracis-33646	115	3	let	let	VERB
bracis-33646	115	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	115	5	{	{	PUNCT
bracis-33646	115	6	m	m	NOUN
bracis-33646	115	7	}	}	PUNCT
bracis-33646	115	8	=	=	PUNCT
bracis-33646	115	9	\langle	\langle	PROPN
bracis-33646	115	10	m	m	PRON
bracis-33646	115	11	,	,	PUNCT
bracis-33646	115	12	\vdash	\vdash	VERB
bracis-33646	115	13	\rangle	\rangle	NOUN
bracis-33646	115	14	\	\	NOUN
bracis-33646	115	15	)	)	PUNCT
bracis-33646	115	16	be	be	AUX
bracis-33646	115	17	an	an	DET
bracis-33646	115	18	abstract	abstract	ADJ
bracis-33646	115	19	model	model	NOUN
bracis-33646	115	20	theory	theory	NOUN
bracis-33646	115	21	inducing	induce	VERB
bracis-33646	115	22	a	a	DET
bracis-33646	115	23	logic	logic	NOUN
bracis-33646	115	24	\(\mathcal	\(\mathcal	ADJ
bracis-33646	115	25	{	{	PUNCT
bracis-33646	115	26	l}\	l}\	PROPN
bracis-33646	115	27	)	)	PUNCT
bracis-33646	115	28	,	,	PUNCT
bracis-33646	115	29	and	and	CCONJ
bracis-33646	115	30	\(o	\(o	PRON
bracis-33646	115	31	\subseteq	\subseteq	PROPN
bracis-33646	115	32	m\	m\	NOUN
bracis-33646	115	33	)	)	PUNCT
bracis-33646	115	34	.	.	PUNCT
bracis-33646	116	1	\(o	\(o	VERB
bracis-33646	116	2	\in	\in	ADJ
bracis-33646	116	3	bo_\mathcal	bo_\mathcal	PROPN
bracis-33646	116	4	{	{	PUNCT
bracis-33646	116	5	m}\	m}\	PROPN
bracis-33646	116	6	)	)	PUNCT
bracis-33646	116	7	iff	iff	VERB
bracis-33646	116	8	\(o	\(o	NOUN
bracis-33646	117	1	=	=	PUNCT
bracis-33646	117	2	\llbracket	\llbracket	PROPN
bracis-33646	117	3	k\rrbracket	k\rrbracket	PROPN
bracis-33646	117	4	\	\	PROPN
bracis-33646	117	5	)	)	PUNCT
bracis-33646	117	6	for	for	ADP
bracis-33646	117	7	some	some	DET
bracis-33646	117	8	\(k\in	\(k\in	X
bracis-33646	117	9	th_\mathcal	th_\mathcal	PROPN
bracis-33646	117	10	{	{	PUNCT
bracis-33646	117	11	l}\	l}\	PROPN
bracis-33646	117	12	)	)	PUNCT
bracis-33646	117	13	.	.	PUNCT
bracis-33646	118	1	with	with	ADP
bracis-33646	118	2	the	the	DET
bracis-33646	118	3	notion	notion	NOUN
bracis-33646	118	4	of	of	ADP
bracis-33646	118	5	a	a	DET
bracis-33646	118	6	basic	basic	ADJ
bracis-33646	118	7	open	open	ADJ
bracis-33646	118	8	set	set	NOUN
bracis-33646	118	9	,	,	PUNCT
bracis-33646	118	10	we	we	PRON
bracis-33646	118	11	can	can	AUX
bracis-33646	118	12	introduce	introduce	VERB
bracis-33646	118	13	a	a	DET
bracis-33646	118	14	notion	notion	NOUN
bracis-33646	118	15	of	of	ADP
bracis-33646	118	16	closure	closure	NOUN
bracis-33646	118	17	in	in	ADP
bracis-33646	118	18	our	our	PRON
bracis-33646	118	19	models	model	NOUN
bracis-33646	118	20	,	,	PUNCT
bracis-33646	118	21	which	which	PRON
bracis-33646	118	22	complements	complement	VERB
bracis-33646	118	23	a	a	DET
bracis-33646	118	24	set	set	NOUN
bracis-33646	118	25	of	of	ADP
bracis-33646	118	26	interpretations	interpretation	NOUN
bracis-33646	118	27	.	.	PUNCT
bracis-33646	119	1	definition	definition	NOUN
bracis-33646	119	2	7	7	NUM
bracis-33646	119	3	let	let	VERB
bracis-33646	119	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	119	5	{	{	PUNCT
bracis-33646	119	6	m	m	NOUN
bracis-33646	119	7	}	}	PUNCT
bracis-33646	119	8	=	=	PUNCT
bracis-33646	119	9	\langle	\langle	PROPN
bracis-33646	119	10	m	m	PRON
bracis-33646	119	11	,	,	PUNCT
bracis-33646	119	12	\vdash	\vdash	VERB
bracis-33646	119	13	\rangle	\rangle	NOUN
bracis-33646	119	14	\	\	NOUN
bracis-33646	119	15	)	)	PUNCT
bracis-33646	119	16	be	be	AUX
bracis-33646	119	17	an	an	DET
bracis-33646	119	18	abstract	abstract	ADJ
bracis-33646	119	19	model	model	NOUN
bracis-33646	119	20	theory	theory	NOUN
bracis-33646	119	21	inducing	induce	VERB
bracis-33646	119	22	a	a	DET
bracis-33646	119	23	logic	logic	NOUN
bracis-33646	119	24	\(\mathcal	\(\mathcal	ADJ
bracis-33646	119	25	{	{	PUNCT
bracis-33646	119	26	l}\	l}\	PROPN
bracis-33646	119	27	)	)	PUNCT
bracis-33646	119	28	,	,	PUNCT
bracis-33646	119	29	and	and	CCONJ
bracis-33646	119	30	\(x	\(x	NOUN
bracis-33646	119	31	\subseteq	\subseteq	PROPN
bracis-33646	119	32	m\	m\	NOUN
bracis-33646	119	33	)	)	PUNCT
bracis-33646	119	34	a	a	DET
bracis-33646	119	35	set	set	NOUN
bracis-33646	119	36	of	of	ADP
bracis-33646	119	37	interpretations	interpretation	NOUN
bracis-33646	119	38	.	.	PUNCT
bracis-33646	120	1	we	we	PRON
bracis-33646	120	2	define	define	VERB
bracis-33646	120	3	the	the	DET
bracis-33646	120	4	closure	closure	NOUN
bracis-33646	120	5	of	of	ADP
bracis-33646	120	6	x	x	PRON
bracis-33646	120	7	,	,	PUNCT
bracis-33646	120	8	denoted	denote	VERB
bracis-33646	120	9	by	by	ADP
bracis-33646	120	10	cl(x	cl(x	NOUN
bracis-33646	120	11	)	)	PUNCT
bracis-33646	120	12	,	,	PUNCT
bracis-33646	120	13	the	the	DET
bracis-33646	120	14	biggest	big	ADJ
bracis-33646	120	15	set	set	NOUN
bracis-33646	120	16	\(o	\(o	PROPN
bracis-33646	120	17	\subseteq	\subseteq	PROPN
bracis-33646	120	18	\mathcal	\mathcal	PROPN
bracis-33646	120	19	{	{	PUNCT
bracis-33646	120	20	l}\	l}\	PROPN
bracis-33646	120	21	)	)	PUNCT
bracis-33646	120	22	,	,	PUNCT
bracis-33646	120	23	s.t	s.t	PROPN
bracis-33646	120	24	.	.	PROPN
bracis-33646	120	25	\(th(o	\(th(o	PROPN
bracis-33646	120	26	)	)	PUNCT
bracis-33646	120	27	=	=	PUNCT
bracis-33646	120	28	th(x)\	th(x)\	NUM
bracis-33646	120	29	)	)	PUNCT
bracis-33646	120	30	.	.	PUNCT
bracis-33646	121	1	it	it	PRON
bracis-33646	121	2	is	be	AUX
bracis-33646	121	3	not	not	PART
bracis-33646	121	4	difficult	difficult	ADJ
bracis-33646	121	5	to	to	PART
bracis-33646	121	6	see	see	VERB
bracis-33646	121	7	that	that	PRON
bracis-33646	121	8	cl(x	cl(x	NOUN
bracis-33646	121	9	)	)	PUNCT
bracis-33646	121	10	exists	exist	VERB
bracis-33646	121	11	and	and	CCONJ
bracis-33646	121	12	is	be	AUX
bracis-33646	121	13	unique	unique	ADJ
bracis-33646	121	14	,	,	PUNCT
bracis-33646	121	15	and	and	CCONJ
bracis-33646	121	16	\(cl(x	\(cl(x	PROPN
bracis-33646	121	17	)	)	PUNCT
bracis-33646	122	1	=	=	SYM
bracis-33646	123	1	\llbracket	\llbracket	PROPN
bracis-33646	123	2	th(x)\rrbracket	th(x)\rrbracket	PROPN
bracis-33646	123	3	\	\	PROPN
bracis-33646	123	4	)	)	PUNCT
bracis-33646	123	5	,	,	PUNCT
bracis-33646	123	6	as	as	ADP
bracis-33646	123	7	\(\mathcal	\(\mathcal	ADJ
bracis-33646	123	8	{	{	PUNCT
bracis-33646	123	9	l}\	l}\	PROPN
bracis-33646	123	10	)	)	PUNCT
bracis-33646	123	11	is	be	AUX
bracis-33646	123	12	tarskian	tarskian	NOUN
bracis-33646	123	13	.	.	PUNCT
bracis-33646	124	1	more	more	ADV
bracis-33646	124	2	so	so	ADV
bracis-33646	124	3	,	,	PUNCT
bracis-33646	124	4	cl	cl	NOUN
bracis-33646	124	5	is	be	AUX
bracis-33646	124	6	,	,	PUNCT
bracis-33646	124	7	in	in	ADP
bracis-33646	124	8	fact	fact	NOUN
bracis-33646	124	9	,	,	PUNCT
bracis-33646	124	10	a	a	DET
bracis-33646	124	11	closure	closure	NOUN
bracis-33646	124	12	operator	operator	NOUN
bracis-33646	124	13	.	.	PUNCT
bracis-33646	125	1	as	as	SCONJ
bracis-33646	125	2	stated	state	VERB
bracis-33646	125	3	before	before	ADV
bracis-33646	125	4	,	,	PUNCT
bracis-33646	125	5	since	since	SCONJ
bracis-33646	125	6	at	at	ADP
bracis-33646	125	7	least	least	ADJ
bracis-33646	125	8	the	the	DET
bracis-33646	125	9	works	work	NOUN
bracis-33646	125	10	of	of	ADP
bracis-33646	125	11	stone	stone	NOUN
bracis-33646	125	12	 	 	SPACE
bracis-33646	126	1	[	[	X
bracis-33646	126	2	20	20	NUM
bracis-33646	126	3	]	]	PUNCT
bracis-33646	126	4	,	,	PUNCT
bracis-33646	126	5	it	it	PRON
bracis-33646	126	6	is	be	AUX
bracis-33646	126	7	well	well	ADV
bracis-33646	126	8	-	-	PUNCT
bracis-33646	126	9	known	know	VERB
bracis-33646	126	10	that	that	SCONJ
bracis-33646	126	11	logics	logic	NOUN
bracis-33646	126	12	have	have	VERB
bracis-33646	126	13	a	a	DET
bracis-33646	126	14	deep	deep	ADJ
bracis-33646	126	15	connection	connection	NOUN
bracis-33646	126	16	with	with	ADP
bracis-33646	126	17	topology	topology	NOUN
bracis-33646	126	18	.	.	PUNCT
bracis-33646	127	1	this	this	DET
bracis-33646	127	2	connection	connection	NOUN
bracis-33646	127	3	is	be	AUX
bracis-33646	127	4	the	the	DET
bracis-33646	127	5	subject	subject	NOUN
bracis-33646	127	6	of	of	ADP
bracis-33646	127	7	study	study	NOUN
bracis-33646	127	8	in	in	ADP
bracis-33646	127	9	areas	area	NOUN
bracis-33646	127	10	such	such	ADJ
bracis-33646	127	11	as	as	ADP
bracis-33646	127	12	abstract	abstract	ADJ
bracis-33646	127	13	model	model	NOUN
bracis-33646	127	14	theory	theory	NOUN
bracis-33646	127	15	,	,	PUNCT
bracis-33646	127	16	topological	topological	ADJ
bracis-33646	127	17	logic	logic	NOUN
bracis-33646	127	18	,	,	PUNCT
bracis-33646	127	19	etc	etc	X
bracis-33646	127	20	.	.	X
bracis-33646	127	21	here	here	ADV
bracis-33646	127	22	,	,	PUNCT
bracis-33646	127	23	we	we	PRON
bracis-33646	127	24	will	will	AUX
bracis-33646	127	25	present	present	VERB
bracis-33646	127	26	how	how	SCONJ
bracis-33646	127	27	topological	topological	ADJ
bracis-33646	127	28	spaces	space	NOUN
bracis-33646	127	29	can	can	AUX
bracis-33646	127	30	be	be	AUX
bracis-33646	127	31	thought	think	VERB
bracis-33646	127	32	of	of	ADP
bracis-33646	127	33	as	as	ADP
bracis-33646	127	34	spaces	space	NOUN
bracis-33646	127	35	of	of	ADP
bracis-33646	127	36	interpretations	interpretation	NOUN
bracis-33646	127	37	for	for	ADP
bracis-33646	127	38	a	a	DET
bracis-33646	127	39	logic	logic	NOUN
bracis-33646	127	40	and	and	CCONJ
bracis-33646	127	41	,	,	PUNCT
bracis-33646	127	42	in	in	ADP
bracis-33646	127	43	doing	do	VERB
bracis-33646	127	44	so	so	ADV
bracis-33646	127	45	,	,	PUNCT
bracis-33646	127	46	help	help	VERB
bracis-33646	127	47	shed	shed	VERB
bracis-33646	127	48	light	light	NOUN
bracis-33646	127	49	on	on	ADP
bracis-33646	127	50	the	the	DET
bracis-33646	127	51	theoretical	theoretical	ADJ
bracis-33646	127	52	inspirations	inspiration	NOUN
bracis-33646	127	53	for	for	ADP
bracis-33646	127	54	our	our	PRON
bracis-33646	127	55	constructions	construction	NOUN
bracis-33646	127	56	.	.	PUNCT
bracis-33646	128	1	definition	definition	NOUN
bracis-33646	128	2	8	8	NUM
bracis-33646	128	3	we	we	PRON
bracis-33646	128	4	call	call	VERB
bracis-33646	128	5	topological	topological	ADJ
bracis-33646	128	6	space	space	NOUN
bracis-33646	128	7	any	any	DET
bracis-33646	128	8	tuple	tuple	NOUN
bracis-33646	128	9	\(\mathcal	\(\mathcal	ADJ
bracis-33646	128	10	{	{	PUNCT
bracis-33646	128	11	w	w	NOUN
bracis-33646	128	12	}	}	PUNCT
bracis-33646	128	13	=	=	PUNCT
bracis-33646	128	14	\langle	\langle	PROPN
bracis-33646	128	15	w	w	PROPN
bracis-33646	128	16	,	,	PUNCT
bracis-33646	128	17	\tau	\tau	PROPN
bracis-33646	128	18	\rangle	\rangle	NOUN
bracis-33646	128	19	\	\	PROPN
bracis-33646	128	20	)	)	PUNCT
bracis-33646	128	21	,	,	PUNCT
bracis-33646	128	22	where	where	SCONJ
bracis-33646	128	23	w	w	NOUN
bracis-33646	128	24	is	be	AUX
bracis-33646	128	25	a	a	DET
bracis-33646	128	26	non	non	ADJ
bracis-33646	128	27	-	-	ADJ
bracis-33646	128	28	empty	empty	ADJ
bracis-33646	128	29	set	set	NOUN
bracis-33646	128	30	and	and	CCONJ
bracis-33646	128	31	\(\tau	\(\tau	ADV
bracis-33646	128	32	\	\	NOUN
bracis-33646	128	33	)	)	PUNCT
bracis-33646	128	34	is	be	AUX
bracis-33646	128	35	a	a	DET
bracis-33646	128	36	collection	collection	NOUN
bracis-33646	128	37	of	of	ADP
bracis-33646	128	38	subsets	subset	NOUN
bracis-33646	128	39	of	of	ADP
bracis-33646	128	40	w	w	ADP
bracis-33646	128	41	satisfying	satisfying	ADJ
bracis-33646	129	1	:	:	PUNCT
bracis-33646	129	2	1	1	X
bracis-33646	129	3	.	.	X
bracis-33646	129	4	\(\emptyset	\(\emptyset	NOUN
bracis-33646	129	5	,	,	PUNCT
bracis-33646	129	6	w\in	w\in	NOUN
bracis-33646	129	7	\tau	\tau	PROPN
bracis-33646	129	8	\	\	PROPN
bracis-33646	129	9	)	)	PUNCT
bracis-33646	129	10	;	;	PUNCT
bracis-33646	130	1	2	2	X
bracis-33646	130	2	.	.	X
bracis-33646	131	1	if	if	SCONJ
bracis-33646	131	2	\(o	\(o	PROPN
bracis-33646	131	3	,	,	PUNCT
bracis-33646	131	4	o'\in	o'\in	NOUN
bracis-33646	131	5	\tau	\tau	ADJ
bracis-33646	131	6	\	\	PROPN
bracis-33646	131	7	)	)	PUNCT
bracis-33646	131	8	,	,	PUNCT
bracis-33646	131	9	then	then	ADV
bracis-33646	131	10	\(o\cap	\(o\cap	VERB
bracis-33646	131	11	o	o	NOUN
bracis-33646	131	12	'	'	PUNCT
bracis-33646	131	13	\in	\in	PROPN
bracis-33646	131	14	\tau	\tau	ADJ
bracis-33646	131	15	\	\	PROPN
bracis-33646	131	16	)	)	PUNCT
bracis-33646	131	17	;	;	PUNCT
bracis-33646	131	18	3	3	X
bracis-33646	131	19	.	.	X
bracis-33646	131	20	if	if	SCONJ
bracis-33646	131	21	\(\mathcal	\(\mathcal	ADJ
bracis-33646	131	22	{	{	PUNCT
bracis-33646	131	23	o}\subseteq	o}\subseteq	PROPN
bracis-33646	131	24	\tau	\tau	PROPN
bracis-33646	131	25	\	\	PROPN
bracis-33646	131	26	)	)	PUNCT
bracis-33646	131	27	,	,	PUNCT
bracis-33646	131	28	then	then	ADV
bracis-33646	131	29	\(\bigcup	\(\bigcup	DET
bracis-33646	131	30	\mathcal	\mathcal	ADJ
bracis-33646	131	31	{	{	PUNCT
bracis-33646	131	32	o	o	NOUN
bracis-33646	131	33	}	}	PUNCT
bracis-33646	131	34	\in	\in	ADJ
bracis-33646	131	35	\tau	\tau	ADJ
bracis-33646	131	36	\	\	PROPN
bracis-33646	131	37	)	)	PUNCT
bracis-33646	131	38	.	.	PUNCT
bracis-33646	132	1	the	the	DET
bracis-33646	132	2	elements	element	NOUN
bracis-33646	132	3	of	of	ADP
bracis-33646	132	4	\(\tau	\(\tau	PROPN
bracis-33646	132	5	\	\	NOUN
bracis-33646	132	6	)	)	PUNCT
bracis-33646	132	7	are	be	AUX
bracis-33646	132	8	called	call	VERB
bracis-33646	132	9	open	open	ADJ
bracis-33646	132	10	sets	set	NOUN
bracis-33646	132	11	of	of	ADP
bracis-33646	132	12	\(\mathcal	\(\mathcal	ADJ
bracis-33646	132	13	{	{	PUNCT
bracis-33646	132	14	w}\	w}\	PROPN
bracis-33646	132	15	)	)	PUNCT
bracis-33646	132	16	.	.	PUNCT
bracis-33646	133	1	definition	definition	NOUN
bracis-33646	133	2	9	9	NUM
bracis-33646	133	3	let	let	VERB
bracis-33646	133	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	133	5	{	{	PUNCT
bracis-33646	133	6	l	l	NOUN
bracis-33646	133	7	}	}	PUNCT
bracis-33646	133	8	=	=	PUNCT
bracis-33646	133	9	\langle	\langle	PROPN
bracis-33646	133	10	l	l	NOUN
bracis-33646	133	11	,	,	PUNCT
bracis-33646	133	12	cn\rangle	cn\rangle	NOUN
bracis-33646	133	13	\	\	NOUN
bracis-33646	133	14	)	)	PUNCT
bracis-33646	133	15	be	be	AUX
bracis-33646	133	16	a	a	DET
bracis-33646	133	17	logic	logic	NOUN
bracis-33646	133	18	and	and	CCONJ
bracis-33646	133	19	\(\mathcal	\(\mathcal	ADJ
bracis-33646	133	20	{	{	PUNCT
bracis-33646	133	21	w	w	NOUN
bracis-33646	133	22	}	}	PUNCT
bracis-33646	133	23	=	=	PUNCT
bracis-33646	133	24	\langle	\langle	PROPN
bracis-33646	133	25	w	w	PROPN
bracis-33646	133	26	,	,	PUNCT
bracis-33646	133	27	\tau	\tau	PROPN
bracis-33646	134	1	\rangle	\rangle	NOUN
bracis-33646	134	2	\	\	PROPN
bracis-33646	134	3	)	)	PUNCT
bracis-33646	134	4	a	a	DET
bracis-33646	134	5	topological	topological	ADJ
bracis-33646	134	6	space	space	NOUN
bracis-33646	134	7	.	.	PUNCT
bracis-33646	135	1	we	we	PRON
bracis-33646	135	2	say	say	VERB
bracis-33646	135	3	\(\mathcal	\(\mathcal	ADJ
bracis-33646	135	4	{	{	PUNCT
bracis-33646	135	5	w}\	w}\	PROPN
bracis-33646	135	6	)	)	PUNCT
bracis-33646	135	7	induces	induce	VERB
bracis-33646	135	8	the	the	DET
bracis-33646	135	9	logic	logic	NOUN
bracis-33646	135	10	\(\mathcal	\(\mathcal	ADJ
bracis-33646	135	11	{	{	PUNCT
bracis-33646	135	12	l}\	l}\	PROPN
bracis-33646	135	13	)	)	PUNCT
bracis-33646	135	14	if	if	SCONJ
bracis-33646	135	15	there	there	PRON
bracis-33646	135	16	is	be	VERB
bracis-33646	135	17	some	some	DET
bracis-33646	135	18	function	function	NOUN
bracis-33646	135	19	\(f	\(f	NOUN
bracis-33646	135	20	:	:	PUNCT
bracis-33646	135	21	\tau	\tau	PROPN
bracis-33646	135	22	\rightarrow	\rightarrow	PROPN
bracis-33646	135	23	th_\mathcal	th_\mathcal	PROPN
bracis-33646	135	24	{	{	PUNCT
bracis-33646	135	25	l}\	l}\	PROPN
bracis-33646	135	26	)	)	PUNCT
bracis-33646	135	27	s.t	s.t	PROPN
bracis-33646	135	28	.	.	PUNCT
bracis-33646	136	1	if	if	SCONJ
bracis-33646	136	2	\(o	\(o	PROPN
bracis-33646	136	3	\subseteq	\subseteq	PROPN
bracis-33646	136	4	o'\	o'\	PROPN
bracis-33646	136	5	)	)	PUNCT
bracis-33646	136	6	then	then	ADV
bracis-33646	136	7	\(f(o	\(f(o	PROPN
bracis-33646	136	8	'	'	PART
bracis-33646	136	9	)	)	PUNCT
bracis-33646	136	10	\subseteq	\subseteq	PROPN
bracis-33646	136	11	f(o)\	f(o)\	PROPN
bracis-33646	136	12	)	)	PUNCT
bracis-33646	136	13	;	;	PUNCT
bracis-33646	136	14	\(f(\bigcup	\(f(\bigcup	X
bracis-33646	137	1	\mathcal	\mathcal	PROPN
bracis-33646	137	2	{	{	PUNCT
bracis-33646	137	3	o	o	NOUN
bracis-33646	137	4	}	}	PUNCT
bracis-33646	137	5	)	)	PUNCT
bracis-33646	137	6	=	=	PUNCT
bracis-33646	138	1	\bigcap	\bigcap	PUNCT
bracis-33646	138	2	_	_	PUNCT
bracis-33646	138	3	{	{	PUNCT
bracis-33646	138	4	o\in	o\in	PROPN
bracis-33646	138	5	\mathcal	\mathcal	PROPN
bracis-33646	138	6	{	{	PUNCT
bracis-33646	138	7	o	o	NOUN
bracis-33646	138	8	}	}	PUNCT
bracis-33646	138	9	}	}	PUNCT
bracis-33646	138	10	f(o)\	f(o)\	NOUN
bracis-33646	138	11	)	)	PUNCT
bracis-33646	138	12	for	for	ADP
bracis-33646	138	13	any	any	DET
bracis-33646	138	14	theories	theory	NOUN
bracis-33646	138	15	\(k	\(k	NOUN
bracis-33646	138	16	,	,	PUNCT
bracis-33646	138	17	k'\in	k'\in	PROPN
bracis-33646	138	18	th_\mathcal	th_\mathcal	PROPN
bracis-33646	138	19	{	{	PUNCT
bracis-33646	138	20	l}\	l}\	PROPN
bracis-33646	138	21	)	)	PUNCT
bracis-33646	138	22	,	,	PUNCT
bracis-33646	138	23	it	it	PRON
bracis-33646	138	24	holds	hold	VERB
bracis-33646	138	25	\(f(\bigcup	\(f(\bigcup	DET
bracis-33646	138	26	f^{-1}(k	f^{-1}(k	SYM
bracis-33646	138	27	)	)	PUNCT
bracis-33646	138	28	\cap	\cap	NOUN
bracis-33646	138	29	\bigcup	\bigcup	PROPN
bracis-33646	138	30	f^{-1}(k	f^{-1}(k	PRON
bracis-33646	138	31	'	'	NUM
bracis-33646	138	32	)	)	PUNCT
bracis-33646	138	33	)	)	PUNCT
bracis-33646	139	1	=	=	PRON
bracis-33646	139	2	cn(k	cn(k	VERB
bracis-33646	139	3	\cup	\cup	VERB
bracis-33646	139	4	k')\	k')\	NOUN
bracis-33646	139	5	)	)	PUNCT
bracis-33646	139	6	in	in	ADP
bracis-33646	139	7	this	this	DET
bracis-33646	139	8	case	case	NOUN
bracis-33646	139	9	,	,	PUNCT
bracis-33646	139	10	we	we	PRON
bracis-33646	139	11	say	say	VERB
bracis-33646	139	12	f	f	PROPN
bracis-33646	139	13	is	be	AUX
bracis-33646	139	14	an	an	DET
bracis-33646	139	15	\(\mathcal	\(\mathcal	ADJ
bracis-33646	139	16	{	{	PUNCT
bracis-33646	139	17	l}\)-interpretation	l}\)-interpretation	NOUN
bracis-33646	139	18	on	on	ADP
bracis-33646	139	19	\(\mathcal	\(\mathcal	ADJ
bracis-33646	139	20	{	{	PUNCT
bracis-33646	139	21	w}\	w}\	PROPN
bracis-33646	139	22	)	)	PUNCT
bracis-33646	139	23	.	.	PUNCT
bracis-33646	140	1	with	with	ADP
bracis-33646	140	2	that	that	PRON
bracis-33646	140	3	,	,	PUNCT
bracis-33646	140	4	it	it	PRON
bracis-33646	140	5	is	be	AUX
bracis-33646	140	6	easy	easy	ADJ
bracis-33646	140	7	to	to	PART
bracis-33646	140	8	see	see	VERB
bracis-33646	140	9	that	that	SCONJ
bracis-33646	140	10	any	any	DET
bracis-33646	140	11	tarskian	tarskian	ADJ
bracis-33646	140	12	logic	logic	NOUN
bracis-33646	140	13	is	be	AUX
bracis-33646	140	14	induced	induce	VERB
bracis-33646	140	15	by	by	ADP
bracis-33646	140	16	some	some	DET
bracis-33646	140	17	topological	topological	ADJ
bracis-33646	140	18	space	space	NOUN
bracis-33646	140	19	since	since	SCONJ
bracis-33646	140	20	we	we	PRON
bracis-33646	140	21	can	can	AUX
bracis-33646	140	22	use	use	VERB
bracis-33646	140	23	the	the	DET
bracis-33646	140	24	lattice	lattice	NOUN
bracis-33646	140	25	of	of	ADP
bracis-33646	140	26	theories	theory	NOUN
bracis-33646	140	27	to	to	PART
bracis-33646	140	28	construct	construct	VERB
bracis-33646	140	29	it	it	PRON
bracis-33646	140	30	,	,	PUNCT
bracis-33646	140	31	in	in	ADP
bracis-33646	140	32	a	a	DET
bracis-33646	140	33	similar	similar	ADJ
bracis-33646	140	34	fashion	fashion	NOUN
bracis-33646	140	35	to	to	ADP
bracis-33646	140	36	what	what	PRON
bracis-33646	140	37	we	we	PRON
bracis-33646	140	38	have	have	AUX
bracis-33646	140	39	done	do	VERB
bracis-33646	140	40	in	in	ADP
bracis-33646	140	41	proposition	proposition	NOUN
bracis-33646	140	42	 	 	SPACE
bracis-33646	140	43	2	2	NUM
bracis-33646	140	44	.	.	PUNCT
bracis-33646	140	45	proposition	proposition	NOUN
bracis-33646	140	46	3	3	NUM
bracis-33646	140	47	let	let	VERB
bracis-33646	140	48	\(\mathcal	\(\mathcal	ADJ
bracis-33646	140	49	{	{	PUNCT
bracis-33646	140	50	l	l	NOUN
bracis-33646	140	51	}	}	PUNCT
bracis-33646	140	52	=	=	PUNCT
bracis-33646	140	53	\langle	\langle	PROPN
bracis-33646	140	54	l	l	NOUN
bracis-33646	140	55	,	,	PUNCT
bracis-33646	140	56	cn\rangle	cn\rangle	NOUN
bracis-33646	140	57	\	\	NOUN
bracis-33646	140	58	)	)	PUNCT
bracis-33646	140	59	be	be	AUX
bracis-33646	140	60	a	a	DET
bracis-33646	140	61	logic	logic	NOUN
bracis-33646	140	62	,	,	PUNCT
bracis-33646	140	63	there	there	PRON
bracis-33646	140	64	is	be	VERB
bracis-33646	140	65	a	a	DET
bracis-33646	140	66	topological	topological	ADJ
bracis-33646	140	67	space	space	NOUN
bracis-33646	140	68	\(\mathcal	\(\mathcal	ADJ
bracis-33646	140	69	{	{	PUNCT
bracis-33646	140	70	w	w	NOUN
bracis-33646	140	71	}	}	PUNCT
bracis-33646	140	72	=	=	PUNCT
bracis-33646	140	73	\langle	\langle	PROPN
bracis-33646	140	74	w	w	PROPN
bracis-33646	140	75	,	,	PUNCT
bracis-33646	140	76	\tau	\tau	PROPN
bracis-33646	140	77	\rangle	\rangle	NOUN
bracis-33646	140	78	\	\	NOUN
bracis-33646	140	79	)	)	PUNCT
bracis-33646	140	80	inducing	induce	VERB
bracis-33646	140	81	\(\mathcal	\(\mathcal	ADJ
bracis-33646	140	82	{	{	PUNCT
bracis-33646	140	83	l}\	l}\	PROPN
bracis-33646	140	84	)	)	PUNCT
bracis-33646	140	85	.	.	PUNCT
bracis-33646	141	1	proof	proof	NOUN
bracis-33646	141	2	take	take	VERB
bracis-33646	141	3	\(\mathcal	\(\mathcal	ADJ
bracis-33646	141	4	{	{	PUNCT
bracis-33646	141	5	w	w	NOUN
bracis-33646	141	6	}	}	PUNCT
bracis-33646	141	7	=	=	PUNCT
bracis-33646	141	8	\langle	\langle	PRON
bracis-33646	141	9	th_\mathcal	th_\mathcal	ADJ
bracis-33646	141	10	{	{	PUNCT
bracis-33646	141	11	l	l	NOUN
bracis-33646	141	12	}	}	PUNCT
bracis-33646	141	13	,	,	PUNCT
bracis-33646	142	1	\tau	\tau	PROPN
bracis-33646	142	2	\rangle	\rangle	NOUN
bracis-33646	142	3	\	\	NOUN
bracis-33646	142	4	)	)	PUNCT
bracis-33646	142	5	s.t	s.t	PROPN
bracis-33646	142	6	.	.	PROPN
bracis-33646	142	7	that	that	DET
bracis-33646	142	8	topology	topology	NOUN
bracis-33646	142	9	\(\tau	\(\tau	VERB
bracis-33646	142	10	\	\	NOUN
bracis-33646	142	11	)	)	PUNCT
bracis-33646	142	12	is	be	AUX
bracis-33646	142	13	the	the	DET
bracis-33646	142	14	upset	upset	ADJ
bracis-33646	142	15	topology	topology	NOUN
bracis-33646	142	16	from	from	ADP
bracis-33646	142	17	the	the	DET
bracis-33646	142	18	lattice	lattice	NOUN
bracis-33646	142	19	of	of	ADP
bracis-33646	142	20	theories	theory	NOUN
bracis-33646	142	21	,	,	PUNCT
bracis-33646	142	22	i.e.	i.e.	X
bracis-33646	142	23	the	the	DET
bracis-33646	142	24	topology	topology	NOUN
bracis-33646	142	25	obtained	obtain	VERB
bracis-33646	142	26	from	from	ADP
bracis-33646	142	27	the	the	DET
bracis-33646	142	28	subbase	subbase	NOUN
bracis-33646	142	29	\(\mathcal	\(\mathcal	ADJ
bracis-33646	142	30	{	{	PUNCT
bracis-33646	142	31	b	b	NOUN
bracis-33646	142	32	}	}	PUNCT
bracis-33646	142	33	=	=	SYM
bracis-33646	142	34	\{\uparrow	\{\uparrow	NUM
bracis-33646	142	35	t~|~t\in	t~|~t\in	ADJ
bracis-33646	142	36	th_\mathcal	th_\mathcal	ADJ
bracis-33646	142	37	{	{	PUNCT
bracis-33646	142	38	l}\}\	l}\}\	NOUN
bracis-33646	142	39	)	)	PUNCT
bracis-33646	142	40	,	,	PUNCT
bracis-33646	142	41	where	where	SCONJ
bracis-33646	142	42	\(\uparrow	\(\uparrow	VERB
bracis-33646	142	43	t	t	PROPN
bracis-33646	142	44	=	=	PUNCT
bracis-33646	142	45	\{t'\in	\{t'\in	NOUN
bracis-33646	142	46	th_\mathcal	th_\mathcal	PROPN
bracis-33646	142	47	{	{	PUNCT
bracis-33646	142	48	l}~|~	l}~|~	PROPN
bracis-33646	142	49	t\subseteq	t\subseteq	PROPN
bracis-33646	142	50	t'\}\	t'\}\	NOUN
bracis-33646	142	51	)	)	PUNCT
bracis-33646	142	52	.	.	PUNCT
bracis-33646	143	1	it	it	PRON
bracis-33646	143	2	is	be	AUX
bracis-33646	143	3	trivial	trivial	ADJ
bracis-33646	143	4	to	to	PART
bracis-33646	143	5	verify	verify	VERB
bracis-33646	143	6	that	that	SCONJ
bracis-33646	143	7	the	the	DET
bracis-33646	143	8	function	function	NOUN
bracis-33646	143	9	\(f(o	\(f(o	VERB
bracis-33646	143	10	)	)	PUNCT
bracis-33646	143	11	=	=	SYM
bracis-33646	143	12	\bigcap	\bigcap	NOUN
bracis-33646	143	13	o\	o\	NOUN
bracis-33646	143	14	)	)	PUNCT
bracis-33646	143	15	is	be	AUX
bracis-33646	143	16	an	an	DET
bracis-33646	143	17	\(\mathcal	\(\mathcal	ADJ
bracis-33646	143	18	{	{	PUNCT
bracis-33646	143	19	l}\)-interpretation	l}\)-interpretation	NOUN
bracis-33646	143	20	on	on	ADP
bracis-33646	143	21	\(\mathcal	\(\mathcal	ADJ
bracis-33646	143	22	{	{	PUNCT
bracis-33646	143	23	w}\	w}\	PROPN
bracis-33646	143	24	)	)	PUNCT
bracis-33646	143	25	.	.	PUNCT
bracis-33646	144	1	by	by	ADP
bracis-33646	144	2	contrasting	contrast	VERB
bracis-33646	144	3	propositions	proposition	NOUN
bracis-33646	144	4	 	 	SPACE
bracis-33646	144	5	2	2	NUM
bracis-33646	144	6	and	and	CCONJ
bracis-33646	144	7	3	3	NUM
bracis-33646	144	8	,	,	PUNCT
bracis-33646	144	9	we	we	PRON
bracis-33646	144	10	are	be	AUX
bracis-33646	144	11	able	able	ADJ
bracis-33646	144	12	to	to	PART
bracis-33646	144	13	see	see	VERB
bracis-33646	144	14	that	that	SCONJ
bracis-33646	144	15	there	there	PRON
bracis-33646	144	16	is	be	VERB
bracis-33646	144	17	a	a	DET
bracis-33646	144	18	strong	strong	ADJ
bracis-33646	144	19	connection	connection	NOUN
bracis-33646	144	20	between	between	ADP
bracis-33646	144	21	abstract	abstract	ADJ
bracis-33646	144	22	model	model	NOUN
bracis-33646	144	23	theories	theory	NOUN
bracis-33646	144	24	and	and	CCONJ
bracis-33646	144	25	topological	topological	ADJ
bracis-33646	144	26	spaces	space	NOUN
bracis-33646	144	27	equipped	equip	VERB
bracis-33646	144	28	with	with	ADP
bracis-33646	144	29	interpretation	interpretation	NOUN
bracis-33646	144	30	functions	function	NOUN
bracis-33646	144	31	.	.	PUNCT
bracis-33646	145	1	lemma	lemma	PROPN
bracis-33646	145	2	3	3	NUM
bracis-33646	145	3	let	let	VERB
bracis-33646	145	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	145	5	{	{	PUNCT
bracis-33646	145	6	w	w	NOUN
bracis-33646	145	7	}	}	PUNCT
bracis-33646	145	8	=	=	PUNCT
bracis-33646	145	9	\langle	\langle	PROPN
bracis-33646	145	10	w	w	PROPN
bracis-33646	145	11	,	,	PUNCT
bracis-33646	145	12	\tau	\tau	PROPN
bracis-33646	145	13	\rangle	\rangle	NOUN
bracis-33646	145	14	\	\	NUM
bracis-33646	145	15	)	)	PUNCT
bracis-33646	145	16	be	be	AUX
bracis-33646	145	17	a	a	DET
bracis-33646	145	18	topological	topological	ADJ
bracis-33646	145	19	space	space	NOUN
bracis-33646	145	20	inducing	induce	VERB
bracis-33646	145	21	a	a	DET
bracis-33646	145	22	logic	logic	NOUN
bracis-33646	145	23	\(\mathcal	\(\mathcal	ADJ
bracis-33646	145	24	{	{	PUNCT
bracis-33646	145	25	l}\	l}\	PROPN
bracis-33646	145	26	)	)	PUNCT
bracis-33646	145	27	and	and	CCONJ
bracis-33646	145	28	\(f:\tau	\(f:\tau	PROPN
bracis-33646	145	29	\mapsto	\mapsto	PROPN
bracis-33646	145	30	th_\mathcal	th_\mathcal	PROPN
bracis-33646	145	31	{	{	PUNCT
bracis-33646	145	32	l}\	l}\	PROPN
bracis-33646	145	33	)	)	PUNCT
bracis-33646	145	34	an	an	DET
bracis-33646	145	35	\(\mathcal	\(\mathcal	ADJ
bracis-33646	145	36	{	{	PUNCT
bracis-33646	145	37	l}\)-interpretation	l}\)-interpretation	NOUN
bracis-33646	145	38	on	on	ADP
bracis-33646	145	39	\(\mathcal	\(\mathcal	ADJ
bracis-33646	145	40	{	{	PUNCT
bracis-33646	145	41	w}\	w}\	PROPN
bracis-33646	145	42	)	)	PUNCT
bracis-33646	145	43	.	.	PUNCT
bracis-33646	146	1	the	the	DET
bracis-33646	146	2	abstract	abstract	ADJ
bracis-33646	146	3	model	model	NOUN
bracis-33646	146	4	theory	theory	NOUN
bracis-33646	146	5	\(\mathcal	\(\mathcal	ADJ
bracis-33646	146	6	{	{	PUNCT
bracis-33646	146	7	m}_\mathcal	m}_\mathcal	ADJ
bracis-33646	146	8	{	{	PUNCT
bracis-33646	146	9	w	w	NOUN
bracis-33646	146	10	}	}	PUNCT
bracis-33646	146	11	=	=	PUNCT
bracis-33646	146	12	\langle	\langle	PROPN
bracis-33646	146	13	w	w	PROPN
bracis-33646	146	14	,	,	PUNCT
bracis-33646	146	15	\vdash	\vdash	VERB
bracis-33646	146	16	\rangle	\rangle	NOUN
bracis-33646	146	17	\	\	NOUN
bracis-33646	146	18	)	)	PUNCT
bracis-33646	146	19	s.t	s.t	PROPN
bracis-33646	146	20	.	.	PROPN
bracis-33646	146	21	\(w\vdash	\(w\vdash	PROPN
bracis-33646	146	22	\varphi	\varphi	PROPN
bracis-33646	146	23	\	\	NOUN
bracis-33646	146	24	)	)	PUNCT
bracis-33646	146	25	if	if	SCONJ
bracis-33646	146	26	\(\varphi	\(\varphi	PUNCT
bracis-33646	146	27	\in	\in	PROPN
bracis-33646	146	28	f(\bigcup	f(\bigcup	PROPN
bracis-33646	146	29	\{o\in	\{o\in	PROPN
bracis-33646	146	30	\tau	\tau	PROPN
bracis-33646	146	31	:	:	PUNCT
bracis-33646	146	32	w\in	w\in	NOUN
bracis-33646	146	33	o\})\	o\})\	NOUN
bracis-33646	146	34	)	)	PUNCT
bracis-33646	146	35	induces	induce	VERB
bracis-33646	146	36	\(\mathcal	\(\mathcal	ADJ
bracis-33646	146	37	{	{	PUNCT
bracis-33646	146	38	l}\	l}\	PROPN
bracis-33646	146	39	)	)	PUNCT
bracis-33646	146	40	.	.	PUNCT
bracis-33646	147	1	furthermore	furthermore	ADV
bracis-33646	147	2	,	,	PUNCT
bracis-33646	147	3	\(bo_{\mathcal	\(bo_{\mathcal	PROPN
bracis-33646	147	4	{	{	PUNCT
bracis-33646	147	5	m}_\mathcal	m}_\mathcal	ADJ
bracis-33646	147	6	{	{	PUNCT
bracis-33646	147	7	w	w	NOUN
bracis-33646	147	8	}	}	PUNCT
bracis-33646	147	9	}	}	PUNCT
bracis-33646	147	10	=	=	SYM
bracis-33646	147	11	\{\cup	\{\cup	ADP
bracis-33646	147	12	f^{-1}(k)~|~k	f^{-1}(k)~|~k	PROPN
bracis-33646	147	13	\in	\in	PROPN
bracis-33646	147	14	th_\mathcal	th_\mathcal	PROPN
bracis-33646	147	15	{	{	PUNCT
bracis-33646	147	16	l}\}\	l}\}\	NOUN
bracis-33646	147	17	)	)	PUNCT
bracis-33646	147	18	.	.	PUNCT
bracis-33646	148	1	notice	notice	VERB
bracis-33646	148	2	that	that	SCONJ
bracis-33646	148	3	lemma	lemma	PROPN
bracis-33646	148	4	 	 	SPACE
bracis-33646	148	5	3	3	NUM
bracis-33646	148	6	above	above	ADV
bracis-33646	148	7	tells	tell	VERB
bracis-33646	148	8	us	we	PRON
bracis-33646	148	9	that	that	SCONJ
bracis-33646	148	10	the	the	DET
bracis-33646	148	11	language	language	NOUN
bracis-33646	148	12	of	of	ADP
bracis-33646	148	13	amts	amts	PROPN
bracis-33646	148	14	and	and	CCONJ
bracis-33646	148	15	topological	topological	ADJ
bracis-33646	148	16	spaces	space	NOUN
bracis-33646	148	17	are	be	AUX
bracis-33646	148	18	interchangeable	interchangeable	ADJ
bracis-33646	148	19	to	to	PART
bracis-33646	148	20	study	study	VERB
bracis-33646	148	21	the	the	DET
bracis-33646	148	22	structure	structure	NOUN
bracis-33646	148	23	of	of	ADP
bracis-33646	148	24	the	the	DET
bracis-33646	148	25	logic	logic	NOUN
bracis-33646	148	26	.	.	PUNCT
bracis-33646	149	1	moreover	moreover	ADV
bracis-33646	149	2	,	,	PUNCT
bracis-33646	149	3	it	it	PRON
bracis-33646	149	4	is	be	AUX
bracis-33646	149	5	easy	easy	ADJ
bracis-33646	149	6	to	to	PART
bracis-33646	149	7	see	see	VERB
bracis-33646	149	8	that	that	SCONJ
bracis-33646	149	9	any	any	DET
bracis-33646	149	10	amt	amt	PROPN
bracis-33646	149	11	defines	define	VERB
bracis-33646	149	12	a	a	DET
bracis-33646	149	13	topological	topological	ADJ
bracis-33646	149	14	space	space	NOUN
bracis-33646	149	15	inducing	induce	VERB
bracis-33646	149	16	the	the	DET
bracis-33646	149	17	same	same	ADJ
bracis-33646	149	18	logic	logic	NOUN
bracis-33646	149	19	.	.	PUNCT
bracis-33646	150	1	lemma	lemma	PROPN
bracis-33646	150	2	4	4	NUM
bracis-33646	150	3	let	let	VERB
bracis-33646	150	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	150	5	{	{	PUNCT
bracis-33646	150	6	m	m	NOUN
bracis-33646	150	7	}	}	PUNCT
bracis-33646	150	8	=	=	PUNCT
bracis-33646	150	9	\langle	\langle	PROPN
bracis-33646	150	10	m	m	PROPN
bracis-33646	150	11	,	,	PUNCT
bracis-33646	150	12	l	l	PROPN
bracis-33646	150	13	,	,	PUNCT
bracis-33646	150	14	\vdash	\vdash	VERB
bracis-33646	150	15	\rangle	\rangle	NOUN
bracis-33646	150	16	\	\	NOUN
bracis-33646	150	17	)	)	PUNCT
bracis-33646	150	18	be	be	AUX
bracis-33646	150	19	an	an	DET
bracis-33646	150	20	abstract	abstract	ADJ
bracis-33646	150	21	model	model	NOUN
bracis-33646	150	22	theory	theory	NOUN
bracis-33646	150	23	inducing	induce	VERB
bracis-33646	150	24	a	a	DET
bracis-33646	150	25	logic	logic	NOUN
bracis-33646	150	26	\(\mathcal	\(\mathcal	ADJ
bracis-33646	150	27	{	{	PUNCT
bracis-33646	150	28	l}\	l}\	PROPN
bracis-33646	150	29	)	)	PUNCT
bracis-33646	150	30	,	,	PUNCT
bracis-33646	150	31	the	the	DET
bracis-33646	150	32	topological	topological	ADJ
bracis-33646	150	33	model	model	NOUN
bracis-33646	150	34	\(\mathcal	\(\mathcal	X
bracis-33646	150	35	{	{	PUNCT
bracis-33646	150	36	w}_{\mathcal	w}_{\mathcal	NOUN
bracis-33646	150	37	{	{	PUNCT
bracis-33646	150	38	m	m	NOUN
bracis-33646	150	39	}	}	PUNCT
bracis-33646	150	40	}	}	PUNCT
bracis-33646	150	41	=	=	PUNCT
bracis-33646	150	42	\langle	\langle	PROPN
bracis-33646	150	43	m	m	NOUN
bracis-33646	150	44	,	,	PUNCT
bracis-33646	150	45	2^m\rangle	2^m\rangle	NUM
bracis-33646	150	46	\	\	NOUN
bracis-33646	150	47	)	)	PUNCT
bracis-33646	150	48	induces	induce	VERB
bracis-33646	150	49	\(\mathcal	\(\mathcal	ADJ
bracis-33646	150	50	{	{	PUNCT
bracis-33646	150	51	l}\	l}\	PROPN
bracis-33646	150	52	)	)	PUNCT
bracis-33646	150	53	and	and	CCONJ
bracis-33646	150	54	\(f	\(f	NUM
bracis-33646	150	55	:	:	PUNCT
bracis-33646	150	56	2^m\mapsto	2^m\mapsto	NUM
bracis-33646	150	57	th_\mathcal	th_\mathcal	ADJ
bracis-33646	150	58	{	{	PUNCT
bracis-33646	150	59	l}\	l}\	PROPN
bracis-33646	150	60	)	)	PUNCT
bracis-33646	150	61	s.t	s.t	PROPN
bracis-33646	150	62	.	.	PUNCT
bracis-33646	150	63	\(f(o	\(f(o	PROPN
bracis-33646	150	64	)	)	PUNCT
bracis-33646	150	65	=	=	SYM
bracis-33646	150	66	\{\varphi	\{\varphi	NUM
bracis-33646	150	67	\in	\in	NOUN
bracis-33646	150	68	l~|~	l~|~	NOUN
bracis-33646	151	1	\forall	\forall	PRON
bracis-33646	151	2	w\in	w\in	NOUN
bracis-33646	151	3	o:~w\vdash	o:~w\vdash	NOUN
bracis-33646	151	4	\varphi	\varphi	ADP
bracis-33646	151	5	\}\	\}\	NOUN
bracis-33646	151	6	)	)	PUNCT
bracis-33646	151	7	is	be	AUX
bracis-33646	151	8	an	an	DET
bracis-33646	151	9	\(\mathcal	\(\mathcal	ADJ
bracis-33646	151	10	{	{	PUNCT
bracis-33646	151	11	l}\)-interpretation	l}\)-interpretation	NOUN
bracis-33646	151	12	on	on	ADP
bracis-33646	151	13	\(\mathcal	\(\mathcal	ADJ
bracis-33646	151	14	{	{	PUNCT
bracis-33646	151	15	w}\	w}\	PROPN
bracis-33646	151	16	)	)	PUNCT
bracis-33646	151	17	.	.	PUNCT
bracis-33646	152	1	we	we	PRON
bracis-33646	152	2	employed	employ	VERB
bracis-33646	152	3	the	the	DET
bracis-33646	152	4	terminology	terminology	NOUN
bracis-33646	152	5	of	of	ADP
bracis-33646	152	6	open	open	ADJ
bracis-33646	152	7	basic	basic	ADJ
bracis-33646	152	8	sets	set	NOUN
bracis-33646	152	9	to	to	ADP
bracis-33646	152	10	the	the	DET
bracis-33646	152	11	sets	set	NOUN
bracis-33646	152	12	\(\llbracket	\(\llbracket	NOUN
bracis-33646	152	13	\vargamma	\vargamma	X
bracis-33646	152	14	\rrbracket	\rrbracket	NOUN
bracis-33646	152	15	\	\	NOUN
bracis-33646	152	16	)	)	PUNCT
bracis-33646	152	17	as	as	ADP
bracis-33646	152	18	a	a	DET
bracis-33646	152	19	foreshadowing	foreshadowing	NOUN
bracis-33646	152	20	of	of	ADP
bracis-33646	152	21	the	the	DET
bracis-33646	152	22	fact	fact	NOUN
bracis-33646	152	23	that	that	SCONJ
bracis-33646	152	24	we	we	PRON
bracis-33646	152	25	employ	employ	VERB
bracis-33646	152	26	exactly	exactly	ADV
bracis-33646	152	27	those	those	DET
bracis-33646	152	28	sets	set	NOUN
bracis-33646	152	29	to	to	PART
bracis-33646	152	30	provide	provide	VERB
bracis-33646	152	31	a	a	DET
bracis-33646	152	32	basis	basis	NOUN
bracis-33646	152	33	for	for	SCONJ
bracis-33646	152	34	the	the	DET
bracis-33646	152	35	canonical	canonical	ADJ
bracis-33646	152	36	topology	topology	NOUN
bracis-33646	152	37	inducing	induce	VERB
bracis-33646	152	38	the	the	DET
bracis-33646	152	39	logic	logic	NOUN
bracis-33646	152	40	.	.	PUNCT
bracis-33646	153	1	in	in	ADP
bracis-33646	153	2	a	a	DET
bracis-33646	153	3	sense	sense	NOUN
bracis-33646	153	4	,	,	PUNCT
bracis-33646	153	5	basic	basic	ADJ
bracis-33646	153	6	open	open	ADJ
bracis-33646	153	7	sets	set	NOUN
bracis-33646	153	8	are	be	AUX
bracis-33646	153	9	the	the	DET
bracis-33646	153	10	‘	'	PUNCT
bracis-33646	153	11	stable	stable	ADJ
bracis-33646	153	12	’	'	PUNCT
bracis-33646	153	13	interpretations	interpretation	NOUN
bracis-33646	153	14	,	,	PUNCT
bracis-33646	153	15	meaning	mean	VERB
bracis-33646	153	16	that	that	SCONJ
bracis-33646	153	17	they	they	PRON
bracis-33646	153	18	are	be	AUX
bracis-33646	153	19	completely	completely	ADV
bracis-33646	153	20	definable	definable	ADJ
bracis-33646	153	21	within	within	ADP
bracis-33646	153	22	the	the	DET
bracis-33646	153	23	logical	logical	ADJ
bracis-33646	153	24	language	language	NOUN
bracis-33646	153	25	.	.	PUNCT
bracis-33646	154	1	4	4	NUM
bracis-33646	154	2	topological	topological	ADJ
bracis-33646	154	3	belief	belief	NOUN
bracis-33646	154	4	change	change	NOUN
bracis-33646	154	5	and	and	CCONJ
bracis-33646	154	6	 	 	SPACE
bracis-33646	154	7	agm	agm	PROPN
bracis-33646	154	8	rationality	rationality	NOUN
bracis-33646	154	9	we	we	PRON
bracis-33646	154	10	begin	begin	VERB
bracis-33646	154	11	our	our	PRON
bracis-33646	154	12	investigation	investigation	NOUN
bracis-33646	154	13	of	of	ADP
bracis-33646	154	14	belief	belief	NOUN
bracis-33646	154	15	change	change	NOUN
bracis-33646	154	16	by	by	ADP
bracis-33646	154	17	proposing	propose	VERB
bracis-33646	154	18	a	a	DET
bracis-33646	154	19	semantic	semantic	ADJ
bracis-33646	154	20	model	model	NOUN
bracis-33646	154	21	for	for	ADP
bracis-33646	154	22	belief	belief	NOUN
bracis-33646	154	23	change	change	NOUN
bracis-33646	154	24	,	,	PUNCT
bracis-33646	154	25	which	which	PRON
bracis-33646	154	26	is	be	AUX
bracis-33646	154	27	agnostic	agnostic	ADJ
bracis-33646	154	28	to	to	ADP
bracis-33646	154	29	the	the	DET
bracis-33646	154	30	underlying	underlie	VERB
bracis-33646	154	31	logic	logic	NOUN
bracis-33646	154	32	.	.	PUNCT
bracis-33646	155	1	notice	notice	VERB
bracis-33646	155	2	that	that	SCONJ
bracis-33646	155	3	,	,	PUNCT
bracis-33646	155	4	differently	differently	ADV
bracis-33646	155	5	from	from	ADP
bracis-33646	155	6	sect	sect	NOUN
bracis-33646	155	7	.	.	PUNCT
bracis-33646	155	8	 	 	SPACE
bracis-33646	156	1	2	2	NUM
bracis-33646	156	2	,	,	PUNCT
bracis-33646	156	3	we	we	PRON
bracis-33646	156	4	will	will	AUX
bracis-33646	156	5	consider	consider	VERB
bracis-33646	156	6	belief	belief	NOUN
bracis-33646	156	7	contractions	contraction	NOUN
bracis-33646	156	8	as	as	ADP
bracis-33646	156	9	operations	operation	NOUN
bracis-33646	156	10	which	which	PRON
bracis-33646	156	11	take	take	VERB
bracis-33646	156	12	two	two	NUM
bracis-33646	156	13	sets	set	NOUN
bracis-33646	156	14	of	of	ADP
bracis-33646	156	15	formulas	formula	NOUN
bracis-33646	156	16	and	and	CCONJ
bracis-33646	156	17	return	return	VERB
bracis-33646	156	18	a	a	DET
bracis-33646	156	19	set	set	NOUN
bracis-33646	156	20	of	of	ADP
bracis-33646	156	21	formulas	formula	NOUN
bracis-33646	156	22	,	,	PUNCT
bracis-33646	156	23	i.e.	i.e.	X
bracis-33646	156	24	a	a	DET
bracis-33646	156	25	function	function	NOUN
bracis-33646	156	26	of	of	ADP
bracis-33646	156	27	the	the	DET
bracis-33646	156	28	form	form	NOUN
bracis-33646	156	29	\(\star	\(\star	NOUN
bracis-33646	156	30	:	:	PUNCT
bracis-33646	156	31	2^l	2^l	NUM
bracis-33646	156	32	\times	\time	VERB
bracis-33646	156	33	2^l	2^l	NUM
bracis-33646	156	34	\mapsto	\mapsto	PROPN
bracis-33646	156	35	2^l\	2^l\	NUM
bracis-33646	156	36	)	)	PUNCT
bracis-33646	156	37	,	,	PUNCT
bracis-33646	156	38	as	as	SCONJ
bracis-33646	156	39	done	do	VERB
bracis-33646	156	40	by	by	ADP
bracis-33646	156	41	ribeiro	ribeiro	PROPN
bracis-33646	156	42	and	and	CCONJ
bracis-33646	156	43	wasserman	wasserman	PROPN
bracis-33646	156	44	 	 	SPACE
bracis-33646	157	1	[	[	X
bracis-33646	157	2	16	16	NUM
bracis-33646	157	3	]	]	PUNCT
bracis-33646	157	4	.	.	PUNCT
bracis-33646	158	1	the	the	DET
bracis-33646	158	2	reason	reason	NOUN
bracis-33646	158	3	for	for	ADP
bracis-33646	158	4	that	that	PRON
bracis-33646	158	5	is	be	AUX
bracis-33646	158	6	some	some	DET
bracis-33646	158	7	non	non	ADJ
bracis-33646	158	8	-	-	ADJ
bracis-33646	158	9	classical	classical	ADJ
bracis-33646	158	10	logic	logic	NOUN
bracis-33646	158	11	may	may	AUX
bracis-33646	158	12	not	not	PART
bracis-33646	158	13	possess	possess	VERB
bracis-33646	158	14	conjunctions	conjunction	NOUN
bracis-33646	158	15	in	in	ADP
bracis-33646	158	16	its	its	PRON
bracis-33646	158	17	language	language	NOUN
bracis-33646	158	18	.	.	PUNCT
bracis-33646	159	1	this	this	PRON
bracis-33646	159	2	means	mean	VERB
bracis-33646	159	3	that	that	SCONJ
bracis-33646	159	4	we	we	PRON
bracis-33646	159	5	are	be	AUX
bracis-33646	159	6	dealing	deal	VERB
bracis-33646	159	7	with	with	ADP
bracis-33646	159	8	multiple	multiple	ADJ
bracis-33646	159	9	contractions	contraction	NOUN
bracis-33646	159	10	,	,	PUNCT
bracis-33646	159	11	rather	rather	ADV
bracis-33646	159	12	than	than	ADP
bracis-33646	159	13	single	single	ADJ
bracis-33646	159	14	contractions	contraction	NOUN
bracis-33646	159	15	.	.	PUNCT
bracis-33646	160	1	more	more	ADV
bracis-33646	160	2	precisely	precisely	ADV
bracis-33646	160	3	with	with	ADP
bracis-33646	160	4	choice	choice	NOUN
bracis-33646	160	5	contractions	contraction	NOUN
bracis-33646	160	6	 	 	SPACE
bracis-33646	161	1	[	[	X
bracis-33646	161	2	6	6	NUM
bracis-33646	161	3	]	]	PUNCT
bracis-33646	161	4	.	.	PUNCT
bracis-33646	162	1	the	the	DET
bracis-33646	162	2	central	central	ADJ
bracis-33646	162	3	notion	notion	NOUN
bracis-33646	162	4	underlying	underlie	VERB
bracis-33646	162	5	most	most	ADJ
bracis-33646	162	6	belief	belief	NOUN
bracis-33646	162	7	change	change	NOUN
bracis-33646	162	8	operations	operation	NOUN
bracis-33646	162	9	is	be	AUX
bracis-33646	162	10	that	that	PRON
bracis-33646	162	11	of	of	ADP
bracis-33646	162	12	choice	choice	NOUN
bracis-33646	162	13	.	.	PUNCT
bracis-33646	163	1	different	different	ADJ
bracis-33646	163	2	constructions	construction	NOUN
bracis-33646	163	3	[	[	X
bracis-33646	163	4	1	1	NUM
bracis-33646	163	5	,	,	PUNCT
bracis-33646	163	6	8	8	NUM
bracis-33646	163	7	,	,	PUNCT
bracis-33646	163	8	15	15	NUM
bracis-33646	163	9	]	]	PUNCT
bracis-33646	163	10	represent	represent	VERB
bracis-33646	163	11	the	the	DET
bracis-33646	163	12	agent	agent	NOUN
bracis-33646	163	13	’s	’s	PART
bracis-33646	163	14	epistemic	epistemic	ADJ
bracis-33646	163	15	commitments	commitment	NOUN
bracis-33646	163	16	by	by	ADP
bracis-33646	163	17	means	mean	NOUN
bracis-33646	163	18	of	of	ADP
bracis-33646	163	19	which	which	PRON
bracis-33646	163	20	beliefs	belief	NOUN
bracis-33646	163	21	the	the	DET
bracis-33646	163	22	agent	agent	NOUN
bracis-33646	163	23	chooses	choose	VERB
bracis-33646	163	24	to	to	PART
bracis-33646	163	25	preserve	preserve	VERB
bracis-33646	163	26	(	(	PUNCT
bracis-33646	163	27	or	or	CCONJ
bracis-33646	163	28	discard	discard	ADJ
bracis-33646	163	29	)	)	PUNCT
bracis-33646	163	30	given	give	VERB
bracis-33646	163	31	new	new	ADJ
bracis-33646	163	32	information	information	NOUN
bracis-33646	163	33	.	.	PUNCT
bracis-33646	164	1	in	in	ADP
bracis-33646	164	2	connection	connection	NOUN
bracis-33646	164	3	with	with	ADP
bracis-33646	164	4	the	the	DET
bracis-33646	164	5	literature	literature	NOUN
bracis-33646	164	6	on	on	ADP
bracis-33646	164	7	conditional	conditional	ADJ
bracis-33646	164	8	logic	logic	NOUN
bracis-33646	164	9	and	and	CCONJ
bracis-33646	164	10	semantic	semantic	ADJ
bracis-33646	164	11	modelling	modelling	NOUN
bracis-33646	164	12	,	,	PUNCT
bracis-33646	164	13	we	we	PRON
bracis-33646	164	14	will	will	AUX
bracis-33646	164	15	represent	represent	VERB
bracis-33646	164	16	this	this	DET
bracis-33646	164	17	choice	choice	NOUN
bracis-33646	164	18	element	element	NOUN
bracis-33646	164	19	as	as	ADP
bracis-33646	164	20	a	a	DET
bracis-33646	164	21	function	function	NOUN
bracis-33646	164	22	selecting	select	VERB
bracis-33646	164	23	elements	element	NOUN
bracis-33646	164	24	from	from	ADP
bracis-33646	164	25	a	a	DET
bracis-33646	164	26	set	set	NOUN
bracis-33646	164	27	.	.	PUNCT
bracis-33646	165	1	we	we	PRON
bracis-33646	165	2	will	will	AUX
bracis-33646	165	3	focus	focus	VERB
bracis-33646	165	4	our	our	PRON
bracis-33646	165	5	presentation	presentation	NOUN
bracis-33646	165	6	on	on	ADP
bracis-33646	165	7	abstract	abstract	ADJ
bracis-33646	165	8	model	model	NOUN
bracis-33646	165	9	theories	theory	NOUN
bracis-33646	165	10	.	.	PUNCT
bracis-33646	166	1	however	however	ADV
bracis-33646	166	2	,	,	PUNCT
bracis-33646	166	3	given	give	VERB
bracis-33646	166	4	lemmas	lemmas	PROPN
bracis-33646	166	5	 	 	SPACE
bracis-33646	166	6	3	3	NUM
bracis-33646	166	7	and	and	CCONJ
bracis-33646	166	8	4	4	NUM
bracis-33646	166	9	,	,	PUNCT
bracis-33646	166	10	the	the	DET
bracis-33646	166	11	same	same	ADJ
bracis-33646	166	12	notions	notion	NOUN
bracis-33646	166	13	could	could	AUX
bracis-33646	166	14	be	be	AUX
bracis-33646	166	15	equivalently	equivalently	ADV
bracis-33646	166	16	described	describe	VERB
bracis-33646	166	17	employing	employ	VERB
bracis-33646	166	18	topological	topological	ADJ
bracis-33646	166	19	spaces	space	NOUN
bracis-33646	166	20	and	and	CCONJ
bracis-33646	166	21	interpretation	interpretation	NOUN
bracis-33646	166	22	functions	function	NOUN
bracis-33646	166	23	.	.	PUNCT
bracis-33646	167	1	definition	definition	NOUN
bracis-33646	167	2	10	10	NUM
bracis-33646	167	3	let	let	VERB
bracis-33646	167	4	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	167	5	{	{	PUNCT
bracis-33646	167	6	l	l	NOUN
bracis-33646	167	7	}	}	PUNCT
bracis-33646	167	8	)	)	PUNCT
bracis-33646	168	1	=	=	PUNCT
bracis-33646	168	2	\langle	\langle	PROPN
bracis-33646	168	3	m	m	PRON
bracis-33646	168	4	,	,	PUNCT
bracis-33646	168	5	\vdash	\vdash	VERB
bracis-33646	168	6	\rangle	\rangle	NOUN
bracis-33646	168	7	\	\	NOUN
bracis-33646	168	8	)	)	PUNCT
bracis-33646	168	9	be	be	AUX
bracis-33646	168	10	an	an	DET
bracis-33646	168	11	amt	amt	PROPN
bracis-33646	168	12	and	and	CCONJ
bracis-33646	168	13	\(x\subseteq	\(x\subseteq	ADJ
bracis-33646	168	14	m\	m\	NOUN
bracis-33646	168	15	)	)	PUNCT
bracis-33646	168	16	a	a	DET
bracis-33646	168	17	set	set	NOUN
bracis-33646	168	18	of	of	ADP
bracis-33646	168	19	points	point	NOUN
bracis-33646	168	20	(	(	PUNCT
bracis-33646	168	21	interpretations	interpretation	NOUN
bracis-33646	168	22	)	)	PUNCT
bracis-33646	168	23	,	,	PUNCT
bracis-33646	168	24	we	we	PRON
bracis-33646	168	25	call	call	VERB
bracis-33646	168	26	a	a	DET
bracis-33646	168	27	semantic	semantic	ADJ
bracis-33646	168	28	selection	selection	NOUN
bracis-33646	168	29	function	function	NOUN
bracis-33646	168	30	(	(	PUNCT
bracis-33646	168	31	ssf	ssf	NOUN
bracis-33646	168	32	)	)	PUNCT
bracis-33646	168	33	on	on	ADP
bracis-33646	168	34	x	x	PUNCT
bracis-33646	168	35	any	any	DET
bracis-33646	168	36	mapping	mapping	NOUN
bracis-33646	168	37	\(f	\(f	NOUN
bracis-33646	168	38	:	:	PUNCT
bracis-33646	168	39	2^m	2^m	NUM
bracis-33646	168	40	\times	\time	NOUN
bracis-33646	168	41	2^m	2^m	NUM
bracis-33646	168	42	\rightarrow	\rightarrow	PROPN
bracis-33646	168	43	2^m\	2^m\	NUM
bracis-33646	168	44	)	)	PUNCT
bracis-33646	168	45	,	,	PUNCT
bracis-33646	168	46	such	such	ADJ
bracis-33646	168	47	that	that	PRON
bracis-33646	168	48	for	for	ADP
bracis-33646	168	49	any	any	DET
bracis-33646	168	50	\(y	\(y	PROPN
bracis-33646	168	51	,	,	PUNCT
bracis-33646	168	52	z\subseteq	z\subseteq	PROPN
bracis-33646	168	53	m\	m\	NOUN
bracis-33646	168	54	)	)	PUNCT
bracis-33646	168	55	,	,	PUNCT
bracis-33646	168	56	it	it	PRON
bracis-33646	168	57	holds	hold	VERB
bracis-33646	168	58	that	that	SCONJ
bracis-33646	168	59	:	:	PUNCT
bracis-33646	168	60	i	i	PRON
bracis-33646	168	61	)	)	PUNCT
bracis-33646	168	62	\(x	\(x	PROPN
bracis-33646	168	63	\subseteq	\subseteq	PROPN
bracis-33646	168	64	f(x	f(x	PROPN
bracis-33646	168	65	,	,	PUNCT
bracis-33646	168	66	y	y	PROPN
bracis-33646	168	67	)	)	PUNCT
bracis-33646	169	1	\subseteq	\subseteq	PROPN
bracis-33646	169	2	x\cup	x\cup	PROPN
bracis-33646	169	3	y\	y\	PROPN
bracis-33646	169	4	)	)	PUNCT
bracis-33646	169	5	ii	ii	NOUN
bracis-33646	169	6	)	)	PUNCT
bracis-33646	169	7	if	if	SCONJ
bracis-33646	169	8	\(y\ne	\(y\ne	PROPN
bracis-33646	169	9	\emptyset	\emptyset	VERB
bracis-33646	169	10	\	\	PROPN
bracis-33646	169	11	)	)	PUNCT
bracis-33646	169	12	,	,	PUNCT
bracis-33646	169	13	then	then	ADV
bracis-33646	169	14	\(f(x	\(f(x	PROPN
bracis-33646	169	15	,	,	PUNCT
bracis-33646	169	16	y)\cap	y)\cap	PROPN
bracis-33646	169	17	y\ne	y\ne	PROPN
bracis-33646	169	18	\emptyset	\emptyset	PROPN
bracis-33646	169	19	\	\	PROPN
bracis-33646	169	20	)	)	PUNCT
bracis-33646	169	21	iii	iii	X
bracis-33646	169	22	)	)	PUNCT
bracis-33646	169	23	if	if	SCONJ
bracis-33646	169	24	\(y\cap	\(y\cap	NOUN
bracis-33646	169	25	x	x	PROPN
bracis-33646	169	26	\ne	\ne	PROPN
bracis-33646	169	27	\emptyset	\emptyset	VERB
bracis-33646	169	28	\	\	NOUN
bracis-33646	169	29	)	)	PUNCT
bracis-33646	169	30	,	,	PUNCT
bracis-33646	169	31	then	then	ADV
bracis-33646	169	32	\(f(x	\(f(x	PROPN
bracis-33646	169	33	,	,	PUNCT
bracis-33646	169	34	y	y	PROPN
bracis-33646	169	35	)	)	PUNCT
bracis-33646	169	36	\subseteq	\subseteq	PROPN
bracis-33646	169	37	x\	x\	NOUN
bracis-33646	169	38	)	)	PUNCT
bracis-33646	169	39	additionally	additionally	ADV
bracis-33646	169	40	,	,	PUNCT
bracis-33646	169	41	we	we	PRON
bracis-33646	169	42	say	say	VERB
bracis-33646	169	43	an	an	DET
bracis-33646	169	44	ssf	ssf	NOUN
bracis-33646	169	45	is	be	AUX
bracis-33646	169	46	uniform	uniform	ADJ
bracis-33646	169	47	if	if	SCONJ
bracis-33646	169	48	it	it	PRON
bracis-33646	169	49	satisfies	satisfy	VERB
bracis-33646	169	50	:	:	PUNCT
bracis-33646	169	51	iv	iv	X
bracis-33646	169	52	)	)	PUNCT
bracis-33646	169	53	if	if	SCONJ
bracis-33646	169	54	\(f(x	\(f(x	PROPN
bracis-33646	169	55	,	,	PUNCT
bracis-33646	169	56	y)\cap	y)\cap	PROPN
bracis-33646	169	57	z	z	PROPN
bracis-33646	169	58	\ne	\ne	PROPN
bracis-33646	169	59	\emptyset	\emptyset	VERB
bracis-33646	169	60	\	\	NOUN
bracis-33646	169	61	)	)	PUNCT
bracis-33646	169	62	and	and	CCONJ
bracis-33646	169	63	\(f(x	\(f(x	NOUN
bracis-33646	169	64	,	,	PUNCT
bracis-33646	169	65	z)\cap	z)\cap	PROPN
bracis-33646	169	66	y	y	NOUN
bracis-33646	169	67	\ne	\ne	PROPN
bracis-33646	169	68	\emptyset	\emptyset	PROPN
bracis-33646	169	69	\	\	NOUN
bracis-33646	169	70	)	)	PUNCT
bracis-33646	169	71	then	then	ADV
bracis-33646	169	72	,	,	PUNCT
bracis-33646	169	73	\(f(x	\(f(x	PROPN
bracis-33646	169	74	,	,	PUNCT
bracis-33646	169	75	y	y	NOUN
bracis-33646	169	76	)	)	PUNCT
bracis-33646	169	77	=	=	SYM
bracis-33646	169	78	f(x	f(x	PROPN
bracis-33646	169	79	,	,	PUNCT
bracis-33646	169	80	z)\	z)\	NUM
bracis-33646	169	81	)	)	PUNCT
bracis-33646	169	82	.	.	PUNCT
bracis-33646	170	1	with	with	ADP
bracis-33646	170	2	semantic	semantic	ADJ
bracis-33646	170	3	selection	selection	NOUN
bracis-33646	170	4	functions	function	NOUN
bracis-33646	170	5	,	,	PUNCT
bracis-33646	170	6	we	we	PRON
bracis-33646	170	7	can	can	AUX
bracis-33646	170	8	finally	finally	ADV
bracis-33646	170	9	define	define	VERB
bracis-33646	170	10	a	a	DET
bracis-33646	170	11	form	form	NOUN
bracis-33646	170	12	of	of	ADP
bracis-33646	170	13	belief	belief	NOUN
bracis-33646	170	14	contraction	contraction	NOUN
bracis-33646	170	15	,	,	PUNCT
bracis-33646	170	16	which	which	PRON
bracis-33646	170	17	we	we	PRON
bracis-33646	170	18	will	will	AUX
bracis-33646	170	19	study	study	VERB
bracis-33646	170	20	in	in	ADP
bracis-33646	170	21	this	this	DET
bracis-33646	170	22	work	work	NOUN
bracis-33646	170	23	.	.	PUNCT
bracis-33646	171	1	we	we	PRON
bracis-33646	171	2	aim	aim	VERB
bracis-33646	171	3	to	to	PART
bracis-33646	171	4	show	show	VERB
bracis-33646	171	5	that	that	SCONJ
bracis-33646	171	6	our	our	PRON
bracis-33646	171	7	semantic	semantic	ADJ
bracis-33646	171	8	selection	selection	NOUN
bracis-33646	171	9	contractions	contraction	NOUN
bracis-33646	171	10	generalise	generalise	VERB
bracis-33646	171	11	different	different	ADJ
bracis-33646	171	12	notions	notion	NOUN
bracis-33646	171	13	of	of	ADP
bracis-33646	171	14	belief	belief	NOUN
bracis-33646	171	15	contractions	contraction	NOUN
bracis-33646	171	16	in	in	ADP
bracis-33646	171	17	the	the	DET
bracis-33646	171	18	literature	literature	NOUN
bracis-33646	171	19	and	and	CCONJ
bracis-33646	171	20	characterise	characterise	PROPN
bracis-33646	171	21	agm	agm	PROPN
bracis-33646	171	22	contractions	contraction	NOUN
bracis-33646	171	23	by	by	ADP
bracis-33646	171	24	means	mean	NOUN
bracis-33646	171	25	of	of	ADP
bracis-33646	171	26	properties	property	NOUN
bracis-33646	171	27	on	on	ADP
bracis-33646	171	28	the	the	DET
bracis-33646	171	29	selection	selection	NOUN
bracis-33646	171	30	function	function	NOUN
bracis-33646	171	31	and	and	CCONJ
bracis-33646	171	32	the	the	DET
bracis-33646	171	33	space	space	NOUN
bracis-33646	171	34	of	of	ADP
bracis-33646	171	35	models	model	NOUN
bracis-33646	171	36	of	of	ADP
bracis-33646	171	37	the	the	DET
bracis-33646	171	38	logic	logic	NOUN
bracis-33646	171	39	.	.	PUNCT
bracis-33646	172	1	definition	definition	NOUN
bracis-33646	172	2	11	11	NUM
bracis-33646	172	3	let	let	VERB
bracis-33646	172	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	172	5	{	{	PUNCT
bracis-33646	172	6	l	l	NOUN
bracis-33646	172	7	}	}	PUNCT
bracis-33646	172	8	=	=	PUNCT
bracis-33646	172	9	\langle	\langle	PROPN
bracis-33646	172	10	l	l	NOUN
bracis-33646	172	11	,	,	PUNCT
bracis-33646	172	12	cn\rangle	cn\rangle	NOUN
bracis-33646	172	13	\	\	NOUN
bracis-33646	172	14	)	)	PUNCT
bracis-33646	172	15	be	be	AUX
bracis-33646	172	16	a	a	DET
bracis-33646	172	17	logic	logic	NOUN
bracis-33646	172	18	,	,	PUNCT
bracis-33646	172	19	we	we	PRON
bracis-33646	172	20	say	say	VERB
bracis-33646	172	21	a	a	DET
bracis-33646	172	22	belief	belief	NOUN
bracis-33646	172	23	change	change	NOUN
bracis-33646	172	24	operator	operator	NOUN
bracis-33646	172	25	\(\dot{-	\(\dot{-	NOUN
bracis-33646	172	26	}	}	PUNCT
bracis-33646	172	27	:	:	PUNCT
bracis-33646	172	28	2^l	2^l	NUM
bracis-33646	172	29	\times	\time	VERB
bracis-33646	172	30	2^l	2^l	NUM
bracis-33646	172	31	\rightarrow	\rightarrow	PROPN
bracis-33646	172	32	2^l\	2^l\	NUM
bracis-33646	172	33	)	)	PUNCT
bracis-33646	172	34	is	be	AUX
bracis-33646	172	35	a	a	DET
bracis-33646	172	36	semantic	semantic	ADJ
bracis-33646	172	37	selection	selection	NOUN
bracis-33646	172	38	contraction	contraction	NOUN
bracis-33646	172	39	operation	operation	NOUN
bracis-33646	172	40	on	on	ADP
bracis-33646	172	41	a	a	DET
bracis-33646	172	42	set	set	NOUN
bracis-33646	172	43	of	of	ADP
bracis-33646	172	44	formulas	formula	NOUN
bracis-33646	172	45	\(b\subseteq	\(b\subseteq	PROPN
bracis-33646	172	46	l\	l\	PROPN
bracis-33646	172	47	)	)	PUNCT
bracis-33646	172	48	,	,	PUNCT
bracis-33646	172	49	if	if	SCONJ
bracis-33646	172	50	there	there	PRON
bracis-33646	172	51	is	be	VERB
bracis-33646	172	52	an	an	DET
bracis-33646	172	53	amt	amt	PROPN
bracis-33646	172	54	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	172	55	{	{	PUNCT
bracis-33646	172	56	l})\	l})\	X
bracis-33646	172	57	)	)	PUNCT
bracis-33646	172	58	and	and	CCONJ
bracis-33646	172	59	an	an	DET
bracis-33646	172	60	ssf	ssf	NOUN
bracis-33646	172	61	f	f	PROPN
bracis-33646	172	62	on	on	ADP
bracis-33646	172	63	\(\llbracket	\(\llbracket	NOUN
bracis-33646	172	64	b\rrbracket	b\rrbracket	X
bracis-33646	172	65	\	\	PROPN
bracis-33646	172	66	)	)	PUNCT
bracis-33646	172	67	s.t	s.t	PROPN
bracis-33646	172	68	.	.	PROPN
bracis-33646	172	69	for	for	ADP
bracis-33646	172	70	any	any	DET
bracis-33646	172	71	set	set	NOUN
bracis-33646	172	72	of	of	ADP
bracis-33646	172	73	formulas	formula	NOUN
bracis-33646	172	74	\(a	\(a	NOUN
bracis-33646	172	75	\subseteq	\subseteq	PROPN
bracis-33646	172	76	l\	l\	NOUN
bracis-33646	172	77	)	)	PUNCT
bracis-33646	172	78	,	,	PUNCT
bracis-33646	172	79	it	it	PRON
bracis-33646	172	80	holds	hold	VERB
bracis-33646	172	81	:	:	PUNCT
bracis-33646	172	82	$	$	SYM
bracis-33646	172	83	$	$	SYM
bracis-33646	172	84	b\dot{-}a	b\dot{-}a	NOUN
bracis-33646	172	85	=	=	SYM
bracis-33646	172	86	th(f(\llbracket	th(f(\llbracket	NOUN
bracis-33646	172	87	b\rrbracket	b\rrbracket	NOUN
bracis-33646	172	88	,	,	PUNCT
bracis-33646	172	89	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	172	90	a\rrbracket	a\rrbracket	NOUN
bracis-33646	172	91	}	}	PUNCT
bracis-33646	172	92	)	)	PUNCT
bracis-33646	172	93	)	)	PUNCT
bracis-33646	173	1	\cap	\cap	PROPN
bracis-33646	173	2	b.$$	b.$$	NOUN
bracis-33646	173	3	in	in	ADP
bracis-33646	173	4	such	such	DET
bracis-33646	173	5	a	a	DET
bracis-33646	173	6	case	case	NOUN
bracis-33646	173	7	,	,	PUNCT
bracis-33646	173	8	we	we	PRON
bracis-33646	173	9	say	say	VERB
bracis-33646	173	10	f	f	PROPN
bracis-33646	173	11	is	be	AUX
bracis-33646	173	12	a	a	DET
bracis-33646	173	13	characteristic	characteristic	ADJ
bracis-33646	173	14	function	function	NOUN
bracis-33646	173	15	for	for	ADP
bracis-33646	173	16	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	173	17	)	)	PUNCT
bracis-33646	173	18	.	.	PUNCT
bracis-33646	174	1	first	first	ADV
bracis-33646	174	2	,	,	PUNCT
bracis-33646	174	3	we	we	PRON
bracis-33646	174	4	show	show	VERB
bracis-33646	174	5	that	that	SCONJ
bracis-33646	174	6	semantic	semantic	ADJ
bracis-33646	174	7	selection	selection	NOUN
bracis-33646	174	8	contractions	contraction	NOUN
bracis-33646	174	9	satisfy	satisfy	VERB
bracis-33646	174	10	the	the	DET
bracis-33646	174	11	basic	basic	ADJ
bracis-33646	174	12	postulates	postulate	NOUN
bracis-33646	174	13	for	for	ADP
bracis-33646	174	14	belief	belief	NOUN
bracis-33646	174	15	contraction	contraction	NOUN
bracis-33646	174	16	.	.	PUNCT
bracis-33646	175	1	proposition	proposition	NOUN
bracis-33646	175	2	4	4	NUM
bracis-33646	175	3	let	let	VERB
bracis-33646	175	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	175	5	{	{	PUNCT
bracis-33646	175	6	l}\	l}\	PROPN
bracis-33646	175	7	)	)	PUNCT
bracis-33646	175	8	be	be	AUX
bracis-33646	175	9	a	a	DET
bracis-33646	175	10	logic	logic	NOUN
bracis-33646	175	11	,	,	PUNCT
bracis-33646	175	12	\(b	\(b	PROPN
bracis-33646	175	13	,	,	PUNCT
bracis-33646	175	14	a	a	PRON
bracis-33646	175	15	,	,	PUNCT
bracis-33646	175	16	a'\subseteq	a'\subseteq	PROPN
bracis-33646	175	17	l\	l\	ADJ
bracis-33646	175	18	)	)	PUNCT
bracis-33646	175	19	be	be	VERB
bracis-33646	175	20	sets	set	NOUN
bracis-33646	175	21	of	of	ADP
bracis-33646	175	22	formulas	formula	NOUN
bracis-33646	175	23	and	and	CCONJ
bracis-33646	175	24	\(\dot{-	\(\dot{-	NOUN
bracis-33646	175	25	}	}	PUNCT
bracis-33646	175	26	:	:	PUNCT
bracis-33646	176	1	2^l	2^l	NUM
bracis-33646	176	2	\times	\time	VERB
bracis-33646	176	3	2^l	2^l	NUM
bracis-33646	176	4	\rightarrow	\rightarrow	PROPN
bracis-33646	176	5	2^l\	2^l\	NUM
bracis-33646	176	6	)	)	PUNCT
bracis-33646	176	7	is	be	AUX
bracis-33646	176	8	a	a	DET
bracis-33646	176	9	semantic	semantic	ADJ
bracis-33646	176	10	selection	selection	NOUN
bracis-33646	176	11	contraction	contraction	NOUN
bracis-33646	176	12	operation	operation	NOUN
bracis-33646	176	13	on	on	ADP
bracis-33646	176	14	b	b	PROPN
bracis-33646	176	15	,	,	PUNCT
bracis-33646	176	16	then	then	ADV
bracis-33646	176	17	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	176	18	)	)	PUNCT
bracis-33646	176	19	satisfies	satisfy	VERB
bracis-33646	176	20	:	:	PUNCT
bracis-33646	176	21	(	(	PUNCT
bracis-33646	176	22	closure	closure	NOUN
bracis-33646	176	23	)	)	PUNCT
bracis-33646	176	24	if	if	SCONJ
bracis-33646	176	25	\(cn(b)=b\	\(cn(b)=b\	PROPN
bracis-33646	176	26	)	)	PUNCT
bracis-33646	176	27	,	,	PUNCT
bracis-33646	176	28	then	then	ADV
bracis-33646	176	29	\(cn(b\dot{-}a	\(cn(b\dot{-}a	PROPN
bracis-33646	176	30	)	)	PUNCT
bracis-33646	177	1	=	=	SYM
bracis-33646	177	2	b\dot{-}a\	b\dot{-}a\	NOUN
bracis-33646	177	3	)	)	PUNCT
bracis-33646	177	4	(	(	PUNCT
bracis-33646	177	5	success	success	NOUN
bracis-33646	177	6	)	)	PUNCT
bracis-33646	177	7	if	if	SCONJ
bracis-33646	177	8	\(a	\(a	NOUN
bracis-33646	177	9	\not	\not	ADV
bracis-33646	177	10	\subseteq	\subseteq	PROPN
bracis-33646	177	11	cn(\emptyset	cn(\emptyset	NOUN
bracis-33646	177	12	)	)	PUNCT
bracis-33646	177	13	\	\	PROPN
bracis-33646	177	14	)	)	PUNCT
bracis-33646	177	15	,	,	PUNCT
bracis-33646	177	16	then	then	ADV
bracis-33646	177	17	\(a\not	\(a\not	PROPN
bracis-33646	177	18	\subseteq	\subseteq	PROPN
bracis-33646	177	19	cn(b	cn(b	PUNCT
bracis-33646	177	20	\dot{-}a)\	\dot{-}a)\	PROPN
bracis-33646	177	21	)	)	PUNCT
bracis-33646	177	22	(	(	PUNCT
bracis-33646	177	23	inclusion	inclusion	NOUN
bracis-33646	177	24	)	)	PUNCT
bracis-33646	177	25	\(b\dot{-}a\subseteq	\(b\dot{-}a\subseteq	PROPN
bracis-33646	177	26	b\	b\	PUNCT
bracis-33646	177	27	)	)	PUNCT
bracis-33646	177	28	‘	'	PUNCT
bracis-33646	177	29	additionally	additionally	ADV
bracis-33646	177	30	,	,	PUNCT
bracis-33646	177	31	if	if	SCONJ
bracis-33646	177	32	the	the	DET
bracis-33646	177	33	characteristic	characteristic	ADJ
bracis-33646	177	34	function	function	NOUN
bracis-33646	177	35	of	of	ADP
bracis-33646	177	36	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	177	37	)	)	PUNCT
bracis-33646	177	38	is	be	AUX
bracis-33646	177	39	uniform	uniform	ADJ
bracis-33646	177	40	,	,	PUNCT
bracis-33646	177	41	then	then	ADV
bracis-33646	177	42	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	177	43	)	)	PUNCT
bracis-33646	177	44	satisfies	satisfie	NOUN
bracis-33646	177	45	(	(	PUNCT
bracis-33646	177	46	uniformity	uniformity	NOUN
bracis-33646	177	47	)	)	PUNCT
bracis-33646	177	48	if	if	SCONJ
bracis-33646	177	49	for	for	ADP
bracis-33646	177	50	any	any	DET
bracis-33646	177	51	\(b'\subseteq	\(b'\subseteq	NUM
bracis-33646	177	52	b\	b\	PRON
bracis-33646	177	53	)	)	PUNCT
bracis-33646	177	54	it	it	PRON
bracis-33646	177	55	holds	hold	VERB
bracis-33646	177	56	that	that	SCONJ
bracis-33646	177	57	\(a	\(a	PROPN
bracis-33646	177	58	\subseteq	\subseteq	PROPN
bracis-33646	177	59	cn(b')\	cn(b')\	PROPN
bracis-33646	177	60	)	)	PUNCT
bracis-33646	177	61	iff	iff	PROPN
bracis-33646	177	62	\(a	\(a	PROPN
bracis-33646	177	63	'	'	PART
bracis-33646	177	64	\subseteq	\subseteq	PROPN
bracis-33646	177	65	cn(b')\	cn(b')\	NOUN
bracis-33646	177	66	)	)	PUNCT
bracis-33646	177	67	,	,	PUNCT
bracis-33646	177	68	then	then	ADV
bracis-33646	177	69	it	it	PRON
bracis-33646	177	70	holds	hold	VERB
bracis-33646	177	71	that	that	SCONJ
bracis-33646	177	72	\(b\dot{-}a	\(b\dot{-}a	PROPN
bracis-33646	177	73	=	=	SYM
bracis-33646	177	74	b\dot{-}a'\	b\dot{-}a'\	PROPN
bracis-33646	177	75	)	)	PUNCT
bracis-33646	177	76	proof	proof	NOUN
bracis-33646	177	77	if	if	SCONJ
bracis-33646	177	78	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	177	79	)	)	PUNCT
bracis-33646	177	80	is	be	AUX
bracis-33646	177	81	a	a	DET
bracis-33646	177	82	semantic	semantic	ADJ
bracis-33646	177	83	selection	selection	NOUN
bracis-33646	177	84	contraction	contraction	NOUN
bracis-33646	177	85	,	,	PUNCT
bracis-33646	177	86	then	then	ADV
bracis-33646	177	87	there	there	PRON
bracis-33646	177	88	is	be	VERB
bracis-33646	177	89	some	some	DET
bracis-33646	177	90	amt	amt	PROPN
bracis-33646	177	91	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	177	92	{	{	PUNCT
bracis-33646	177	93	l	l	NOUN
bracis-33646	177	94	}	}	PUNCT
bracis-33646	177	95	)	)	PUNCT
bracis-33646	178	1	=	=	PUNCT
bracis-33646	178	2	\langle	\langle	NUM
bracis-33646	178	3	m,\vdash	m,\vdash	NOUN
bracis-33646	178	4	\rangle	\rangle	NOUN
bracis-33646	178	5	\	\	NOUN
bracis-33646	178	6	)	)	PUNCT
bracis-33646	178	7	and	and	CCONJ
bracis-33646	178	8	a	a	DET
bracis-33646	178	9	semantic	semantic	ADJ
bracis-33646	178	10	selection	selection	NOUN
bracis-33646	178	11	function	function	NOUN
bracis-33646	178	12	f	f	PROPN
bracis-33646	178	13	,	,	PUNCT
bracis-33646	178	14	s.t	s.t	PROPN
bracis-33646	178	15	.	.	PROPN
bracis-33646	178	16	,	,	PUNCT
bracis-33646	178	17	f	f	PROPN
bracis-33646	178	18	is	be	AUX
bracis-33646	178	19	a	a	DET
bracis-33646	178	20	characteristic	characteristic	ADJ
bracis-33646	178	21	function	function	NOUN
bracis-33646	178	22	for	for	ADP
bracis-33646	178	23	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	178	24	)	)	PUNCT
bracis-33646	178	25	.	.	PUNCT
bracis-33646	179	1	the	the	DET
bracis-33646	179	2	satisfaction	satisfaction	NOUN
bracis-33646	179	3	of	of	ADP
bracis-33646	179	4	the	the	DET
bracis-33646	179	5	closure	closure	NOUN
bracis-33646	179	6	and	and	CCONJ
bracis-33646	179	7	inclusion	inclusion	NOUN
bracis-33646	179	8	postulates	postulate	NOUN
bracis-33646	179	9	is	be	AUX
bracis-33646	179	10	trivial	trivial	ADJ
bracis-33646	179	11	by	by	ADP
bracis-33646	179	12	definition	definition	NOUN
bracis-33646	179	13	of	of	ADP
bracis-33646	179	14	a	a	DET
bracis-33646	179	15	semantic	semantic	ADJ
bracis-33646	179	16	selection	selection	NOUN
bracis-33646	179	17	contraction	contraction	NOUN
bracis-33646	179	18	.	.	PUNCT
bracis-33646	180	1	let	let	VERB
bracis-33646	180	2	us	we	PRON
bracis-33646	180	3	show	show	VERB
bracis-33646	180	4	that	that	SCONJ
bracis-33646	180	5	the	the	DET
bracis-33646	180	6	other	other	ADJ
bracis-33646	180	7	two	two	NUM
bracis-33646	180	8	hold	hold	NOUN
bracis-33646	180	9	.	.	PUNCT
bracis-33646	181	1	(	(	PUNCT
bracis-33646	181	2	success	success	NOUN
bracis-33646	181	3	):	):	PUNCT
bracis-33646	181	4	if	if	SCONJ
bracis-33646	181	5	\(a	\(a	NOUN
bracis-33646	181	6	\not	\not	ADV
bracis-33646	181	7	\subseteq	\subseteq	PROPN
bracis-33646	181	8	cn(\emptyset	cn(\emptyset	NOUN
bracis-33646	181	9	)	)	PUNCT
bracis-33646	181	10	\	\	PROPN
bracis-33646	181	11	)	)	PUNCT
bracis-33646	181	12	,	,	PUNCT
bracis-33646	181	13	then	then	ADV
bracis-33646	181	14	\(\llbracket	\(\llbracket	NOUN
bracis-33646	181	15	a\rrbracket	a\rrbracket	PRON
bracis-33646	181	16	\ne	\ne	PROPN
bracis-33646	181	17	m\	m\	NOUN
bracis-33646	181	18	)	)	PUNCT
bracis-33646	181	19	,	,	PUNCT
bracis-33646	181	20	i.e.	i.e.	X
bracis-33646	181	21	\(\overline{\llbracket	\(\overline{\llbracket	VERB
bracis-33646	181	22	a\rrbracket	a\rrbracket	NOUN
bracis-33646	181	23	}	}	PUNCT
bracis-33646	181	24	\ne	\ne	PROPN
bracis-33646	181	25	\emptyset	\emptyset	VERB
bracis-33646	181	26	\	\	NOUN
bracis-33646	181	27	)	)	PUNCT
bracis-33646	181	28	.	.	PUNCT
bracis-33646	182	1	then	then	ADV
bracis-33646	182	2	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	182	3	b\rrbracket	b\rrbracket	NOUN
bracis-33646	182	4	,	,	PUNCT
bracis-33646	182	5	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	182	6	a\rrbracket	a\rrbracket	NOUN
bracis-33646	182	7	}	}	PUNCT
bracis-33646	182	8	)	)	PUNCT
bracis-33646	182	9	\cap	\cap	PROPN
bracis-33646	182	10	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	182	11	a\rrbracket	a\rrbracket	PRON
bracis-33646	182	12	}	}	PUNCT
bracis-33646	182	13	\ne	\ne	PROPN
bracis-33646	182	14	\emptyset	\emptyset	VERB
bracis-33646	182	15	\	\	NOUN
bracis-33646	182	16	)	)	PUNCT
bracis-33646	182	17	.	.	PUNCT
bracis-33646	183	1	as	as	ADP
bracis-33646	183	2	such	such	ADJ
bracis-33646	183	3	,	,	PUNCT
bracis-33646	183	4	there	there	PRON
bracis-33646	183	5	is	be	VERB
bracis-33646	183	6	some	some	DET
bracis-33646	183	7	\(m	\(m	ADJ
bracis-33646	183	8	\in	\in	PROPN
bracis-33646	183	9	f(\llbracket	f(\llbracket	NOUN
bracis-33646	183	10	b\rrbracket	b\rrbracket	NOUN
bracis-33646	183	11	,	,	PUNCT
bracis-33646	183	12	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	183	13	a\rrbracket	a\rrbracket	NOUN
bracis-33646	183	14	}	}	PUNCT
bracis-33646	183	15	)	)	PUNCT
bracis-33646	183	16	\	\	PROPN
bracis-33646	183	17	)	)	PUNCT
bracis-33646	183	18	,	,	PUNCT
bracis-33646	183	19	s.t	s.t	PROPN
bracis-33646	183	20	.	.	PROPN
bracis-33646	183	21	\(m\not	\(m\not	PROPN
bracis-33646	183	22	\vdash	\vdash	PROPN
bracis-33646	183	23	a\	a\	NOUN
bracis-33646	183	24	)	)	PUNCT
bracis-33646	183	25	and	and	CCONJ
bracis-33646	183	26	\(a\not	\(a\not	PROPN
bracis-33646	183	27	\subseteq	\subseteq	PROPN
bracis-33646	183	28	th(f(\llbracket	th(f(\llbracket	NOUN
bracis-33646	183	29	b\rrbracket	b\rrbracket	NOUN
bracis-33646	183	30	,	,	PUNCT
bracis-33646	183	31	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	183	32	a\rrbracket	a\rrbracket	NOUN
bracis-33646	183	33	}	}	PUNCT
bracis-33646	183	34	)	)	PUNCT
bracis-33646	183	35	)	)	PUNCT
bracis-33646	184	1	\	\	NOUN
bracis-33646	184	2	)	)	PUNCT
bracis-33646	184	3	in	in	ADP
bracis-33646	184	4	other	other	ADJ
bracis-33646	184	5	words	word	NOUN
bracis-33646	184	6	,	,	PUNCT
bracis-33646	184	7	\(a	\(a	NOUN
bracis-33646	184	8	\not	\not	ADV
bracis-33646	184	9	\subseteq	\subseteq	PROPN
bracis-33646	184	10	b\dot{-}a\	b\dot{-}a\	NOUN
bracis-33646	184	11	)	)	PUNCT
bracis-33646	184	12	.	.	PUNCT
bracis-33646	185	1	(	(	PUNCT
bracis-33646	185	2	uniformity	uniformity	NOUN
bracis-33646	185	3	)	)	PUNCT
bracis-33646	185	4	let	let	VERB
bracis-33646	185	5	\(a	\(a	PROPN
bracis-33646	185	6	,	,	PUNCT
bracis-33646	185	7	a	a	PRON
bracis-33646	185	8	'	'	PUNCT
bracis-33646	185	9	\subseteq	\subseteq	PROPN
bracis-33646	185	10	l\	l\	PROPN
bracis-33646	185	11	)	)	PUNCT
bracis-33646	185	12	s.t	s.t	PROPN
bracis-33646	185	13	.	.	PROPN
bracis-33646	185	14	for	for	ADP
bracis-33646	185	15	any	any	DET
bracis-33646	185	16	\(b'\subseteq	\(b'\subseteq	PROPN
bracis-33646	185	17	b\	b\	PUNCT
bracis-33646	185	18	)	)	PUNCT
bracis-33646	185	19	it	it	PRON
bracis-33646	185	20	holds	hold	VERB
bracis-33646	185	21	that	that	SCONJ
bracis-33646	185	22	\(a	\(a	PROPN
bracis-33646	185	23	\subseteq	\subseteq	PROPN
bracis-33646	185	24	cn(b')\	cn(b')\	PROPN
bracis-33646	185	25	)	)	PUNCT
bracis-33646	185	26	iff	iff	PROPN
bracis-33646	185	27	\(a	\(a	PROPN
bracis-33646	185	28	'	'	PART
bracis-33646	185	29	\subseteq	\subseteq	PROPN
bracis-33646	185	30	cn(b')\	cn(b')\	NOUN
bracis-33646	185	31	)	)	PUNCT
bracis-33646	185	32	.	.	PUNCT
bracis-33646	186	1	if	if	SCONJ
bracis-33646	186	2	\(a\not	\(a\not	PROPN
bracis-33646	186	3	\subseteq	\subseteq	PROPN
bracis-33646	186	4	b\	b\	PUNCT
bracis-33646	186	5	)	)	PUNCT
bracis-33646	186	6	,	,	PUNCT
bracis-33646	186	7	then	then	ADV
bracis-33646	186	8	\(\overline{\llbracket	\(\overline{\llbracket	VERB
bracis-33646	186	9	a\rrbracket	a\rrbracket	DET
bracis-33646	186	10	}	}	PUNCT
bracis-33646	186	11	\cap	\cap	NOUN
bracis-33646	186	12	\llbracket	\llbracket	PROPN
bracis-33646	186	13	b\rrbracket	b\rrbracket	NOUN
bracis-33646	186	14	\ne	\ne	PROPN
bracis-33646	186	15	\emptyset	\emptyset	PROPN
bracis-33646	186	16	\	\	NOUN
bracis-33646	186	17	)	)	PUNCT
bracis-33646	186	18	and	and	CCONJ
bracis-33646	186	19	,	,	PUNCT
bracis-33646	186	20	by	by	ADP
bracis-33646	186	21	condition	condition	NOUN
bracis-33646	186	22	iii	iii	NOUN
bracis-33646	186	23	)	)	PUNCT
bracis-33646	186	24	of	of	ADP
bracis-33646	186	25	definition	definition	NOUN
bracis-33646	186	26	 	 	SPACE
bracis-33646	186	27	10	10	NUM
bracis-33646	186	28	,	,	PUNCT
bracis-33646	186	29	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	186	30	b\rrbracket	b\rrbracket	NOUN
bracis-33646	186	31	,	,	PUNCT
bracis-33646	186	32	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	186	33	a\rrbracket	a\rrbracket	NOUN
bracis-33646	186	34	}	}	PUNCT
bracis-33646	186	35	)	)	PUNCT
bracis-33646	187	1	=	=	SYM
bracis-33646	187	2	\llbracket	\llbracket	PROPN
bracis-33646	187	3	b\rrbracket	b\rrbracket	NOUN
bracis-33646	187	4	\	\	PROPN
bracis-33646	187	5	)	)	PUNCT
bracis-33646	187	6	.	.	PUNCT
bracis-33646	188	1	as	as	ADP
bracis-33646	188	2	such	such	ADJ
bracis-33646	188	3	,	,	PUNCT
bracis-33646	188	4	we	we	PRON
bracis-33646	188	5	only	only	ADV
bracis-33646	188	6	need	need	VERB
bracis-33646	188	7	to	to	PART
bracis-33646	188	8	consider	consider	VERB
bracis-33646	188	9	the	the	DET
bracis-33646	188	10	case	case	NOUN
bracis-33646	188	11	in	in	ADP
bracis-33646	188	12	which	which	PRON
bracis-33646	188	13	\(a	\(a	PROPN
bracis-33646	188	14	,	,	PUNCT
bracis-33646	188	15	a'\subseteq	a'\subseteq	PROPN
bracis-33646	188	16	cn(b)\	cn(b)\	X
bracis-33646	188	17	)	)	PUNCT
bracis-33646	188	18	.	.	PUNCT
bracis-33646	189	1	there	there	PRON
bracis-33646	189	2	are	be	VERB
bracis-33646	189	3	two	two	NUM
bracis-33646	189	4	cases	case	NOUN
bracis-33646	189	5	to	to	PART
bracis-33646	189	6	consider	consider	VERB
bracis-33646	189	7	:	:	PUNCT
bracis-33646	189	8	\(a	\(a	PROPN
bracis-33646	189	9	\subseteq	\subseteq	PROPN
bracis-33646	189	10	cn(b\dot{-	cn(b\dot{-	PROPN
bracis-33646	189	11	}	}	PUNCT
bracis-33646	189	12	a)\	a)\	NOUN
bracis-33646	189	13	)	)	PUNCT
bracis-33646	189	14	and	and	CCONJ
bracis-33646	189	15	\(a	\(a	NOUN
bracis-33646	189	16	\not	\not	ADV
bracis-33646	189	17	\subseteq	\subseteq	PROPN
bracis-33646	189	18	cn(b\dot{-	cn(b\dot{-	PROPN
bracis-33646	189	19	}	}	PUNCT
bracis-33646	189	20	a)\	a)\	NOUN
bracis-33646	189	21	)	)	PUNCT
bracis-33646	189	22	.	.	PUNCT
bracis-33646	190	1	in	in	ADP
bracis-33646	190	2	the	the	DET
bracis-33646	190	3	first	first	ADJ
bracis-33646	190	4	case	case	NOUN
bracis-33646	190	5	,	,	PUNCT
bracis-33646	190	6	\(a	\(a	NOUN
bracis-33646	190	7	\subseteq	\subseteq	PROPN
bracis-33646	190	8	cn(\emptyset	cn(\emptyset	NOUN
bracis-33646	190	9	)	)	PUNCT
bracis-33646	190	10	\	\	PROPN
bracis-33646	190	11	)	)	PUNCT
bracis-33646	190	12	,	,	PUNCT
bracis-33646	190	13	by	by	ADP
bracis-33646	190	14	(	(	PUNCT
bracis-33646	190	15	success	success	NOUN
bracis-33646	190	16	)	)	PUNCT
bracis-33646	190	17	,	,	PUNCT
bracis-33646	190	18	thus	thus	ADV
bracis-33646	190	19	,	,	PUNCT
bracis-33646	190	20	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	190	21	b\rrbracket	b\rrbracket	NOUN
bracis-33646	190	22	,	,	PUNCT
bracis-33646	190	23	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	190	24	a\rrbracket	a\rrbracket	NOUN
bracis-33646	190	25	}	}	PUNCT
bracis-33646	190	26	)	)	PUNCT
bracis-33646	191	1	=	=	PUNCT
bracis-33646	191	2	\llbracket	\llbracket	PROPN
bracis-33646	191	3	b\rrbracket	b\rrbracket	NOUN
bracis-33646	191	4	=	=	SYM
bracis-33646	191	5	f(\llbracket	f(\llbracket	NOUN
bracis-33646	191	6	b\rrbracket	b\rrbracket	NOUN
bracis-33646	191	7	,	,	PUNCT
bracis-33646	191	8	\overline{\llbracket	\overline{\llbracket	ADJ
bracis-33646	191	9	a'\rrbracket	a'\rrbracket	NOUN
bracis-33646	191	10	}	}	PUNCT
bracis-33646	191	11	)	)	PUNCT
bracis-33646	191	12	\	\	NOUN
bracis-33646	191	13	)	)	PUNCT
bracis-33646	191	14	and	and	CCONJ
bracis-33646	191	15	\(a'\subseteq	\(a'\subseteq	ADJ
bracis-33646	191	16	cn(b\dot{-}a')\	cn(b\dot{-}a')\	NOUN
bracis-33646	191	17	)	)	PUNCT
bracis-33646	191	18	,	,	PUNCT
bracis-33646	191	19	by	by	ADP
bracis-33646	191	20	condition	condition	NOUN
bracis-33646	191	21	i	i	PROPN
bracis-33646	191	22	)	)	PUNCT
bracis-33646	191	23	of	of	ADP
bracis-33646	191	24	definition	definition	NOUN
bracis-33646	191	25	 	 	SPACE
bracis-33646	191	26	10	10	NUM
bracis-33646	191	27	.	.	PUNCT
bracis-33646	192	1	in	in	ADP
bracis-33646	192	2	the	the	DET
bracis-33646	192	3	second	second	ADJ
bracis-33646	192	4	case	case	NOUN
bracis-33646	192	5	,	,	PUNCT
bracis-33646	192	6	as	as	ADP
bracis-33646	192	7	\(b\dot{-}a	\(b\dot{-}a	PROPN
bracis-33646	192	8	\subseteq	\subseteq	PROPN
bracis-33646	192	9	b\	b\	NOUN
bracis-33646	192	10	)	)	PUNCT
bracis-33646	192	11	,	,	PUNCT
bracis-33646	192	12	then	then	ADV
bracis-33646	192	13	\(a\not	\(a\not	PROPN
bracis-33646	192	14	\subseteq	\subseteq	PROPN
bracis-33646	192	15	cn(b\dot{-}a)\	cn(b\dot{-}a)\	NOUN
bracis-33646	192	16	)	)	PUNCT
bracis-33646	192	17	implies	imply	VERB
bracis-33646	192	18	\(a'\not	\(a'\not	ADV
bracis-33646	192	19	\subseteq	\subseteq	PROPN
bracis-33646	192	20	cn(b\dot{-}a)\	cn(b\dot{-}a)\	NOUN
bracis-33646	192	21	)	)	PUNCT
bracis-33646	192	22	and	and	CCONJ
bracis-33646	192	23	,	,	PUNCT
bracis-33646	192	24	in	in	ADP
bracis-33646	192	25	particular	particular	ADJ
bracis-33646	192	26	,	,	PUNCT
bracis-33646	192	27	\(a	\(a	PROPN
bracis-33646	192	28	'	'	PUNCT
bracis-33646	192	29	\not	\not	ADV
bracis-33646	192	30	\subseteq	\subseteq	PROPN
bracis-33646	192	31	th(f(\llbracket	th(f(\llbracket	PRON
bracis-33646	192	32	b\rrbracket	b\rrbracket	NOUN
bracis-33646	192	33	,	,	PUNCT
bracis-33646	192	34	\overline{\llbracket	\overline{\llbracket	ADJ
bracis-33646	192	35	a'\rrbracket	a'\rrbracket	NOUN
bracis-33646	192	36	}	}	PUNCT
bracis-33646	192	37	)	)	PUNCT
bracis-33646	192	38	)	)	PUNCT
bracis-33646	193	1	\	\	PROPN
bracis-33646	193	2	)	)	PUNCT
bracis-33646	193	3	.	.	PUNCT
bracis-33646	194	1	as	as	ADP
bracis-33646	194	2	such	such	ADJ
bracis-33646	194	3	,	,	PUNCT
bracis-33646	194	4	it	it	PRON
bracis-33646	194	5	must	must	AUX
bracis-33646	194	6	be	be	AUX
bracis-33646	194	7	the	the	DET
bracis-33646	194	8	case	case	NOUN
bracis-33646	194	9	that	that	SCONJ
bracis-33646	194	10	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	194	11	b\rrbracket	b\rrbracket	NOUN
bracis-33646	194	12	,	,	PUNCT
bracis-33646	194	13	\overline{\llbracket	\overline{\llbracket	ADJ
bracis-33646	194	14	a'\rrbracket	a'\rrbracket	NOUN
bracis-33646	194	15	}	}	PUNCT
bracis-33646	194	16	)	)	PUNCT
bracis-33646	194	17	\cap	\cap	PROPN
bracis-33646	194	18	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	194	19	a\rrbracket	a\rrbracket	PRON
bracis-33646	194	20	}	}	PUNCT
bracis-33646	194	21	\ne	\ne	PROPN
bracis-33646	194	22	\emptyset	\emptyset	VERB
bracis-33646	194	23	\	\	NOUN
bracis-33646	194	24	)	)	PUNCT
bracis-33646	194	25	.	.	PUNCT
bracis-33646	195	1	conversely	conversely	ADV
bracis-33646	195	2	,	,	PUNCT
bracis-33646	195	3	we	we	PRON
bracis-33646	195	4	may	may	AUX
bracis-33646	195	5	also	also	ADV
bracis-33646	195	6	conclude	conclude	VERB
bracis-33646	195	7	that	that	SCONJ
bracis-33646	195	8	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	195	9	b\rrbracket	b\rrbracket	NOUN
bracis-33646	195	10	,	,	PUNCT
bracis-33646	195	11	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	195	12	a\rrbracket	a\rrbracket	NOUN
bracis-33646	195	13	}	}	PUNCT
bracis-33646	195	14	)	)	PUNCT
bracis-33646	195	15	\cap	\cap	PROPN
bracis-33646	195	16	\overline{\llbracket	\overline{\llbracket	ADJ
bracis-33646	195	17	a'\rrbracket	a'\rrbracket	NOUN
bracis-33646	195	18	}	}	PUNCT
bracis-33646	195	19	\ne	\ne	PROPN
bracis-33646	195	20	\emptyset	\emptyset	VERB
bracis-33646	195	21	\	\	NOUN
bracis-33646	195	22	)	)	PUNCT
bracis-33646	195	23	,	,	PUNCT
bracis-33646	195	24	thus	thus	ADV
bracis-33646	195	25	,	,	PUNCT
bracis-33646	195	26	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	195	27	b\rrbracket	b\rrbracket	NOUN
bracis-33646	195	28	,	,	PUNCT
bracis-33646	195	29	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	195	30	a\rrbracket	a\rrbracket	NOUN
bracis-33646	195	31	}	}	PUNCT
bracis-33646	195	32	)	)	PUNCT
bracis-33646	196	1	=	=	SYM
bracis-33646	196	2	f(\llbracket	f(\llbracket	NOUN
bracis-33646	196	3	b\rrbracket	b\rrbracket	NOUN
bracis-33646	196	4	,	,	PUNCT
bracis-33646	196	5	\overline{\llbracket	\overline{\llbracket	ADJ
bracis-33646	196	6	a'\rrbracket	a'\rrbracket	NOUN
bracis-33646	196	7	}	}	PUNCT
bracis-33646	196	8	)	)	PUNCT
bracis-33646	196	9	\	\	NOUN
bracis-33646	196	10	)	)	PUNCT
bracis-33646	196	11	,	,	PUNCT
bracis-33646	196	12	since	since	SCONJ
bracis-33646	196	13	f	f	PROPN
bracis-33646	196	14	is	be	AUX
bracis-33646	196	15	uniform	uniform	ADJ
bracis-33646	196	16	,	,	PUNCT
bracis-33646	196	17	and	and	CCONJ
bracis-33646	196	18	\(b\dot{-	\(b\dot{-	ADJ
bracis-33646	196	19	}	}	PUNCT
bracis-33646	196	20	a	a	DET
bracis-33646	196	21	=	=	SYM
bracis-33646	196	22	b\dot{-}a'\	b\dot{-}a'\	PROPN
bracis-33646	196	23	)	)	PUNCT
bracis-33646	196	24	.	.	PUNCT
bracis-33646	196	25	   	   	SPACE
bracis-33646	197	1	\(\square	\(\square	VERB
bracis-33646	197	2	\	\	NOUN
bracis-33646	197	3	)	)	PUNCT
bracis-33646	197	4	our	our	PRON
bracis-33646	197	5	interest	interest	NOUN
bracis-33646	197	6	now	now	ADV
bracis-33646	197	7	is	be	AUX
bracis-33646	197	8	investigating	investigate	VERB
bracis-33646	197	9	which	which	PRON
bracis-33646	197	10	properties	property	NOUN
bracis-33646	197	11	of	of	ADP
bracis-33646	197	12	semantic	semantic	ADJ
bracis-33646	197	13	selection	selection	NOUN
bracis-33646	197	14	functions	function	NOUN
bracis-33646	197	15	imply	imply	VERB
bracis-33646	197	16	adequate	adequate	ADJ
bracis-33646	197	17	behaviours	behaviour	NOUN
bracis-33646	197	18	in	in	ADP
bracis-33646	197	19	their	their	PRON
bracis-33646	197	20	respective	respective	ADJ
bracis-33646	197	21	selection	selection	NOUN
bracis-33646	197	22	contractions	contraction	NOUN
bracis-33646	197	23	.	.	PUNCT
bracis-33646	198	1	proposition	proposition	NOUN
bracis-33646	198	2	5	5	NUM
bracis-33646	198	3	let	let	VERB
bracis-33646	198	4	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	198	5	{	{	PUNCT
bracis-33646	198	6	l	l	NOUN
bracis-33646	198	7	}	}	PUNCT
bracis-33646	198	8	)	)	PUNCT
bracis-33646	199	1	=	=	PUNCT
bracis-33646	199	2	\langle	\langle	PROPN
bracis-33646	199	3	m	m	PRON
bracis-33646	199	4	,	,	PUNCT
bracis-33646	199	5	\vdash	\vdash	VERB
bracis-33646	199	6	\rangle	\rangle	NOUN
bracis-33646	199	7	\	\	NOUN
bracis-33646	199	8	)	)	PUNCT
bracis-33646	199	9	be	be	AUX
bracis-33646	199	10	an	an	DET
bracis-33646	199	11	amt	amt	NOUN
bracis-33646	199	12	inducing	induce	VERB
bracis-33646	199	13	logic	logic	NOUN
bracis-33646	199	14	\(\mathcal	\(\mathcal	ADJ
bracis-33646	199	15	{	{	PUNCT
bracis-33646	199	16	l	l	NOUN
bracis-33646	199	17	}	}	PUNCT
bracis-33646	199	18	=	=	PUNCT
bracis-33646	199	19	\langle	\langle	PROPN
bracis-33646	199	20	l	l	NOUN
bracis-33646	199	21	,	,	PUNCT
bracis-33646	199	22	cn\rangle	cn\rangle	NOUN
bracis-33646	199	23	\	\	PROPN
bracis-33646	199	24	)	)	PUNCT
bracis-33646	199	25	,	,	PUNCT
bracis-33646	199	26	and	and	CCONJ
bracis-33646	199	27	\(b	\(b	NOUN
bracis-33646	199	28	,	,	PUNCT
bracis-33646	199	29	a	a	DET
bracis-33646	199	30	\subseteq	\subseteq	PROPN
bracis-33646	199	31	th_\mathcal	th_\mathcal	PROPN
bracis-33646	199	32	{	{	PUNCT
bracis-33646	199	33	l}\	l}\	PROPN
bracis-33646	199	34	)	)	PUNCT
bracis-33646	199	35	theories	theorie	VERB
bracis-33646	199	36	s.t	s.t	PROPN
bracis-33646	199	37	.	.	PROPN
bracis-33646	199	38	\(a	\(a	PROPN
bracis-33646	200	1	\not	\not	ADV
bracis-33646	200	2	\subseteq	\subseteq	PROPN
bracis-33646	200	3	b\	b\	VERB
bracis-33646	200	4	)	)	PUNCT
bracis-33646	200	5	.	.	PUNCT
bracis-33646	201	1	if	if	SCONJ
bracis-33646	201	2	cn	cn	PROPN
bracis-33646	201	3	is	be	AUX
bracis-33646	201	4	compact	compact	ADJ
bracis-33646	201	5	,	,	PUNCT
bracis-33646	201	6	for	for	ADP
bracis-33646	201	7	any	any	DET
bracis-33646	201	8	\(b	\(b	NOUN
bracis-33646	201	9	'	'	PART
bracis-33646	201	10	\in	\in	PROPN
bracis-33646	201	11	b\bot	b\bot	PROPN
bracis-33646	201	12	a\	a\	PROPN
bracis-33646	201	13	)	)	PUNCT
bracis-33646	201	14	,	,	PUNCT
bracis-33646	201	15	there	there	PRON
bracis-33646	201	16	is	be	VERB
bracis-33646	201	17	some	some	DET
bracis-33646	201	18	\(w\in	\(w\in	NOUN
bracis-33646	201	19	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	201	20	a\rrbracket	a\rrbracket	PRON
bracis-33646	201	21	}	}	PUNCT
bracis-33646	201	22	\	\	NOUN
bracis-33646	201	23	)	)	PUNCT
bracis-33646	201	24	s.t	s.t	PROPN
bracis-33646	201	25	.	.	PROPN
bracis-33646	201	26	\(b	\(b	PROPN
bracis-33646	201	27	'	'	PART
bracis-33646	201	28	=	=	SYM
bracis-33646	201	29	th(\llbracket	th(\llbracket	PROPN
bracis-33646	201	30	b\rrbracket	b\rrbracket	NOUN
bracis-33646	201	31	\cup	\cup	PROPN
bracis-33646	201	32	\{m\})\	\{m\})\	ADP
bracis-33646	201	33	)	)	PUNCT
bracis-33646	201	34	.	.	PUNCT
bracis-33646	202	1	if	if	SCONJ
bracis-33646	202	2	\(\mathcal	\(\mathcal	ADJ
bracis-33646	202	3	{	{	PUNCT
bracis-33646	202	4	l}\	l}\	PROPN
bracis-33646	202	5	)	)	PUNCT
bracis-33646	202	6	is	be	AUX
bracis-33646	202	7	agm	agm	PROPN
bracis-33646	202	8	-	-	PUNCT
bracis-33646	202	9	compliant	compliant	NOUN
bracis-33646	202	10	,	,	PUNCT
bracis-33646	202	11	for	for	ADP
bracis-33646	202	12	any	any	DET
bracis-33646	202	13	\(b	\(b	NOUN
bracis-33646	202	14	'	'	PART
bracis-33646	202	15	\in	\in	PROPN
bracis-33646	202	16	b^{-(a)}\	b^{-(a)}\	PROPN
bracis-33646	202	17	)	)	PUNCT
bracis-33646	202	18	there	there	PRON
bracis-33646	202	19	is	be	VERB
bracis-33646	202	20	\(x	\(x	ADJ
bracis-33646	202	21	\subseteq	\subseteq	PROPN
bracis-33646	202	22	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	202	23	a\rrbracket	a\rrbracket	DET
bracis-33646	202	24	}	}	PUNCT
bracis-33646	202	25	\	\	NOUN
bracis-33646	202	26	)	)	PUNCT
bracis-33646	202	27	s.t	s.t	PROPN
bracis-33646	202	28	.	.	PROPN
bracis-33646	202	29	\(b	\(b	PROPN
bracis-33646	202	30	'	'	PART
bracis-33646	202	31	=	=	SYM
bracis-33646	202	32	th(\llbracket	th(\llbracket	PROPN
bracis-33646	202	33	b\rrbracket	b\rrbracket	NOUN
bracis-33646	202	34	\cup	\cup	PROPN
bracis-33646	202	35	x)\	x)\	PROPN
bracis-33646	202	36	)	)	PUNCT
bracis-33646	202	37	.	.	PUNCT
bracis-33646	203	1	the	the	DET
bracis-33646	203	2	above	above	ADJ
bracis-33646	203	3	result	result	NOUN
bracis-33646	203	4	indicates	indicate	VERB
bracis-33646	203	5	that	that	SCONJ
bracis-33646	203	6	both	both	DET
bracis-33646	203	7	agm	agm	PROPN
bracis-33646	203	8	’s	’s	PART
bracis-33646	203	9	rational	rational	ADJ
bracis-33646	203	10	contractions	contraction	NOUN
bracis-33646	203	11	and	and	CCONJ
bracis-33646	203	12	hansson	hansson	PROPN
bracis-33646	203	13	’s	’s	PART
bracis-33646	203	14	belief	belief	NOUN
bracis-33646	203	15	base	base	NOUN
bracis-33646	203	16	contraction	contraction	NOUN
bracis-33646	203	17	could	could	AUX
bracis-33646	203	18	,	,	PUNCT
bracis-33646	203	19	in	in	ADP
bracis-33646	203	20	principle	principle	NOUN
bracis-33646	203	21	,	,	PUNCT
bracis-33646	203	22	be	be	AUX
bracis-33646	203	23	defined	define	VERB
bracis-33646	203	24	by	by	ADP
bracis-33646	203	25	means	mean	NOUN
bracis-33646	203	26	of	of	ADP
bracis-33646	203	27	a	a	DET
bracis-33646	203	28	semantic	semantic	ADJ
bracis-33646	203	29	selection	selection	NOUN
bracis-33646	203	30	function	function	NOUN
bracis-33646	203	31	that	that	PRON
bracis-33646	203	32	chooses	choose	VERB
bracis-33646	203	33	an	an	DET
bracis-33646	203	34	appropriate	appropriate	ADJ
bracis-33646	203	35	set	set	NOUN
bracis-33646	203	36	of	of	ADP
bracis-33646	203	37	models	model	NOUN
bracis-33646	203	38	to	to	PART
bracis-33646	203	39	define	define	VERB
bracis-33646	203	40	the	the	DET
bracis-33646	203	41	contraction	contraction	NOUN
bracis-33646	203	42	.	.	PUNCT
bracis-33646	204	1	the	the	DET
bracis-33646	204	2	question	question	NOUN
bracis-33646	204	3	that	that	PRON
bracis-33646	204	4	now	now	ADV
bracis-33646	204	5	remains	remain	VERB
bracis-33646	204	6	is	be	AUX
bracis-33646	204	7	:	:	PUNCT
bracis-33646	204	8	which	which	DET
bracis-33646	204	9	conditions	condition	NOUN
bracis-33646	204	10	could	could	AUX
bracis-33646	204	11	be	be	AUX
bracis-33646	204	12	enforced	enforce	VERB
bracis-33646	204	13	on	on	ADP
bracis-33646	204	14	ssfs	ssfs	ADJ
bracis-33646	204	15	to	to	PART
bracis-33646	204	16	define	define	VERB
bracis-33646	204	17	these	these	DET
bracis-33646	204	18	operations	operation	NOUN
bracis-33646	204	19	?	?	PUNCT
bracis-33646	205	1	from	from	ADP
bracis-33646	205	2	now	now	ADV
bracis-33646	205	3	on	on	ADV
bracis-33646	205	4	,	,	PUNCT
bracis-33646	205	5	we	we	PRON
bracis-33646	205	6	will	will	AUX
bracis-33646	205	7	focus	focus	VERB
bracis-33646	205	8	on	on	ADP
bracis-33646	205	9	studying	study	VERB
bracis-33646	205	10	the	the	DET
bracis-33646	205	11	conditions	condition	NOUN
bracis-33646	205	12	of	of	ADP
bracis-33646	205	13	an	an	DET
bracis-33646	205	14	ssf	ssf	NOUN
bracis-33646	205	15	to	to	PART
bracis-33646	205	16	ensure	ensure	VERB
bracis-33646	205	17	the	the	DET
bracis-33646	205	18	respective	respective	ADJ
bracis-33646	205	19	contraction	contraction	NOUN
bracis-33646	205	20	is	be	AUX
bracis-33646	205	21	rational	rational	ADJ
bracis-33646	205	22	.	.	PUNCT
bracis-33646	206	1	the	the	DET
bracis-33646	206	2	study	study	NOUN
bracis-33646	206	3	of	of	ADP
bracis-33646	206	4	partial	partial	ADJ
bracis-33646	206	5	meet	meet	NOUN
bracis-33646	206	6	contractions	contraction	NOUN
bracis-33646	206	7	in	in	ADP
bracis-33646	206	8	the	the	DET
bracis-33646	206	9	framework	framework	NOUN
bracis-33646	206	10	of	of	ADP
bracis-33646	206	11	semantic	semantic	ADJ
bracis-33646	206	12	selection	selection	NOUN
bracis-33646	206	13	contractions	contraction	NOUN
bracis-33646	206	14	will	will	AUX
bracis-33646	206	15	be	be	AUX
bracis-33646	206	16	relegated	relegate	VERB
bracis-33646	206	17	to	to	ADP
bracis-33646	206	18	future	future	ADJ
bracis-33646	206	19	work	work	NOUN
bracis-33646	206	20	.	.	PUNCT
bracis-33646	207	1	definition	definition	NOUN
bracis-33646	207	2	12	12	NUM
bracis-33646	207	3	let	let	VERB
bracis-33646	207	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	207	5	{	{	PUNCT
bracis-33646	207	6	m	m	NOUN
bracis-33646	207	7	}	}	PUNCT
bracis-33646	207	8	=	=	PUNCT
bracis-33646	207	9	\langle	\langle	PROPN
bracis-33646	207	10	m	m	PROPN
bracis-33646	207	11	,	,	PUNCT
bracis-33646	207	12	l	l	PROPN
bracis-33646	207	13	,	,	PUNCT
bracis-33646	207	14	\vdash	\vdash	VERB
bracis-33646	207	15	\rangle	\rangle	NOUN
bracis-33646	207	16	\	\	NOUN
bracis-33646	207	17	)	)	PUNCT
bracis-33646	207	18	be	be	AUX
bracis-33646	207	19	an	an	DET
bracis-33646	207	20	amt	amt	PROPN
bracis-33646	207	21	,	,	PUNCT
bracis-33646	207	22	\(x	\(x	ADJ
bracis-33646	207	23	\in	\in	PROPN
bracis-33646	207	24	bo_{\mathcal	bo_{\mathcal	PROPN
bracis-33646	207	25	{	{	PUNCT
bracis-33646	207	26	m}}\	m}}\	PROPN
bracis-33646	207	27	)	)	PUNCT
bracis-33646	207	28	be	be	AUX
bracis-33646	207	29	a	a	DET
bracis-33646	207	30	b.o.s	b.o.s	NOUN
bracis-33646	207	31	,	,	PUNCT
bracis-33646	207	32	and	and	CCONJ
bracis-33646	207	33	f	f	PROPN
bracis-33646	207	34	be	be	AUX
bracis-33646	207	35	an	an	DET
bracis-33646	207	36	ssf	ssf	NOUN
bracis-33646	207	37	on	on	ADP
bracis-33646	207	38	x.	x.	NOUN
bracis-33646	208	1	we	we	PRON
bracis-33646	208	2	say	say	VERB
bracis-33646	208	3	f	f	PROPN
bracis-33646	208	4	is	be	AUX
bracis-33646	208	5	topological	topological	ADJ
bracis-33646	208	6	in	in	ADP
bracis-33646	208	7	x	x	PUNCT
bracis-33646	208	8	if	if	SCONJ
bracis-33646	208	9	for	for	ADP
bracis-33646	208	10	any	any	DET
bracis-33646	208	11	y	y	PROPN
bracis-33646	208	12	s.t	s.t	PROPN
bracis-33646	208	13	.	.	PUNCT
bracis-33646	208	14	\(\overline{y	\(\overline{y	PROPN
bracis-33646	208	15	}	}	PUNCT
bracis-33646	208	16	\in	\in	PROPN
bracis-33646	208	17	bo_{\mathcal	bo_{\mathcal	PROPN
bracis-33646	208	18	{	{	PUNCT
bracis-33646	208	19	m}}\	m}}\	PROPN
bracis-33646	208	20	)	)	PUNCT
bracis-33646	208	21	,	,	PUNCT
bracis-33646	208	22	it	it	PRON
bracis-33646	208	23	holds	hold	VERB
bracis-33646	208	24	that	that	SCONJ
bracis-33646	208	25	\(f(x	\(f(x	NOUN
bracis-33646	208	26	,	,	PUNCT
bracis-33646	208	27	y	y	NOUN
bracis-33646	208	28	)	)	PUNCT
bracis-33646	208	29	\in	\in	PROPN
bracis-33646	208	30	bo_{\mathcal	bo_{\mathcal	PROPN
bracis-33646	208	31	{	{	PUNCT
bracis-33646	208	32	m}}\	m}}\	PROPN
bracis-33646	208	33	)	)	PUNCT
bracis-33646	208	34	.	.	PUNCT
bracis-33646	209	1	we	we	PRON
bracis-33646	209	2	say	say	VERB
bracis-33646	209	3	a	a	DET
bracis-33646	209	4	selections	selection	NOUN
bracis-33646	209	5	contraction	contraction	NOUN
bracis-33646	209	6	operator	operator	NOUN
bracis-33646	209	7	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	209	8	)	)	PUNCT
bracis-33646	209	9	on	on	ADP
bracis-33646	209	10	a	a	DET
bracis-33646	209	11	set	set	NOUN
bracis-33646	209	12	of	of	ADP
bracis-33646	209	13	formulas	formula	NOUN
bracis-33646	209	14	b	b	PROPN
bracis-33646	209	15	is	be	AUX
bracis-33646	209	16	topological	topological	ADJ
bracis-33646	209	17	if	if	SCONJ
bracis-33646	209	18	there	there	PRON
bracis-33646	209	19	is	be	VERB
bracis-33646	209	20	some	some	DET
bracis-33646	209	21	topological	topological	ADJ
bracis-33646	209	22	ssf	ssf	NOUN
bracis-33646	209	23	f	f	PROPN
bracis-33646	209	24	on	on	ADP
bracis-33646	209	25	\(\llbracket	\(\llbracket	NOUN
bracis-33646	209	26	b\rrbracket	b\rrbracket	X
bracis-33646	209	27	\	\	PROPN
bracis-33646	209	28	)	)	PUNCT
bracis-33646	209	29	.	.	PUNCT
bracis-33646	210	1	we	we	PRON
bracis-33646	210	2	now	now	ADV
bracis-33646	210	3	show	show	VERB
bracis-33646	210	4	that	that	SCONJ
bracis-33646	210	5	topological	topological	ADJ
bracis-33646	210	6	contractions	contraction	NOUN
bracis-33646	210	7	are	be	AUX
bracis-33646	210	8	agm	agm	PROPN
bracis-33646	210	9	rational	rational	ADJ
bracis-33646	210	10	contractions	contraction	NOUN
bracis-33646	210	11	.	.	PUNCT
bracis-33646	211	1	theorem	theorem	NOUN
bracis-33646	211	2	1	1	NUM
bracis-33646	211	3	let	let	VERB
bracis-33646	211	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	211	5	{	{	PUNCT
bracis-33646	211	6	l}\	l}\	PROPN
bracis-33646	211	7	)	)	PUNCT
bracis-33646	211	8	be	be	AUX
bracis-33646	211	9	a	a	DET
bracis-33646	211	10	logic	logic	NOUN
bracis-33646	211	11	,	,	PUNCT
bracis-33646	211	12	\(k\in	\(k\in	PROPN
bracis-33646	211	13	th_\mathcal	th_\mathcal	PROPN
bracis-33646	211	14	{	{	PUNCT
bracis-33646	211	15	l}\	l}\	PROPN
bracis-33646	211	16	)	)	PUNCT
bracis-33646	211	17	be	be	AUX
bracis-33646	211	18	a	a	DET
bracis-33646	211	19	theory	theory	NOUN
bracis-33646	211	20	and	and	CCONJ
bracis-33646	211	21	\(\dot{-	\(\dot{-	NOUN
bracis-33646	211	22	}	}	PUNCT
bracis-33646	211	23	:	:	PUNCT
bracis-33646	212	1	2^l	2^l	NUM
bracis-33646	212	2	\times	\time	VERB
bracis-33646	212	3	2^l	2^l	NUM
bracis-33646	212	4	\rightarrow	\rightarrow	PROPN
bracis-33646	212	5	2^l\	2^l\	NUM
bracis-33646	212	6	)	)	PUNCT
bracis-33646	212	7	be	be	AUX
bracis-33646	212	8	a	a	DET
bracis-33646	212	9	topological	topological	ADJ
bracis-33646	212	10	semantic	semantic	ADJ
bracis-33646	212	11	selection	selection	NOUN
bracis-33646	212	12	contraction	contraction	NOUN
bracis-33646	212	13	on	on	ADP
bracis-33646	212	14	k.	k.	PROPN
bracis-33646	212	15	then	then	ADV
bracis-33646	212	16	,	,	PUNCT
bracis-33646	212	17	for	for	ADP
bracis-33646	212	18	any	any	DET
bracis-33646	212	19	\(a	\(a	NOUN
bracis-33646	212	20	,	,	PUNCT
bracis-33646	212	21	a'\subseteq	a'\subseteq	PROPN
bracis-33646	212	22	l\	l\	ADJ
bracis-33646	212	23	)	)	PUNCT
bracis-33646	212	24	,	,	PUNCT
bracis-33646	212	25	it	it	PRON
bracis-33646	212	26	holds	hold	VERB
bracis-33646	212	27	that	that	SCONJ
bracis-33646	212	28	:	:	PUNCT
bracis-33646	212	29	(	(	PUNCT
bracis-33646	212	30	closure	closure	NOUN
bracis-33646	212	31	)	)	PUNCT
bracis-33646	212	32	\(k\dot{-}a	\(k\dot{-}a	PROPN
bracis-33646	212	33	=	=	SYM
bracis-33646	212	34	cn(k\dot{-}a)\	cn(k\dot{-}a)\	PROPN
bracis-33646	212	35	)	)	PUNCT
bracis-33646	212	36	(	(	PUNCT
bracis-33646	212	37	success	success	NOUN
bracis-33646	212	38	)	)	PUNCT
bracis-33646	212	39	if	if	SCONJ
bracis-33646	212	40	\(a	\(a	NOUN
bracis-33646	212	41	\not	\not	ADV
bracis-33646	212	42	\subseteq	\subseteq	PROPN
bracis-33646	212	43	cn(\emptyset	cn(\emptyset	NOUN
bracis-33646	212	44	)	)	PUNCT
bracis-33646	212	45	\	\	PROPN
bracis-33646	212	46	)	)	PUNCT
bracis-33646	212	47	,	,	PUNCT
bracis-33646	212	48	then	then	ADV
bracis-33646	212	49	\(a\not	\(a\not	PROPN
bracis-33646	212	50	\subseteq	\subseteq	PROPN
bracis-33646	212	51	cn(b	cn(b	PUNCT
bracis-33646	212	52	\dot{-}a)\	\dot{-}a)\	PROPN
bracis-33646	212	53	)	)	PUNCT
bracis-33646	212	54	(	(	PUNCT
bracis-33646	212	55	inclusion	inclusion	NOUN
bracis-33646	212	56	)	)	PUNCT
bracis-33646	212	57	\(b\dot{-}a\subseteq	\(b\dot{-}a\subseteq	PROPN
bracis-33646	212	58	b\	b\	PUNCT
bracis-33646	212	59	)	)	PUNCT
bracis-33646	212	60	(	(	PUNCT
bracis-33646	212	61	vacuity	vacuity	NOUN
bracis-33646	212	62	)	)	PUNCT
bracis-33646	212	63	if	if	SCONJ
bracis-33646	212	64	\(a\not	\(a\not	PROPN
bracis-33646	212	65	\subseteq	\subseteq	VERB
bracis-33646	212	66	k\	k\	PROPN
bracis-33646	212	67	)	)	PUNCT
bracis-33646	212	68	then	then	ADV
bracis-33646	212	69	\(k\dot{-}a	\(k\dot{-}a	VERB
bracis-33646	212	70	=	=	SYM
bracis-33646	212	71	k\	k\	NOUN
bracis-33646	212	72	)	)	PUNCT
bracis-33646	212	73	(	(	PUNCT
bracis-33646	212	74	recovery	recovery	NOUN
bracis-33646	212	75	)	)	PUNCT
bracis-33646	212	76	\(k	\(k	NOUN
bracis-33646	213	1	\subseteq	\subseteq	PROPN
bracis-33646	213	2	cn(k\dot{-}a	cn(k\dot{-}a	VERB
bracis-33646	213	3	\cup	\cup	NOUN
bracis-33646	213	4	a)\	a)\	NUM
bracis-33646	213	5	)	)	PUNCT
bracis-33646	213	6	(	(	PUNCT
bracis-33646	213	7	extensionality	extensionality	NOUN
bracis-33646	213	8	)	)	PUNCT
bracis-33646	213	9	if	if	SCONJ
bracis-33646	213	10	\(cn(a	\(cn(a	PROPN
bracis-33646	213	11	)	)	PUNCT
bracis-33646	213	12	=	=	SYM
bracis-33646	213	13	cn(a')\	cn(a')\	PROPN
bracis-33646	213	14	)	)	PUNCT
bracis-33646	213	15	then	then	ADV
bracis-33646	213	16	\(k\dot{-}a	\(k\dot{-}a	PROPN
bracis-33646	213	17	=	=	SYM
bracis-33646	213	18	k\dot{-}a'\	k\dot{-}a'\	PROPN
bracis-33646	213	19	)	)	PUNCT
bracis-33646	213	20	proof	proof	NOUN
bracis-33646	213	21	notice	notice	VERB
bracis-33646	213	22	that	that	SCONJ
bracis-33646	213	23	(	(	PUNCT
bracis-33646	213	24	extensionality	extensionality	NOUN
bracis-33646	213	25	)	)	PUNCT
bracis-33646	213	26	and	and	CCONJ
bracis-33646	213	27	(	(	PUNCT
bracis-33646	213	28	closure	closure	NOUN
bracis-33646	213	29	)	)	PUNCT
bracis-33646	213	30	follow	follow	VERB
bracis-33646	213	31	directly	directly	ADV
bracis-33646	213	32	from	from	ADP
bracis-33646	213	33	the	the	DET
bracis-33646	213	34	fact	fact	NOUN
bracis-33646	213	35	that	that	SCONJ
bracis-33646	213	36	k	k	PROPN
bracis-33646	213	37	is	be	AUX
bracis-33646	213	38	a	a	DET
bracis-33646	213	39	theory	theory	NOUN
bracis-33646	213	40	and	and	CCONJ
bracis-33646	213	41	from	from	ADP
bracis-33646	213	42	the	the	DET
bracis-33646	213	43	definition	definition	NOUN
bracis-33646	213	44	of	of	ADP
bracis-33646	213	45	a	a	DET
bracis-33646	213	46	selection	selection	NOUN
bracis-33646	213	47	contraction	contraction	NOUN
bracis-33646	213	48	.	.	PUNCT
bracis-33646	214	1	for	for	ADP
bracis-33646	214	2	the	the	DET
bracis-33646	214	3	other	other	ADJ
bracis-33646	214	4	postulates	postulate	NOUN
bracis-33646	214	5	,	,	PUNCT
bracis-33646	214	6	let	let	VERB
bracis-33646	214	7	us	we	PRON
bracis-33646	214	8	take	take	VERB
bracis-33646	214	9	a	a	DET
bracis-33646	214	10	model	model	NOUN
bracis-33646	214	11	theory	theory	NOUN
bracis-33646	214	12	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	214	13	{	{	PUNCT
bracis-33646	214	14	l})\	l})\	X
bracis-33646	214	15	)	)	PUNCT
bracis-33646	214	16	and	and	CCONJ
bracis-33646	214	17	an	an	DET
bracis-33646	214	18	ssf	ssf	NOUN
bracis-33646	214	19	f	f	X
bracis-33646	214	20	which	which	PRON
bracis-33646	214	21	characterise	characterise	VERB
bracis-33646	214	22	\(\dot{-}\	\(\dot{-}\	PROPN
bracis-33646	214	23	)	)	PUNCT
bracis-33646	214	24	on	on	ADP
bracis-33646	214	25	the	the	DET
bracis-33646	214	26	set	set	PROPN
bracis-33646	214	27	b.	b.	PROPN
bracis-33646	214	28	as	as	ADP
bracis-33646	214	29	(	(	PUNCT
bracis-33646	214	30	success	success	NOUN
bracis-33646	214	31	)	)	PUNCT
bracis-33646	214	32	and	and	CCONJ
bracis-33646	214	33	(	(	PUNCT
bracis-33646	214	34	inclusion	inclusion	NOUN
bracis-33646	214	35	)	)	PUNCT
bracis-33646	214	36	have	have	AUX
bracis-33646	214	37	been	be	AUX
bracis-33646	214	38	proved	prove	VERB
bracis-33646	214	39	in	in	ADP
bracis-33646	214	40	proposition	proposition	NOUN
bracis-33646	214	41	 	 	SPACE
bracis-33646	214	42	4	4	NUM
bracis-33646	214	43	,	,	PUNCT
bracis-33646	214	44	we	we	PRON
bracis-33646	214	45	will	will	AUX
bracis-33646	214	46	focus	focus	VERB
bracis-33646	214	47	on	on	ADP
bracis-33646	214	48	the	the	DET
bracis-33646	214	49	remaining	remain	VERB
bracis-33646	214	50	postulates	postulate	NOUN
bracis-33646	214	51	.	.	PUNCT
bracis-33646	215	1	we	we	PRON
bracis-33646	215	2	briefly	briefly	ADV
bracis-33646	215	3	discussed	discuss	VERB
bracis-33646	215	4	(	(	PUNCT
bracis-33646	215	5	vacuity	vacuity	NOUN
bracis-33646	215	6	)	)	PUNCT
bracis-33646	215	7	in	in	ADP
bracis-33646	215	8	the	the	DET
bracis-33646	215	9	proof	proof	NOUN
bracis-33646	215	10	of	of	ADP
bracis-33646	215	11	(	(	PUNCT
bracis-33646	215	12	uniformity	uniformity	NOUN
bracis-33646	215	13	)	)	PUNCT
bracis-33646	215	14	in	in	ADP
bracis-33646	215	15	proposition	proposition	NOUN
bracis-33646	215	16	 	 	SPACE
bracis-33646	215	17	4	4	NUM
bracis-33646	215	18	,	,	PUNCT
bracis-33646	215	19	but	but	CCONJ
bracis-33646	215	20	let	let	VERB
bracis-33646	215	21	us	we	PRON
bracis-33646	215	22	show	show	VERB
bracis-33646	215	23	the	the	DET
bracis-33646	215	24	complete	complete	ADJ
bracis-33646	215	25	reasoning	reasoning	NOUN
bracis-33646	215	26	here	here	ADV
bracis-33646	215	27	.	.	PUNCT
bracis-33646	216	1	take	take	VERB
bracis-33646	216	2	\(a	\(a	NOUN
bracis-33646	216	3	\not	\not	ADV
bracis-33646	216	4	\subseteq	\subseteq	PROPN
bracis-33646	216	5	k\	k\	PROPN
bracis-33646	216	6	)	)	PUNCT
bracis-33646	216	7	,	,	PUNCT
bracis-33646	216	8	then	then	ADV
bracis-33646	216	9	\(\llbracket	\(\llbracket	PROPN
bracis-33646	216	10	k\rrbracket	k\rrbracket	PROPN
bracis-33646	216	11	\cap	\cap	PROPN
bracis-33646	216	12	\overline{\llbracket	\overline{\llbracket	VERB
bracis-33646	216	13	a\rrbracket	a\rrbracket	PRON
bracis-33646	216	14	}	}	PUNCT
bracis-33646	216	15	\ne	\ne	PROPN
bracis-33646	216	16	\emptyset	\emptyset	VERB
bracis-33646	216	17	\	\	NOUN
bracis-33646	216	18	)	)	PUNCT
bracis-33646	216	19	.	.	PUNCT
bracis-33646	217	1	as	as	ADP
bracis-33646	217	2	such	such	ADJ
bracis-33646	217	3	,	,	PUNCT
bracis-33646	217	4	\(f(\llbracket	\(f(\llbracket	ADJ
bracis-33646	217	5	k\rrbracket	k\rrbracket	NOUN
bracis-33646	217	6	,	,	PUNCT
bracis-33646	217	7	\llbracket	\llbracket	PROPN
bracis-33646	217	8	k\rrbracket	k\rrbracket	PROPN
bracis-33646	217	9	)	)	PUNCT
bracis-33646	217	10	\cap	\cap	PROPN
bracis-33646	217	11	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	217	12	a\rrbracket	a\rrbracket	NOUN
bracis-33646	217	13	}	}	PUNCT
bracis-33646	217	14	=	=	SYM
bracis-33646	217	15	\llbracket	\llbracket	PROPN
bracis-33646	217	16	k\rrbracket	k\rrbracket	PROPN
bracis-33646	217	17	\cap	\cap	NOUN
bracis-33646	217	18	\overline{\llbracket	\overline{\llbracket	VERB
bracis-33646	217	19	a\rrbracket	a\rrbracket	PRON
bracis-33646	217	20	}	}	PUNCT
bracis-33646	217	21	\ne	\ne	PROPN
bracis-33646	217	22	\emptyset	\emptyset	VERB
bracis-33646	217	23	\	\	NOUN
bracis-33646	217	24	)	)	PUNCT
bracis-33646	217	25	.	.	PUNCT
bracis-33646	218	1	on	on	ADP
bracis-33646	218	2	the	the	DET
bracis-33646	218	3	other	other	ADJ
bracis-33646	218	4	hand	hand	NOUN
bracis-33646	218	5	,	,	PUNCT
bracis-33646	218	6	\(f(\llbracket	\(f(\llbracket	NOUN
bracis-33646	218	7	k\rrbracket	k\rrbracket	NOUN
bracis-33646	218	8	,	,	PUNCT
bracis-33646	218	9	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	218	10	a\rrbracket	a\rrbracket	NOUN
bracis-33646	218	11	}	}	PUNCT
bracis-33646	218	12	)	)	PUNCT
bracis-33646	218	13	\cap	\cap	PROPN
bracis-33646	218	14	\llbracket	\llbracket	PROPN
bracis-33646	218	15	k\rrbracket	k\rrbracket	PROPN
bracis-33646	218	16	\ne	\ne	PROPN
bracis-33646	218	17	\emptyset	\emptyset	VERB
bracis-33646	218	18	\	\	NOUN
bracis-33646	218	19	)	)	PUNCT
bracis-33646	218	20	.	.	PUNCT
bracis-33646	219	1	thus	thus	ADV
bracis-33646	219	2	,	,	PUNCT
bracis-33646	219	3	\(f(\llbracket	\(f(\llbracket	ADP
bracis-33646	219	4	k\rrbracket	k\rrbracket	NOUN
bracis-33646	219	5	,	,	PUNCT
bracis-33646	219	6	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	219	7	a\rrbracket	a\rrbracket	NOUN
bracis-33646	219	8	}	}	PUNCT
bracis-33646	219	9	)	)	PUNCT
bracis-33646	220	1	=	=	SYM
bracis-33646	220	2	\llbracket	\llbracket	PROPN
bracis-33646	220	3	k\rrbracket	k\rrbracket	PROPN
bracis-33646	220	4	\	\	PROPN
bracis-33646	220	5	)	)	PUNCT
bracis-33646	220	6	and	and	CCONJ
bracis-33646	220	7	\(k\dot{-}a	\(k\dot{-}a	PROPN
bracis-33646	220	8	=	=	SYM
bracis-33646	220	9	k\	k\	NOUN
bracis-33646	220	10	)	)	PUNCT
bracis-33646	220	11	.	.	PUNCT
bracis-33646	221	1	to	to	PART
bracis-33646	221	2	prove	prove	VERB
bracis-33646	221	3	(	(	PUNCT
bracis-33646	221	4	recovery	recovery	NOUN
bracis-33646	221	5	)	)	PUNCT
bracis-33646	221	6	,	,	PUNCT
bracis-33646	221	7	we	we	PRON
bracis-33646	221	8	just	just	ADV
bracis-33646	221	9	need	need	VERB
bracis-33646	221	10	to	to	PART
bracis-33646	221	11	observe	observe	VERB
bracis-33646	221	12	that	that	SCONJ
bracis-33646	221	13	,	,	PUNCT
bracis-33646	221	14	since	since	SCONJ
bracis-33646	221	15	f	f	PROPN
bracis-33646	221	16	is	be	AUX
bracis-33646	221	17	topological	topological	ADJ
bracis-33646	221	18	and	and	CCONJ
bracis-33646	221	19	\(\llbracket	\(\llbracket	NOUN
bracis-33646	221	20	k\dot{-}a\rrbracket	k\dot{-}a\rrbracket	NOUN
bracis-33646	221	21	=	=	PUNCT
bracis-33646	221	22	f(\llbracket	f(\llbracket	NOUN
bracis-33646	221	23	k\rrbracket	k\rrbracket	NOUN
bracis-33646	221	24	,	,	PUNCT
bracis-33646	221	25	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	221	26	a\rrbracket	a\rrbracket	NOUN
bracis-33646	221	27	}	}	PUNCT
bracis-33646	221	28	)	)	PUNCT
bracis-33646	221	29	\	\	NOUN
bracis-33646	221	30	)	)	PUNCT
bracis-33646	221	31	,	,	PUNCT
bracis-33646	221	32	it	it	PRON
bracis-33646	221	33	holds	hold	VERB
bracis-33646	221	34	that	that	SCONJ
bracis-33646	221	35	$	$	SYM
bracis-33646	221	36	$	$	SYM
bracis-33646	221	37	\begin{array}{ll	\begin{array}{ll	PROPN
bracis-33646	221	38	}	}	PUNCT
bracis-33646	221	39	\llbracket	\llbracket	PROPN
bracis-33646	221	40	cn	cn	PROPN
bracis-33646	221	41	(	(	PUNCT
bracis-33646	221	42	k\dot{-}a	k\dot{-}a	PROPN
bracis-33646	221	43	\cup	\cup	VERB
bracis-33646	221	44	a)\rrbracket	a)\rrbracket	ADJ
bracis-33646	221	45	&	&	CCONJ
bracis-33646	222	1	=	=	SYM
bracis-33646	222	2	\llbracket	\llbracket	PROPN
bracis-33646	222	3	k\dot{-}a\rrbracket	k\dot{-}a\rrbracket	PROPN
bracis-33646	222	4	\cap	\cap	VERB
bracis-33646	222	5	\llbracket	\llbracket	PROPN
bracis-33646	223	1	a\rrbracket	a\rrbracket	DET
bracis-33646	223	2	\\	\\	NOUN
bracis-33646	223	3	&	&	CCONJ
bracis-33646	223	4	=	=	SYM
bracis-33646	223	5	f(\llbracket	f(\llbracket	NOUN
bracis-33646	223	6	k\rrbracket	k\rrbracket	NOUN
bracis-33646	223	7	,	,	PUNCT
bracis-33646	223	8	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	223	9	a\rrbracket	a\rrbracket	NOUN
bracis-33646	223	10	}	}	PUNCT
bracis-33646	223	11	)	)	PUNCT
bracis-33646	223	12	\cap	\cap	PROPN
bracis-33646	223	13	\llbracket	\llbracket	PROPN
bracis-33646	223	14	a\rrbracket	a\rrbracket	DET
bracis-33646	223	15	\\	\\	NOUN
bracis-33646	223	16	&	&	CCONJ
bracis-33646	223	17	=	=	PRON
bracis-33646	223	18	(	(	PUNCT
bracis-33646	223	19	\llbracket	\llbracket	PROPN
bracis-33646	223	20	k\rrbracket	k\rrbracket	NOUN
bracis-33646	223	21	\cup	\cup	ADP
bracis-33646	223	22	x	x	SYM
bracis-33646	223	23	)	)	PUNCT
bracis-33646	223	24	\cap	\cap	PROPN
bracis-33646	223	25	\llbracket	\llbracket	PROPN
bracis-33646	223	26	a\rrbracket	a\rrbracket	PRON
bracis-33646	223	27	,	,	PUNCT
bracis-33646	223	28	~\text	~\text	PROPN
bracis-33646	223	29	{	{	PUNCT
bracis-33646	223	30	for	for	ADP
bracis-33646	223	31	}	}	PUNCT
bracis-33646	223	32	\text	\text	PROPN
bracis-33646	223	33	{	{	PUNCT
bracis-33646	223	34	some	some	PRON
bracis-33646	223	35	}	}	PUNCT
bracis-33646	223	36	~x\subseteq	~x\subseteq	PUNCT
bracis-33646	223	37	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	223	38	a\rrbracket	a\rrbracket	PRON
bracis-33646	223	39	}	}	PUNCT
bracis-33646	223	40	\\	\\	NOUN
bracis-33646	223	41	&	&	CCONJ
bracis-33646	223	42	=	=	SYM
bracis-33646	223	43	\llbracket	\llbracket	PROPN
bracis-33646	223	44	k\rrbracket	k\rrbracket	PROPN
bracis-33646	223	45	\cap	\cap	NOUN
bracis-33646	223	46	\llbracket	\llbracket	PROPN
bracis-33646	223	47	a\rrbracket	a\rrbracket	PRON
bracis-33646	223	48	\end{array}$$	\end{array}$$	VERB
bracis-33646	223	49	since	since	SCONJ
bracis-33646	223	50	\(\llbracket	\(\llbracket	PROPN
bracis-33646	223	51	cn	cn	PROPN
bracis-33646	223	52	(	(	PUNCT
bracis-33646	223	53	k\dot{-}a	k\dot{-}a	PROPN
bracis-33646	223	54	\cup	\cup	VERB
bracis-33646	223	55	a)\rrbracket	a)\rrbracket	ADV
bracis-33646	223	56	\subseteq	\subseteq	PROPN
bracis-33646	223	57	\llbracket	\llbracket	PROPN
bracis-33646	223	58	k\rrbracket	k\rrbracket	PROPN
bracis-33646	223	59	\	\	PROPN
bracis-33646	223	60	)	)	PUNCT
bracis-33646	223	61	,	,	PUNCT
bracis-33646	223	62	we	we	PRON
bracis-33646	223	63	conclude	conclude	VERB
bracis-33646	223	64	\(k	\(k	NOUN
bracis-33646	223	65	\subseteq	\subseteq	PROPN
bracis-33646	223	66	cn(k\dot{-}a	cn(k\dot{-}a	VERB
bracis-33646	223	67	\cup	\cup	NOUN
bracis-33646	223	68	a)\	a)\	NUM
bracis-33646	223	69	)	)	PUNCT
bracis-33646	223	70	.	.	PUNCT
bracis-33646	223	71	   	   	SPACE
bracis-33646	224	1	\(\square	\(\square	VERB
bracis-33646	224	2	\	\	NOUN
bracis-33646	224	3	)	)	PUNCT
bracis-33646	224	4	more	more	ADV
bracis-33646	224	5	yet	yet	ADV
bracis-33646	224	6	,	,	PUNCT
bracis-33646	224	7	any	any	DET
bracis-33646	224	8	semantic	semantic	ADJ
bracis-33646	224	9	selection	selection	NOUN
bracis-33646	224	10	contraction	contraction	NOUN
bracis-33646	224	11	which	which	PRON
bracis-33646	224	12	is	be	AUX
bracis-33646	224	13	rational	rational	ADJ
bracis-33646	224	14	is	be	AUX
bracis-33646	224	15	topological	topological	ADJ
bracis-33646	224	16	.	.	PUNCT
bracis-33646	225	1	theorem	theorem	ADJ
bracis-33646	225	2	2	2	NUM
bracis-33646	225	3	let	let	VERB
bracis-33646	225	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	225	5	{	{	PUNCT
bracis-33646	225	6	l}\	l}\	PROPN
bracis-33646	225	7	)	)	PUNCT
bracis-33646	225	8	be	be	AUX
bracis-33646	225	9	a	a	DET
bracis-33646	225	10	logic	logic	NOUN
bracis-33646	225	11	,	,	PUNCT
bracis-33646	225	12	\(k\in	\(k\in	PROPN
bracis-33646	225	13	th_\mathcal	th_\mathcal	PROPN
bracis-33646	225	14	{	{	PUNCT
bracis-33646	225	15	l}\	l}\	PROPN
bracis-33646	225	16	)	)	PUNCT
bracis-33646	225	17	be	be	AUX
bracis-33646	225	18	a	a	DET
bracis-33646	225	19	theory	theory	NOUN
bracis-33646	225	20	and	and	CCONJ
bracis-33646	225	21	\(\dot{-	\(\dot{-	NOUN
bracis-33646	225	22	}	}	PUNCT
bracis-33646	225	23	:	:	PUNCT
bracis-33646	226	1	2^l	2^l	NUM
bracis-33646	226	2	\times	\time	VERB
bracis-33646	226	3	2^l	2^l	NUM
bracis-33646	226	4	\mapsto	\mapsto	PROPN
bracis-33646	226	5	2^l\	2^l\	NUM
bracis-33646	226	6	)	)	PUNCT
bracis-33646	226	7	be	be	AUX
bracis-33646	226	8	a	a	DET
bracis-33646	226	9	semantic	semantic	ADJ
bracis-33646	226	10	selection	selection	NOUN
bracis-33646	226	11	contraction	contraction	NOUN
bracis-33646	226	12	on	on	ADP
bracis-33646	226	13	k	k	X
bracis-33646	226	14	satisfying	satisfying	ADJ
bracis-33646	226	15	(	(	PUNCT
bracis-33646	226	16	closure	closure	NOUN
bracis-33646	226	17	)	)	PUNCT
bracis-33646	226	18	,	,	PUNCT
bracis-33646	226	19	(	(	PUNCT
bracis-33646	226	20	success),(inclusion	success),(inclusion	NOUN
bracis-33646	226	21	)	)	PUNCT
bracis-33646	226	22	,	,	PUNCT
bracis-33646	226	23	(	(	PUNCT
bracis-33646	226	24	vacuity),(recovery	vacuity),(recovery	NOUN
bracis-33646	226	25	)	)	PUNCT
bracis-33646	226	26	,	,	PUNCT
bracis-33646	226	27	and	and	CCONJ
bracis-33646	226	28	(	(	PUNCT
bracis-33646	226	29	extensionality	extensionality	NOUN
bracis-33646	226	30	)	)	PUNCT
bracis-33646	226	31	for	for	ADP
bracis-33646	226	32	any	any	DET
bracis-33646	226	33	\(a\subseteq	\(a\subseteq	ADJ
bracis-33646	226	34	l\	l\	NOUN
bracis-33646	226	35	)	)	PUNCT
bracis-33646	226	36	,	,	PUNCT
bracis-33646	226	37	then	then	ADV
bracis-33646	226	38	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	226	39	)	)	PUNCT
bracis-33646	226	40	is	be	AUX
bracis-33646	226	41	topological	topological	ADJ
bracis-33646	226	42	.	.	PUNCT
bracis-33646	227	1	proof	proof	NOUN
bracis-33646	227	2	as	as	ADP
bracis-33646	227	3	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	227	4	)	)	PUNCT
bracis-33646	227	5	is	be	AUX
bracis-33646	227	6	a	a	DET
bracis-33646	227	7	semantic	semantic	ADJ
bracis-33646	227	8	selection	selection	NOUN
bracis-33646	227	9	contraction	contraction	NOUN
bracis-33646	227	10	,	,	PUNCT
bracis-33646	227	11	it	it	PRON
bracis-33646	227	12	means	mean	VERB
bracis-33646	227	13	that	that	SCONJ
bracis-33646	227	14	there	there	PRON
bracis-33646	227	15	is	be	VERB
bracis-33646	227	16	some	some	DET
bracis-33646	227	17	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	227	18	{	{	PUNCT
bracis-33646	227	19	l	l	NOUN
bracis-33646	227	20	}	}	PUNCT
bracis-33646	227	21	)	)	PUNCT
bracis-33646	228	1	=	=	PUNCT
bracis-33646	229	1	\langle	\langle	PROPN
bracis-33646	229	2	m	m	PRON
bracis-33646	229	3	,	,	PUNCT
bracis-33646	229	4	\vdash	\vdash	VERB
bracis-33646	229	5	\rangle	\rangle	NOUN
bracis-33646	229	6	\	\	NOUN
bracis-33646	229	7	)	)	PUNCT
bracis-33646	229	8	and	and	CCONJ
bracis-33646	229	9	an	an	DET
bracis-33646	229	10	ssf	ssf	PROPN
bracis-33646	229	11	f	f	PROPN
bracis-33646	229	12	s.t	s.t	PROPN
bracis-33646	229	13	.	.	PROPN
bracis-33646	230	1	for	for	ADP
bracis-33646	230	2	any	any	DET
bracis-33646	230	3	\(a	\(a	ADJ
bracis-33646	230	4	\in	\in	ADJ
bracis-33646	230	5	th_\mathcal	th_\mathcal	PROPN
bracis-33646	230	6	{	{	PUNCT
bracis-33646	230	7	l}\	l}\	PROPN
bracis-33646	230	8	)	)	PUNCT
bracis-33646	230	9	,	,	PUNCT
bracis-33646	230	10	\(k\dot{-}a	\(k\dot{-}a	NOUN
bracis-33646	230	11	=	=	SYM
bracis-33646	230	12	th(f(\llbracket	th(f(\llbracket	PROPN
bracis-33646	230	13	k\rrbracket	k\rrbracket	NOUN
bracis-33646	230	14	,	,	PUNCT
bracis-33646	230	15	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	230	16	a\rrbracket	a\rrbracket	NOUN
bracis-33646	230	17	}	}	PUNCT
bracis-33646	230	18	)	)	PUNCT
bracis-33646	230	19	\	\	NOUN
bracis-33646	230	20	)	)	PUNCT
bracis-33646	230	21	.	.	PUNCT
bracis-33646	231	1	let	let	VERB
bracis-33646	231	2	us	we	PRON
bracis-33646	231	3	construct	construct	VERB
bracis-33646	231	4	a	a	DET
bracis-33646	231	5	function	function	NOUN
bracis-33646	231	6	\(f'\	\(f'\	NOUN
bracis-33646	231	7	)	)	PUNCT
bracis-33646	231	8	as	as	ADP
bracis-33646	231	9	$	$	SYM
bracis-33646	231	10	$	$	SYM
bracis-33646	231	11	f'(x	f'(x	NOUN
bracis-33646	231	12	,	,	PUNCT
bracis-33646	231	13	y	y	NOUN
bracis-33646	231	14	)	)	PUNCT
bracis-33646	231	15	=	=	SYM
bracis-33646	231	16	{	{	PUNCT
bracis-33646	231	17	\left\	\left\	PROPN
bracis-33646	231	18	{	{	PUNCT
bracis-33646	231	19	\begin{array}{ll	\begin{array}{ll	PROPN
bracis-33646	231	20	}	}	PUNCT
bracis-33646	231	21	f(x	f(x	PROPN
bracis-33646	231	22	,	,	PUNCT
bracis-33646	231	23	y	y	PROPN
bracis-33646	231	24	)	)	PUNCT
bracis-33646	231	25	&	&	CCONJ
bracis-33646	231	26	\text	\text	PROPN
bracis-33646	231	27	{	{	PUNCT
bracis-33646	231	28	if	if	SCONJ
bracis-33646	231	29	}	}	PUNCT
bracis-33646	231	30	~x\ne	~x\ne	PROPN
bracis-33646	231	31	\llbracket	\llbracket	PROPN
bracis-33646	231	32	k\rrbracket	k\rrbracket	PROPN
bracis-33646	231	33	\\	\\	NOUN
bracis-33646	231	34	cl(f(x	cl(f(x	NOUN
bracis-33646	231	35	,	,	PUNCT
bracis-33646	231	36	y))\cap	y))\cap	NOUN
bracis-33646	231	37	(	(	PUNCT
bracis-33646	231	38	x\cup	x\cup	PROPN
bracis-33646	231	39	y	y	PROPN
bracis-33646	231	40	)	)	PUNCT
bracis-33646	231	41	&	&	CCONJ
bracis-33646	231	42	\text	\text	PROPN
bracis-33646	231	43	{	{	PUNCT
bracis-33646	231	44	if	if	SCONJ
bracis-33646	231	45	}	}	PUNCT
bracis-33646	231	46	~x=	~x=	NUM
bracis-33646	231	47	\llbracket	\llbracket	PROPN
bracis-33646	231	48	k\rrbracket	k\rrbracket	NOUN
bracis-33646	231	49	\\	\\	NOUN
bracis-33646	231	50	\end{array}\right	\end{array}\right	PROPN
bracis-33646	231	51	.	.	PUNCT
bracis-33646	232	1	}	}	PUNCT
bracis-33646	232	2	$	$	SYM
bracis-33646	232	3	$	$	NOUN
bracis-33646	232	4	we	we	PRON
bracis-33646	232	5	need	need	VERB
bracis-33646	232	6	to	to	PART
bracis-33646	232	7	show	show	VERB
bracis-33646	232	8	that	that	SCONJ
bracis-33646	232	9	\(f'\	\(f'\	NOUN
bracis-33646	232	10	)	)	PUNCT
bracis-33646	232	11	is	be	AUX
bracis-33646	232	12	ssf	ssf	NOUN
bracis-33646	232	13	on	on	ADP
bracis-33646	232	14	\(x=\llbracket	\(x=\llbracket	NOUN
bracis-33646	232	15	k\rrbracket	k\rrbracket	X
bracis-33646	232	16	\	\	NOUN
bracis-33646	232	17	)	)	PUNCT
bracis-33646	232	18	and	and	CCONJ
bracis-33646	232	19	that	that	SCONJ
bracis-33646	232	20	it	it	PRON
bracis-33646	232	21	is	be	AUX
bracis-33646	232	22	topological	topological	ADJ
bracis-33646	232	23	on	on	ADP
bracis-33646	232	24	x.	x.	PROPN
bracis-33646	232	25	i	i	PROPN
bracis-33646	232	26	)	)	PUNCT
bracis-33646	232	27	notice	notice	VERB
bracis-33646	232	28	\(x	\(x	PROPN
bracis-33646	232	29	\subseteq	\subseteq	PROPN
bracis-33646	232	30	f'(x	f'(x	PROPN
bracis-33646	232	31	,	,	PUNCT
bracis-33646	232	32	y	y	PROPN
bracis-33646	232	33	)	)	PUNCT
bracis-33646	233	1	\subseteq	\subseteq	PROPN
bracis-33646	233	2	x\cup	x\cup	PROPN
bracis-33646	233	3	y\	y\	NOUN
bracis-33646	233	4	)	)	PUNCT
bracis-33646	233	5	is	be	AUX
bracis-33646	233	6	immediate	immediate	ADJ
bracis-33646	233	7	by	by	ADP
bracis-33646	233	8	construction	construction	NOUN
bracis-33646	233	9	,	,	PUNCT
bracis-33646	233	10	as	as	SCONJ
bracis-33646	233	11	\(x	\(x	NOUN
bracis-33646	233	12	\subseteq	\subseteq	PROPN
bracis-33646	233	13	f(x	f(x	PROPN
bracis-33646	233	14	,	,	PUNCT
bracis-33646	233	15	y	y	PROPN
bracis-33646	233	16	)	)	PUNCT
bracis-33646	233	17	\subseteq	\subseteq	PROPN
bracis-33646	233	18	x\cup	x\cup	PROPN
bracis-33646	233	19	y\	y\	NOUN
bracis-33646	233	20	)	)	PUNCT
bracis-33646	233	21	,	,	PUNCT
bracis-33646	233	22	since	since	SCONJ
bracis-33646	233	23	f	f	PROPN
bracis-33646	233	24	is	be	AUX
bracis-33646	233	25	an	an	DET
bracis-33646	233	26	ssf	ssf	NOUN
bracis-33646	233	27	,	,	PUNCT
bracis-33646	233	28	and	and	CCONJ
bracis-33646	233	29	\(z	\(z	DET
bracis-33646	233	30	\subseteq	\subseteq	PROPN
bracis-33646	233	31	cl(z)\	cl(z)\	NOUN
bracis-33646	233	32	)	)	PUNCT
bracis-33646	233	33	.	.	PUNCT
bracis-33646	234	1	ii	ii	X
bracis-33646	234	2	)	)	PUNCT
bracis-33646	234	3	if	if	SCONJ
bracis-33646	234	4	\(y\ne	\(y\ne	PROPN
bracis-33646	234	5	\emptyset	\emptyset	VERB
bracis-33646	234	6	\	\	PROPN
bracis-33646	234	7	)	)	PUNCT
bracis-33646	234	8	,	,	PUNCT
bracis-33646	234	9	then	then	ADV
bracis-33646	234	10	\(f(x	\(f(x	PROPN
bracis-33646	234	11	,	,	PUNCT
bracis-33646	234	12	y)\cap	y)\cap	PROPN
bracis-33646	234	13	y\ne	y\ne	PROPN
bracis-33646	234	14	\emptyset	\emptyset	VERB
bracis-33646	234	15	\	\	PROPN
bracis-33646	234	16	)	)	PUNCT
bracis-33646	234	17	,	,	PUNCT
bracis-33646	234	18	thus	thus	ADV
bracis-33646	234	19	\(cl(f(x	\(cl(f(x	PROPN
bracis-33646	234	20	,	,	PUNCT
bracis-33646	234	21	y))\cap	y))\cap	NOUN
bracis-33646	234	22	y	y	PROPN
bracis-33646	234	23	\ne	\ne	PROPN
bracis-33646	234	24	\emptyset	\emptyset	VERB
bracis-33646	234	25	\	\	PROPN
bracis-33646	234	26	)	)	PUNCT
bracis-33646	234	27	,	,	PUNCT
bracis-33646	234	28	and	and	CCONJ
bracis-33646	234	29	\(f'(x	\(f'(x	NOUN
bracis-33646	234	30	,	,	PUNCT
bracis-33646	234	31	y)\cap	y)\cap	PROPN
bracis-33646	234	32	y	y	PROPN
bracis-33646	234	33	\ne	\ne	PROPN
bracis-33646	234	34	\emptyset	\emptyset	VERB
bracis-33646	234	35	\	\	PROPN
bracis-33646	234	36	)	)	PUNCT
bracis-33646	234	37	.	.	PUNCT
bracis-33646	235	1	iii	iii	X
bracis-33646	235	2	)	)	PUNCT
bracis-33646	235	3	take	take	VERB
bracis-33646	235	4	\(y\subseteq	\(y\subseteq	PROPN
bracis-33646	235	5	m\	m\	NOUN
bracis-33646	235	6	)	)	PUNCT
bracis-33646	235	7	,	,	PUNCT
bracis-33646	235	8	s.t	s.t	PROPN
bracis-33646	235	9	.	.	PROPN
bracis-33646	235	10	\(x\cap	\(x\cap	PROPN
bracis-33646	235	11	y	y	PROPN
bracis-33646	235	12	\ne	\ne	PROPN
bracis-33646	235	13	\emptyset	\emptyset	PROPN
bracis-33646	235	14	\	\	PROPN
bracis-33646	235	15	)	)	PUNCT
bracis-33646	235	16	,	,	PUNCT
bracis-33646	235	17	then	then	ADV
bracis-33646	235	18	\(f(x	\(f(x	PROPN
bracis-33646	235	19	,	,	PUNCT
bracis-33646	235	20	y	y	NOUN
bracis-33646	235	21	)	)	PUNCT
bracis-33646	235	22	=	=	NOUN
bracis-33646	235	23	x\	x\	NOUN
bracis-33646	235	24	)	)	PUNCT
bracis-33646	235	25	,	,	PUNCT
bracis-33646	235	26	thus	thus	ADV
bracis-33646	235	27	\	\	PROPN
bracis-33646	235	28	(	(	PUNCT
bracis-33646	235	29	f'(x	f'(x	NOUN
bracis-33646	235	30	,	,	PUNCT
bracis-33646	235	31	y	y	PROPN
bracis-33646	235	32	)	)	PUNCT
bracis-33646	235	33	=	=	SYM
bracis-33646	235	34	cl(x	cl(x	X
bracis-33646	235	35	)	)	PUNCT
bracis-33646	235	36	=	=	PUNCT
bracis-33646	235	37	x\	x\	NOUN
bracis-33646	235	38	)	)	PUNCT
bracis-33646	235	39	since	since	SCONJ
bracis-33646	235	40	\(x=	\(x=	PROPN
bracis-33646	235	41	\llbracket	\llbracket	PROPN
bracis-33646	235	42	k\rrbracket	k\rrbracket	PROPN
bracis-33646	235	43	\	\	PROPN
bracis-33646	235	44	)	)	PUNCT
bracis-33646	235	45	.	.	PUNCT
bracis-33646	236	1	iv	iv	X
bracis-33646	236	2	)	)	PUNCT
bracis-33646	236	3	take	take	VERB
bracis-33646	236	4	\(y	\(y	NUM
bracis-33646	236	5	\in	\in	PROPN
bracis-33646	236	6	bo_{mod(\mathcal	bo_{mod(\mathcal	PROPN
bracis-33646	236	7	{	{	PUNCT
bracis-33646	236	8	l})}\	l})}\	PROPN
bracis-33646	236	9	)	)	PUNCT
bracis-33646	236	10	,	,	PUNCT
bracis-33646	236	11	\(f'(x,\overline{y	\(f'(x,\overline{y	NOUN
bracis-33646	236	12	}	}	PUNCT
bracis-33646	236	13	)	)	PUNCT
bracis-33646	237	1	=	=	SYM
bracis-33646	237	2	cl(f(x,\overline{y	cl(f(x,\overline{y	NOUN
bracis-33646	237	3	}	}	PUNCT
bracis-33646	237	4	)	)	PUNCT
bracis-33646	237	5	)	)	PUNCT
bracis-33646	237	6	\cap	\cap	PROPN
bracis-33646	237	7	(	(	PUNCT
bracis-33646	237	8	x\cup	x\cup	PROPN
bracis-33646	237	9	y)\	y)\	NUM
bracis-33646	237	10	)	)	PUNCT
bracis-33646	237	11	.	.	PUNCT
bracis-33646	238	1	first	first	ADV
bracis-33646	238	2	,	,	PUNCT
bracis-33646	238	3	let	let	VERB
bracis-33646	238	4	us	we	PRON
bracis-33646	238	5	see	see	VERB
bracis-33646	238	6	that	that	DET
bracis-33646	238	7	\(th(f'(x	\(th(f'(x	NOUN
bracis-33646	238	8	,	,	PUNCT
bracis-33646	238	9	y	y	NOUN
bracis-33646	238	10	)	)	PUNCT
bracis-33646	238	11	)	)	PUNCT
bracis-33646	239	1	=	=	PUNCT
bracis-33646	239	2	th(f(x	th(f(x	ADP
bracis-33646	239	3	,	,	PUNCT
bracis-33646	239	4	y))\	y))\	PROPN
bracis-33646	239	5	)	)	PUNCT
bracis-33646	239	6	.	.	PUNCT
bracis-33646	240	1	we	we	PRON
bracis-33646	240	2	known	know	VERB
bracis-33646	240	3	that	that	DET
bracis-33646	240	4	\(th(f(x	\(th(f(x	PROPN
bracis-33646	240	5	,	,	PUNCT
bracis-33646	240	6	y	y	PROPN
bracis-33646	240	7	)	)	PUNCT
bracis-33646	240	8	)	)	PUNCT
bracis-33646	241	1	=	=	SYM
bracis-33646	241	2	th(cl(f(x	th(cl(f(x	PROPN
bracis-33646	241	3	,	,	PUNCT
bracis-33646	241	4	y))\	y))\	PROPN
bracis-33646	241	5	)	)	PUNCT
bracis-33646	241	6	,	,	PUNCT
bracis-33646	241	7	by	by	ADP
bracis-33646	241	8	definition	definition	NOUN
bracis-33646	241	9	,	,	PUNCT
bracis-33646	241	10	and	and	CCONJ
bracis-33646	241	11	\(f'(x	\(f'(x	NOUN
bracis-33646	241	12	,	,	PUNCT
bracis-33646	241	13	y	y	PROPN
bracis-33646	241	14	)	)	PUNCT
bracis-33646	241	15	\subseteq	\subseteq	PROPN
bracis-33646	241	16	cl(f(x	cl(f(x	PROPN
bracis-33646	241	17	,	,	PUNCT
bracis-33646	241	18	y))\	y))\	PROPN
bracis-33646	241	19	)	)	PUNCT
bracis-33646	241	20	,	,	PUNCT
bracis-33646	241	21	thus	thus	ADV
bracis-33646	241	22	it	it	PRON
bracis-33646	241	23	holds	hold	VERB
bracis-33646	241	24	that	that	DET
bracis-33646	241	25	\(th(f(x	\(th(f(x	NOUN
bracis-33646	241	26	,	,	PUNCT
bracis-33646	241	27	y	y	PROPN
bracis-33646	241	28	)	)	PUNCT
bracis-33646	241	29	)	)	PUNCT
bracis-33646	242	1	\subseteq	\subseteq	PROPN
bracis-33646	242	2	th(f'(x	th(f'(x	NOUN
bracis-33646	242	3	,	,	PUNCT
bracis-33646	242	4	y))\	y))\	PROPN
bracis-33646	242	5	)	)	PUNCT
bracis-33646	242	6	.	.	PUNCT
bracis-33646	243	1	furthermore	furthermore	ADV
bracis-33646	243	2	,	,	PUNCT
bracis-33646	243	3	as	as	ADP
bracis-33646	243	4	\(f(x	\(f(x	PROPN
bracis-33646	243	5	,	,	PUNCT
bracis-33646	243	6	y	y	PROPN
bracis-33646	243	7	)	)	PUNCT
bracis-33646	243	8	\subseteq	\subseteq	PROPN
bracis-33646	243	9	cl(f(x	cl(f(x	PROPN
bracis-33646	243	10	,	,	PUNCT
bracis-33646	243	11	y))\	y))\	PROPN
bracis-33646	243	12	)	)	PUNCT
bracis-33646	243	13	and	and	CCONJ
bracis-33646	243	14	\(f(x	\(f(x	PROPN
bracis-33646	243	15	,	,	PUNCT
bracis-33646	243	16	y)\subseteq	y)\subseteq	NOUN
bracis-33646	243	17	x\cup	x\cup	PROPN
bracis-33646	243	18	y\	y\	NOUN
bracis-33646	243	19	)	)	PUNCT
bracis-33646	243	20	,	,	PUNCT
bracis-33646	243	21	it	it	PRON
bracis-33646	243	22	holds	hold	VERB
bracis-33646	243	23	that	that	SCONJ
bracis-33646	243	24	\(f(x	\(f(x	NOUN
bracis-33646	243	25	,	,	PUNCT
bracis-33646	243	26	y	y	PROPN
bracis-33646	243	27	)	)	PUNCT
bracis-33646	243	28	\subseteq	\subseteq	PROPN
bracis-33646	243	29	f'(x	f'(x	NOUN
bracis-33646	243	30	,	,	PUNCT
bracis-33646	243	31	y)\	y)\	NUM
bracis-33646	243	32	)	)	PUNCT
bracis-33646	243	33	.	.	PUNCT
bracis-33646	244	1	thus	thus	ADV
bracis-33646	244	2	\(th(f'(x	\(th(f'(x	VERB
bracis-33646	244	3	,	,	PUNCT
bracis-33646	244	4	y	y	NOUN
bracis-33646	244	5	)	)	PUNCT
bracis-33646	244	6	)	)	PUNCT
bracis-33646	245	1	\subseteq	\subseteq	PROPN
bracis-33646	245	2	th(f(x	th(f(x	ADP
bracis-33646	245	3	,	,	PUNCT
bracis-33646	245	4	y))\	y))\	PROPN
bracis-33646	245	5	)	)	PUNCT
bracis-33646	245	6	.	.	PUNCT
bracis-33646	246	1	let	let	VERB
bracis-33646	246	2	\(k	\(k	NOUN
bracis-33646	246	3	'	'	PART
bracis-33646	246	4	=	=	SYM
bracis-33646	246	5	th(f'(x	th(f'(x	PROPN
bracis-33646	246	6	,	,	PUNCT
bracis-33646	246	7	y))\	y))\	PROPN
bracis-33646	246	8	)	)	PUNCT
bracis-33646	246	9	.	.	PUNCT
bracis-33646	247	1	since	since	SCONJ
bracis-33646	247	2	\(th(f'(x	\(th(f'(x	PROPN
bracis-33646	247	3	,	,	PUNCT
bracis-33646	247	4	y	y	NOUN
bracis-33646	247	5	)	)	PUNCT
bracis-33646	247	6	)	)	PUNCT
bracis-33646	248	1	=	=	PUNCT
bracis-33646	248	2	th(f(x	th(f(x	ADP
bracis-33646	248	3	,	,	PUNCT
bracis-33646	248	4	y))\	y))\	PROPN
bracis-33646	248	5	)	)	PUNCT
bracis-33646	248	6	,	,	PUNCT
bracis-33646	248	7	\(x	\(x	NOUN
bracis-33646	248	8	=	=	SYM
bracis-33646	248	9	\llbracket	\llbracket	PROPN
bracis-33646	248	10	k\rrbracket	k\rrbracket	PROPN
bracis-33646	248	11	\	\	PROPN
bracis-33646	248	12	)	)	PUNCT
bracis-33646	248	13	,	,	PUNCT
bracis-33646	248	14	\(\overline{y}\in	\(\overline{y}\in	VERB
bracis-33646	248	15	bo_{mod(\mathcal	bo_{mod(\mathcal	PROPN
bracis-33646	248	16	{	{	PUNCT
bracis-33646	248	17	l})}\	l})}\	PROPN
bracis-33646	248	18	)	)	PUNCT
bracis-33646	248	19	,	,	PUNCT
bracis-33646	248	20	and	and	CCONJ
bracis-33646	248	21	f	f	PROPN
bracis-33646	248	22	is	be	AUX
bracis-33646	248	23	the	the	DET
bracis-33646	248	24	characteristic	characteristic	ADJ
bracis-33646	248	25	ssf	ssf	NOUN
bracis-33646	248	26	of	of	ADP
bracis-33646	248	27	\	\	PROPN
bracis-33646	248	28	(	(	PUNCT
bracis-33646	248	29	\dot{-}\	\dot{-}\	NOUN
bracis-33646	248	30	)	)	PUNCT
bracis-33646	248	31	,	,	PUNCT
bracis-33646	248	32	then	then	ADV
bracis-33646	248	33	\(k	\(k	NOUN
bracis-33646	248	34	'	'	PART
bracis-33646	248	35	=	=	SYM
bracis-33646	248	36	k	k	PROPN
bracis-33646	248	37	\dot{-	\dot{-	PROPN
bracis-33646	248	38	}	}	PUNCT
bracis-33646	248	39	th(\overline{y})\	th(\overline{y})\	ADV
bracis-33646	248	40	)	)	PUNCT
bracis-33646	248	41	.	.	PUNCT
bracis-33646	249	1	now	now	ADV
bracis-33646	249	2	,	,	PUNCT
bracis-33646	249	3	take	take	VERB
bracis-33646	249	4	\(w\in	\(w\in	PUNCT
bracis-33646	249	5	\llbracket	\llbracket	PROPN
bracis-33646	249	6	k'\rrbracket	k'\rrbracket	PROPN
bracis-33646	249	7	\	\	PROPN
bracis-33646	249	8	)	)	PUNCT
bracis-33646	249	9	and	and	CCONJ
bracis-33646	249	10	suppose	suppose	VERB
bracis-33646	249	11	\(w\not	\(w\not	PROPN
bracis-33646	249	12	\in	\in	PROPN
bracis-33646	249	13	x\cup	x\cup	PROPN
bracis-33646	249	14	y\	y\	PROPN
bracis-33646	249	15	)	)	PUNCT
bracis-33646	249	16	,	,	PUNCT
bracis-33646	249	17	then	then	ADV
bracis-33646	249	18	\(w\in	\(w\in	PUNCT
bracis-33646	249	19	\overline{x	\overline{x	PROPN
bracis-33646	249	20	}	}	PUNCT
bracis-33646	249	21	\cap	\cap	PROPN
bracis-33646	249	22	\overline{y}\	\overline{y}\	PROPN
bracis-33646	249	23	)	)	PUNCT
bracis-33646	249	24	.	.	PUNCT
bracis-33646	250	1	from	from	ADP
bracis-33646	250	2	\(w\vdash	\(w\vdash	PROPN
bracis-33646	250	3	k'\	k'\	PROPN
bracis-33646	250	4	)	)	PUNCT
bracis-33646	250	5	,	,	PUNCT
bracis-33646	250	6	we	we	PRON
bracis-33646	250	7	conclude	conclude	VERB
bracis-33646	250	8	that	that	DET
bracis-33646	250	9	\(w\vdash	\(w\vdash	VERB
bracis-33646	250	10	k	k	PROPN
bracis-33646	250	11	\dot{-	\dot{-	PROPN
bracis-33646	250	12	}	}	PUNCT
bracis-33646	250	13	th(\overline{y})\	th(\overline{y})\	ADV
bracis-33646	250	14	)	)	PUNCT
bracis-33646	250	15	and	and	CCONJ
bracis-33646	250	16	,	,	PUNCT
bracis-33646	250	17	from	from	ADP
bracis-33646	250	18	\(w\in	\(w\in	PROPN
bracis-33646	250	19	\overline{y}\	\overline{y}\	PROPN
bracis-33646	250	20	)	)	PUNCT
bracis-33646	250	21	,	,	PUNCT
bracis-33646	250	22	we	we	PRON
bracis-33646	250	23	conclude	conclude	VERB
bracis-33646	250	24	that	that	SCONJ
bracis-33646	250	25	\(w\vdash	\(w\vdash	VERB
bracis-33646	250	26	th(\overline{y})\	th(\overline{y})\	ADV
bracis-33646	250	27	)	)	PUNCT
bracis-33646	250	28	.	.	PUNCT
bracis-33646	251	1	since	since	SCONJ
bracis-33646	251	2	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	251	3	)	)	PUNCT
bracis-33646	251	4	is	be	AUX
bracis-33646	251	5	a	a	DET
bracis-33646	251	6	rational	rational	ADJ
bracis-33646	251	7	contraction	contraction	NOUN
bracis-33646	251	8	,	,	PUNCT
bracis-33646	251	9	thus	thus	ADV
bracis-33646	251	10	satisfying	satisfy	VERB
bracis-33646	251	11	(	(	PUNCT
bracis-33646	251	12	recovery	recovery	NOUN
bracis-33646	251	13	)	)	PUNCT
bracis-33646	251	14	,	,	PUNCT
bracis-33646	251	15	it	it	PRON
bracis-33646	251	16	must	must	AUX
bracis-33646	251	17	hold	hold	VERB
bracis-33646	251	18	that	that	DET
bracis-33646	251	19	\(w\vdash	\(w\vdash	VERB
bracis-33646	251	20	k\	k\	NOUN
bracis-33646	251	21	)	)	PUNCT
bracis-33646	251	22	,	,	PUNCT
bracis-33646	251	23	i.e.	i.e.	X
bracis-33646	251	24	\(w\in	\(w\in	X
bracis-33646	251	25	\llbracket	\llbracket	PROPN
bracis-33646	251	26	k\rrbracket	k\rrbracket	NOUN
bracis-33646	251	27	=	=	SYM
bracis-33646	251	28	x\	x\	NOUN
bracis-33646	251	29	)	)	PUNCT
bracis-33646	251	30	.	.	PUNCT
bracis-33646	252	1	but	but	CCONJ
bracis-33646	252	2	this	this	PRON
bracis-33646	252	3	contradicts	contradict	VERB
bracis-33646	252	4	the	the	DET
bracis-33646	252	5	fact	fact	NOUN
bracis-33646	252	6	that	that	SCONJ
bracis-33646	252	7	\(w\in	\(w\in	PUNCT
bracis-33646	252	8	\overline{x}\	\overline{x}\	PROPN
bracis-33646	252	9	)	)	PUNCT
bracis-33646	252	10	.	.	PUNCT
bracis-33646	253	1	then	then	ADV
bracis-33646	253	2	it	it	PRON
bracis-33646	253	3	must	must	AUX
bracis-33646	253	4	hold	hold	VERB
bracis-33646	253	5	that	that	DET
bracis-33646	253	6	\(\llbracket	\(\llbracket	NOUN
bracis-33646	253	7	k'\rrbracket	k'\rrbracket	PROPN
bracis-33646	253	8	\subseteq	\subseteq	PROPN
bracis-33646	253	9	x\cup	x\cup	PROPN
bracis-33646	253	10	y\	y\	NOUN
bracis-33646	253	11	)	)	PUNCT
bracis-33646	253	12	and	and	CCONJ
bracis-33646	253	13	\(f'(x	\(f'(x	NOUN
bracis-33646	253	14	,	,	PUNCT
bracis-33646	253	15	y	y	NOUN
bracis-33646	253	16	)	)	PUNCT
bracis-33646	253	17	=	=	PUNCT
bracis-33646	254	1	\llbracket	\llbracket	PROPN
bracis-33646	254	2	k'\rrbracket	k'\rrbracket	PROPN
bracis-33646	254	3	\in	\in	PROPN
bracis-33646	254	4	bo_{mod(\mathcal	bo_{mod(\mathcal	PROPN
bracis-33646	254	5	{	{	PUNCT
bracis-33646	254	6	l})}\	l})}\	PROPN
bracis-33646	254	7	)	)	PUNCT
bracis-33646	254	8	.	.	PUNCT
bracis-33646	255	1	thus	thus	ADV
bracis-33646	255	2	\(f'\	\(f'\	NOUN
bracis-33646	255	3	)	)	PUNCT
bracis-33646	255	4	is	be	AUX
bracis-33646	255	5	topological	topological	ADJ
bracis-33646	255	6	.	.	PUNCT
bracis-33646	255	7	   	   	SPACE
bracis-33646	256	1	\(\square	\(\square	VERB
bracis-33646	256	2	\	\	NOUN
bracis-33646	256	3	)	)	PUNCT
bracis-33646	256	4	notice	notice	NOUN
bracis-33646	256	5	in	in	ADP
bracis-33646	256	6	the	the	DET
bracis-33646	256	7	proof	proof	NOUN
bracis-33646	256	8	above	above	ADP
bracis-33646	256	9	that	that	SCONJ
bracis-33646	256	10	the	the	DET
bracis-33646	256	11	requirement	requirement	NOUN
bracis-33646	256	12	of	of	ADP
bracis-33646	256	13	satisfying	satisfy	VERB
bracis-33646	256	14	the	the	DET
bracis-33646	256	15	(	(	PUNCT
bracis-33646	256	16	recovery	recovery	NOUN
bracis-33646	256	17	)	)	PUNCT
bracis-33646	256	18	postulate	postulate	NOUN
bracis-33646	256	19	is	be	AUX
bracis-33646	256	20	essential	essential	ADJ
bracis-33646	256	21	to	to	PART
bracis-33646	256	22	construct	construct	VERB
bracis-33646	256	23	a	a	DET
bracis-33646	256	24	topological	topological	ADJ
bracis-33646	256	25	ssf	ssf	NOUN
bracis-33646	256	26	.	.	PUNCT
bracis-33646	257	1	as	as	ADP
bracis-33646	257	2	(	(	PUNCT
bracis-33646	257	3	recovery	recovery	NOUN
bracis-33646	257	4	)	)	PUNCT
bracis-33646	257	5	is	be	AUX
bracis-33646	257	6	a	a	DET
bracis-33646	257	7	central	central	ADJ
bracis-33646	257	8	property	property	NOUN
bracis-33646	257	9	of	of	ADP
bracis-33646	257	10	rational	rational	ADJ
bracis-33646	257	11	contractions	contraction	NOUN
bracis-33646	257	12	,	,	PUNCT
bracis-33646	257	13	i.e.	i.e.	X
bracis-33646	257	14	it	it	PRON
bracis-33646	257	15	is	be	AUX
bracis-33646	257	16	the	the	DET
bracis-33646	257	17	postulate	postulate	NOUN
bracis-33646	257	18	differentiating	differentiate	VERB
bracis-33646	257	19	these	these	DET
bracis-33646	257	20	operations	operation	NOUN
bracis-33646	257	21	from	from	ADP
bracis-33646	257	22	others	other	NOUN
bracis-33646	257	23	in	in	ADP
bracis-33646	257	24	the	the	DET
bracis-33646	257	25	literature	literature	NOUN
bracis-33646	257	26	,	,	PUNCT
bracis-33646	257	27	such	such	ADJ
bracis-33646	257	28	as	as	ADP
bracis-33646	257	29	withdraws	withdraw	NOUN
bracis-33646	257	30	,	,	PUNCT
bracis-33646	257	31	partial	partial	ADJ
bracis-33646	257	32	meet	meet	NOUN
bracis-33646	257	33	,	,	PUNCT
bracis-33646	257	34	etc	etc	X
bracis-33646	257	35	.	.	X
bracis-33646	257	36	,	,	PUNCT
bracis-33646	257	37	it	it	PRON
bracis-33646	257	38	indicates	indicate	VERB
bracis-33646	257	39	that	that	SCONJ
bracis-33646	257	40	our	our	PRON
bracis-33646	257	41	notion	notion	NOUN
bracis-33646	257	42	of	of	ADP
bracis-33646	257	43	topological	topological	ADJ
bracis-33646	257	44	encodes	encode	NOUN
bracis-33646	257	45	the	the	DET
bracis-33646	257	46	central	central	ADJ
bracis-33646	257	47	aspects	aspect	NOUN
bracis-33646	257	48	of	of	ADP
bracis-33646	257	49	agm	agm	PROPN
bracis-33646	257	50	rationality	rationality	NOUN
bracis-33646	257	51	.	.	PUNCT
bracis-33646	258	1	4.1	4.1	NUM
bracis-33646	258	2	on	on	ADP
bracis-33646	258	3	the	the	DET
bracis-33646	258	4	 	 	SPACE
bracis-33646	258	5	existence	existence	NOUN
bracis-33646	258	6	of	of	ADP
bracis-33646	258	7	 	 	SPACE
bracis-33646	258	8	topological	topological	ADJ
bracis-33646	258	9	contractions	contraction	NOUN
bracis-33646	258	10	we	we	PRON
bracis-33646	258	11	now	now	ADV
bracis-33646	258	12	turn	turn	VERB
bracis-33646	258	13	our	our	PRON
bracis-33646	258	14	attention	attention	NOUN
bracis-33646	258	15	to	to	ADP
bracis-33646	258	16	investigating	investigate	VERB
bracis-33646	258	17	sufficient	sufficient	ADJ
bracis-33646	258	18	and	and	CCONJ
bracis-33646	258	19	necessary	necessary	ADJ
bracis-33646	258	20	conditions	condition	NOUN
bracis-33646	258	21	for	for	ADP
bracis-33646	258	22	the	the	DET
bracis-33646	258	23	definability	definability	NOUN
bracis-33646	258	24	of	of	ADP
bracis-33646	258	25	topological	topological	ADJ
bracis-33646	258	26	contractions	contraction	NOUN
bracis-33646	258	27	in	in	ADP
bracis-33646	258	28	a	a	DET
bracis-33646	258	29	given	give	VERB
bracis-33646	258	30	logic	logic	NOUN
bracis-33646	258	31	.	.	PUNCT
bracis-33646	259	1	this	this	DET
bracis-33646	259	2	investigation	investigation	NOUN
bracis-33646	259	3	is	be	AUX
bracis-33646	259	4	closely	closely	ADV
bracis-33646	259	5	related	relate	VERB
bracis-33646	259	6	to	to	ADP
bracis-33646	259	7	those	those	PRON
bracis-33646	259	8	of	of	ADP
bracis-33646	259	9	flouris	flouris	PROPN
bracis-33646	259	10	 	 	SPACE
bracis-33646	260	1	[	[	X
bracis-33646	260	2	5	5	NUM
bracis-33646	260	3	]	]	PUNCT
bracis-33646	260	4	and	and	CCONJ
bracis-33646	260	5	ribeiro	ribeiro	PROPN
bracis-33646	260	6	et	et	PROPN
bracis-33646	260	7	al	al	PROPN
bracis-33646	260	8	.	.	PUNCT
bracis-33646	260	9	 	 	SPACE
bracis-33646	261	1	[	[	X
bracis-33646	261	2	15	15	NUM
bracis-33646	261	3	]	]	PUNCT
bracis-33646	261	4	,	,	PUNCT
bracis-33646	261	5	for	for	ADP
bracis-33646	261	6	example	example	NOUN
bracis-33646	261	7	,	,	PUNCT
bracis-33646	261	8	but	but	CCONJ
bracis-33646	261	9	employing	employ	VERB
bracis-33646	261	10	the	the	DET
bracis-33646	261	11	technical	technical	ADJ
bracis-33646	261	12	framework	framework	NOUN
bracis-33646	261	13	of	of	ADP
bracis-33646	261	14	abstract	abstract	ADJ
bracis-33646	261	15	model	model	NOUN
bracis-33646	261	16	theory	theory	NOUN
bracis-33646	261	17	and	and	CCONJ
bracis-33646	261	18	topology	topology	NOUN
bracis-33646	261	19	.	.	PUNCT
bracis-33646	262	1	first	first	ADV
bracis-33646	262	2	,	,	PUNCT
bracis-33646	262	3	an	an	DET
bracis-33646	262	4	obvious	obvious	ADJ
bracis-33646	262	5	observation	observation	NOUN
bracis-33646	262	6	is	be	AUX
bracis-33646	262	7	that	that	SCONJ
bracis-33646	262	8	topological	topological	ADJ
bracis-33646	262	9	functions	function	NOUN
bracis-33646	262	10	can	can	AUX
bracis-33646	262	11	be	be	AUX
bracis-33646	262	12	constructed	construct	VERB
bracis-33646	262	13	whenever	whenever	SCONJ
bracis-33646	262	14	there	there	PRON
bracis-33646	262	15	are	be	VERB
bracis-33646	262	16	appropriate	appropriate	ADJ
bracis-33646	262	17	basic	basic	ADJ
bracis-33646	262	18	open	open	ADJ
bracis-33646	262	19	sets	set	NOUN
bracis-33646	262	20	.	.	PUNCT
bracis-33646	263	1	lemma	lemma	PROPN
bracis-33646	263	2	5	5	NUM
bracis-33646	263	3	let	let	VERB
bracis-33646	263	4	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	263	5	{	{	PUNCT
bracis-33646	263	6	l})\	l})\	X
bracis-33646	263	7	)	)	PUNCT
bracis-33646	263	8	be	be	VERB
bracis-33646	263	9	a	a	DET
bracis-33646	263	10	regular	regular	ADJ
bracis-33646	263	11	abstract	abstract	ADJ
bracis-33646	263	12	model	model	NOUN
bracis-33646	263	13	theory	theory	NOUN
bracis-33646	263	14	and	and	CCONJ
bracis-33646	263	15	\(x	\(x	ADJ
bracis-33646	263	16	\in	\in	PROPN
bracis-33646	263	17	bo_{mod(\mathcal	bo_{mod(\mathcal	PROPN
bracis-33646	263	18	{	{	PUNCT
bracis-33646	263	19	l})}\	l})}\	PROPN
bracis-33646	263	20	)	)	PUNCT
bracis-33646	263	21	be	be	AUX
bracis-33646	263	22	a	a	DET
bracis-33646	263	23	b.o.s	b.o.s	NOUN
bracis-33646	263	24	.	.	PUNCT
bracis-33646	264	1	there	there	PRON
bracis-33646	264	2	is	be	VERB
bracis-33646	264	3	a	a	DET
bracis-33646	264	4	topological	topological	ADJ
bracis-33646	264	5	semantic	semantic	ADJ
bracis-33646	264	6	selection	selection	NOUN
bracis-33646	264	7	function	function	NOUN
bracis-33646	264	8	f	f	PROPN
bracis-33646	264	9	on	on	ADP
bracis-33646	264	10	x	x	PROPN
bracis-33646	264	11	iff	iff	PROPN
bracis-33646	264	12	for	for	ADP
bracis-33646	264	13	any	any	DET
bracis-33646	264	14	b.o.s	b.o.s	NOUN
bracis-33646	264	15	.	.	PUNCT
bracis-33646	265	1	\(y\in	\(y\in	X
bracis-33646	266	1	bo_{mod(\mathcal	bo_{mod(\mathcal	PROPN
bracis-33646	266	2	{	{	PUNCT
bracis-33646	266	3	l})}\	l})}\	PROPN
bracis-33646	266	4	)	)	PUNCT
bracis-33646	266	5	s.t	s.t	PROPN
bracis-33646	266	6	.	.	PROPN
bracis-33646	266	7	\(\overline{y	\(\overline{y	PROPN
bracis-33646	266	8	}	}	PUNCT
bracis-33646	266	9	\cap	\cap	PROPN
bracis-33646	266	10	x=\emptyset	x=\emptyset	NOUN
bracis-33646	266	11	\	\	PROPN
bracis-33646	266	12	)	)	PUNCT
bracis-33646	266	13	,	,	PUNCT
bracis-33646	266	14	there	there	PRON
bracis-33646	266	15	is	be	VERB
bracis-33646	266	16	some	some	DET
bracis-33646	266	17	b.o.s	b.o.s	PROPN
bracis-33646	266	18	.	.	PUNCT
bracis-33646	267	1	\(z\in	\(z\in	X
bracis-33646	267	2	bo_{mod(\mathcal	bo_{mod(\mathcal	PROPN
bracis-33646	267	3	{	{	PUNCT
bracis-33646	267	4	l})}\	l})}\	PROPN
bracis-33646	267	5	)	)	PUNCT
bracis-33646	267	6	s.t	s.t	PROPN
bracis-33646	267	7	.	.	PROPN
bracis-33646	267	8	\(x	\(x	PROPN
bracis-33646	268	1	\subset	\subset	PROPN
bracis-33646	268	2	z	z	PROPN
bracis-33646	268	3	\subseteq	\subseteq	PROPN
bracis-33646	268	4	x	x	PART
bracis-33646	268	5	\cup	\cup	VERB
bracis-33646	268	6	\overline{y}\	\overline{y}\	NUM
bracis-33646	268	7	)	)	PUNCT
bracis-33646	268	8	.	.	PUNCT
bracis-33646	269	1	notice	notice	VERB
bracis-33646	269	2	that	that	SCONJ
bracis-33646	269	3	lemma	lemma	PROPN
bracis-33646	269	4	 	 	SPACE
bracis-33646	269	5	5	5	NUM
bracis-33646	269	6	above	above	ADV
bracis-33646	269	7	is	be	AUX
bracis-33646	269	8	directly	directly	ADV
bracis-33646	269	9	related	relate	VERB
bracis-33646	269	10	to	to	ADP
bracis-33646	269	11	proposition	proposition	NOUN
bracis-33646	269	12	 	 	SPACE
bracis-33646	269	13	1	1	NUM
bracis-33646	269	14	.	.	PUNCT
bracis-33646	270	1	in	in	ADP
bracis-33646	270	2	fact	fact	NOUN
bracis-33646	270	3	,	,	PUNCT
bracis-33646	270	4	the	the	DET
bracis-33646	270	5	results	result	NOUN
bracis-33646	270	6	can	can	AUX
bracis-33646	270	7	be	be	AUX
bracis-33646	270	8	directly	directly	ADV
bracis-33646	270	9	translated	translate	VERB
bracis-33646	270	10	into	into	ADP
bracis-33646	270	11	each	each	DET
bracis-33646	270	12	other	other	ADJ
bracis-33646	270	13	.	.	PUNCT
bracis-33646	271	1	as	as	ADP
bracis-33646	271	2	such	such	ADJ
bracis-33646	271	3	,	,	PUNCT
bracis-33646	271	4	this	this	PRON
bracis-33646	271	5	informs	inform	VERB
bracis-33646	271	6	us	we	PRON
bracis-33646	271	7	that	that	SCONJ
bracis-33646	271	8	any	any	DET
bracis-33646	271	9	agm	agm	PROPN
bracis-33646	271	10	rational	rational	ADJ
bracis-33646	271	11	contraction	contraction	NOUN
bracis-33646	271	12	is	be	AUX
bracis-33646	271	13	,	,	PUNCT
bracis-33646	271	14	in	in	ADP
bracis-33646	271	15	fact	fact	NOUN
bracis-33646	271	16	,	,	PUNCT
bracis-33646	271	17	a	a	DET
bracis-33646	271	18	topological	topological	ADJ
bracis-33646	271	19	semantic	semantic	ADJ
bracis-33646	271	20	selection	selection	NOUN
bracis-33646	271	21	contraction	contraction	NOUN
bracis-33646	271	22	.	.	PUNCT
bracis-33646	272	1	also	also	ADV
bracis-33646	272	2	,	,	PUNCT
bracis-33646	272	3	in	in	ADP
bracis-33646	272	4	the	the	DET
bracis-33646	272	5	face	face	NOUN
bracis-33646	272	6	of	of	ADP
bracis-33646	272	7	flouris	flouris	NOUN
bracis-33646	272	8	’	'	PUNCT
bracis-33646	272	9	 	 	SPACE
bracis-33646	272	10	[	[	X
bracis-33646	272	11	5	5	NUM
bracis-33646	272	12	,	,	PUNCT
bracis-33646	272	13	theorem	theorem	VERB
bracis-33646	272	14	4.2	4.2	NUM
bracis-33646	272	15	]	]	PUNCT
bracis-33646	272	16	characterisation	characterisation	NOUN
bracis-33646	272	17	of	of	ADP
bracis-33646	272	18	agm	agm	PROPN
bracis-33646	272	19	-	-	PUNCT
bracis-33646	272	20	compliance	compliance	NOUN
bracis-33646	272	21	by	by	ADP
bracis-33646	272	22	cuts	cut	NOUN
bracis-33646	272	23	,	,	PUNCT
bracis-33646	272	24	a	a	DET
bracis-33646	272	25	similar	similar	ADJ
bracis-33646	272	26	characterisation	characterisation	NOUN
bracis-33646	272	27	could	could	AUX
bracis-33646	272	28	be	be	AUX
bracis-33646	272	29	encoded	encode	VERB
bracis-33646	272	30	within	within	ADP
bracis-33646	272	31	our	our	PRON
bracis-33646	272	32	language	language	NOUN
bracis-33646	272	33	.	.	PUNCT
bracis-33646	273	1	since	since	SCONJ
bracis-33646	273	2	this	this	DET
bracis-33646	273	3	result	result	NOUN
bracis-33646	273	4	does	do	AUX
bracis-33646	273	5	not	not	PART
bracis-33646	273	6	increase	increase	VERB
bracis-33646	273	7	our	our	PRON
bracis-33646	273	8	understanding	understanding	NOUN
bracis-33646	273	9	of	of	ADP
bracis-33646	273	10	agm	agm	PROPN
bracis-33646	273	11	compliance	compliance	NOUN
bracis-33646	273	12	and	and	CCONJ
bracis-33646	273	13	the	the	DET
bracis-33646	273	14	definability	definability	NOUN
bracis-33646	273	15	of	of	ADP
bracis-33646	273	16	topological	topological	ADJ
bracis-33646	273	17	functions	function	NOUN
bracis-33646	273	18	,	,	PUNCT
bracis-33646	273	19	we	we	PRON
bracis-33646	273	20	will	will	AUX
bracis-33646	273	21	omit	omit	VERB
bracis-33646	273	22	it	it	PRON
bracis-33646	273	23	in	in	ADP
bracis-33646	273	24	this	this	DET
bracis-33646	273	25	work	work	NOUN
bracis-33646	273	26	.	.	PUNCT
bracis-33646	274	1	lemma	lemma	PROPN
bracis-33646	274	2	 	 	SPACE
bracis-33646	274	3	5	5	NUM
bracis-33646	274	4	,	,	PUNCT
bracis-33646	274	5	however	however	ADV
bracis-33646	274	6	,	,	PUNCT
bracis-33646	274	7	can	can	AUX
bracis-33646	274	8	be	be	AUX
bracis-33646	274	9	employed	employ	VERB
bracis-33646	274	10	to	to	PART
bracis-33646	274	11	show	show	VERB
bracis-33646	274	12	that	that	SCONJ
bracis-33646	274	13	some	some	DET
bracis-33646	274	14	logics	logic	NOUN
bracis-33646	274	15	are	be	AUX
bracis-33646	274	16	not	not	PART
bracis-33646	274	17	agm	agm	ADJ
bracis-33646	274	18	-	-	PUNCT
bracis-33646	274	19	compatible	compatible	ADJ
bracis-33646	274	20	.	.	PUNCT
bracis-33646	275	1	example	example	NOUN
bracis-33646	276	1	1	1	NUM
bracis-33646	276	2	let	let	VERB
bracis-33646	276	3	us	we	PRON
bracis-33646	276	4	consider	consider	VERB
bracis-33646	276	5	the	the	DET
bracis-33646	276	6	intuitionistic	intuitionistic	ADJ
bracis-33646	276	7	propositional	propositional	ADJ
bracis-33646	276	8	logic	logic	NOUN
bracis-33646	276	9	with	with	ADP
bracis-33646	276	10	one	one	NUM
bracis-33646	276	11	propositional	propositional	ADJ
bracis-33646	276	12	symbol	symbol	NOUN
bracis-33646	276	13	p	p	NOUN
bracis-33646	276	14	,	,	PUNCT
bracis-33646	276	15	\(\mathcal	\(\mathcal	ADJ
bracis-33646	276	16	{	{	PUNCT
bracis-33646	276	17	l}_i	l}_i	PROPN
bracis-33646	276	18	=	=	SYM
bracis-33646	276	19	\langle	\langle	PROPN
bracis-33646	276	20	l_0	l_0	NOUN
bracis-33646	276	21	,	,	PUNCT
bracis-33646	276	22	cn\rangle	cn\rangle	NOUN
bracis-33646	276	23	\	\	NOUN
bracis-33646	276	24	)	)	PUNCT
bracis-33646	276	25	and	and	CCONJ
bracis-33646	276	26	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	276	27	{	{	PUNCT
bracis-33646	276	28	l}_i)\	l}_i)\	PROPN
bracis-33646	276	29	)	)	PUNCT
bracis-33646	276	30	its	its	PRON
bracis-33646	276	31	canonical	canonical	ADJ
bracis-33646	276	32	model	model	NOUN
bracis-33646	276	33	theory	theory	NOUN
bracis-33646	276	34	,	,	PUNCT
bracis-33646	276	35	i.e.	i.e.	X
bracis-33646	276	36	the	the	DET
bracis-33646	276	37	model	model	NOUN
bracis-33646	276	38	theory	theory	NOUN
bracis-33646	276	39	obtained	obtain	VERB
bracis-33646	276	40	from	from	ADP
bracis-33646	276	41	its	its	PRON
bracis-33646	276	42	theory	theory	NOUN
bracis-33646	276	43	space	space	NOUN
bracis-33646	276	44	,	,	PUNCT
bracis-33646	276	45	as	as	ADP
bracis-33646	276	46	in	in	ADP
bracis-33646	276	47	the	the	DET
bracis-33646	276	48	proof	proof	NOUN
bracis-33646	276	49	of	of	ADP
bracis-33646	276	50	proposition	proposition	NOUN
bracis-33646	276	51	 	 	SPACE
bracis-33646	276	52	2	2	NUM
bracis-33646	276	53	.	.	PUNCT
bracis-33646	277	1	the	the	DET
bracis-33646	277	2	b.o.s	b.o.s	PROPN
bracis-33646	277	3	.	.	PROPN
bracis-33646	277	4	’s	’s	PART
bracis-33646	277	5	of	of	ADP
bracis-33646	277	6	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	277	7	{	{	PUNCT
bracis-33646	277	8	l}_i)\	l}_i)\	NOUN
bracis-33646	277	9	)	)	PUNCT
bracis-33646	277	10	form	form	VERB
bracis-33646	277	11	a	a	DET
bracis-33646	277	12	complete	complete	ADJ
bracis-33646	277	13	lattice	lattice	NOUN
bracis-33646	277	14	regarding	regard	VERB
bracis-33646	277	15	the	the	DET
bracis-33646	277	16	inclusion	inclusion	NOUN
bracis-33646	277	17	order	order	NOUN
bracis-33646	277	18	,	,	PUNCT
bracis-33646	277	19	corresponding	correspond	VERB
bracis-33646	277	20	to	to	ADP
bracis-33646	277	21	the	the	DET
bracis-33646	277	22	rieger	rieger	PROPN
bracis-33646	277	23	-	-	PUNCT
bracis-33646	277	24	nishimura	nishimura	PROPN
bracis-33646	277	25	lattice	lattice	PROPN
bracis-33646	277	26	of	of	ADP
bracis-33646	277	27	intuitionistic	intuitionistic	ADJ
bracis-33646	277	28	theories	theory	NOUN
bracis-33646	277	29	,	,	PUNCT
bracis-33646	277	30	depicted	depict	VERB
bracis-33646	277	31	in	in	ADP
bracis-33646	277	32	fig	fig	NOUN
bracis-33646	277	33	.	.	PUNCT
bracis-33646	277	34	 	 	SPACE
bracis-33646	278	1	1	1	NUM
bracis-33646	278	2	.	.	PUNCT
bracis-33646	279	1	any	any	DET
bracis-33646	279	2	b.o.s	b.o.s	PROPN
bracis-33646	279	3	.	.	PUNCT
bracis-33646	280	1	in	in	ADP
bracis-33646	280	2	it	it	PRON
bracis-33646	280	3	contains	contain	VERB
bracis-33646	280	4	all	all	DET
bracis-33646	280	5	sets	set	NOUN
bracis-33646	280	6	below	below	ADP
bracis-33646	280	7	it	it	PRON
bracis-33646	280	8	in	in	ADP
bracis-33646	280	9	the	the	DET
bracis-33646	280	10	lattice	lattice	NOUN
bracis-33646	280	11	.	.	PUNCT
bracis-33646	281	1	consider	consider	VERB
bracis-33646	281	2	now	now	ADV
bracis-33646	281	3	the	the	DET
bracis-33646	281	4	theories	theory	NOUN
bracis-33646	281	5	\(k	\(k	NOUN
bracis-33646	281	6	=	=	SYM
bracis-33646	281	7	cn(\lnot	cn(\lnot	NOUN
bracis-33646	281	8	p)\	p)\	NOUN
bracis-33646	281	9	)	)	PUNCT
bracis-33646	281	10	and	and	CCONJ
bracis-33646	281	11	set	set	VERB
bracis-33646	281	12	\(a	\(a	NOUN
bracis-33646	281	13	=	=	PUNCT
bracis-33646	281	14	cn(p\vee	cn(p\vee	NOUN
bracis-33646	281	15	\lnot	\lnot	PROPN
bracis-33646	281	16	p)\	p)\	NOUN
bracis-33646	281	17	)	)	PUNCT
bracis-33646	281	18	,	,	PUNCT
bracis-33646	281	19	as	as	SCONJ
bracis-33646	281	20	one	one	PRON
bracis-33646	281	21	can	can	AUX
bracis-33646	281	22	see	see	VERB
bracis-33646	281	23	in	in	ADP
bracis-33646	281	24	fig	fig	NOUN
bracis-33646	281	25	.	.	PUNCT
bracis-33646	281	26	 	 	SPACE
bracis-33646	282	1	1	1	NUM
bracis-33646	282	2	,	,	PUNCT
bracis-33646	282	3	there	there	PRON
bracis-33646	282	4	is	be	VERB
bracis-33646	282	5	no	no	DET
bracis-33646	282	6	theory	theory	NOUN
bracis-33646	282	7	\(\vargamma	\(\vargamma	NOUN
bracis-33646	282	8	'	'	PUNCT
bracis-33646	282	9	\	\	NOUN
bracis-33646	282	10	)	)	PUNCT
bracis-33646	282	11	s.t	s.t	PROPN
bracis-33646	282	12	.	.	PROPN
bracis-33646	282	13	\(cn(\emptyset	\(cn(\emptyset	PROPN
bracis-33646	282	14	)	)	PUNCT
bracis-33646	283	1	\subset	\subset	PROPN
bracis-33646	283	2	k'\	k'\	PROPN
bracis-33646	283	3	)	)	PUNCT
bracis-33646	283	4	,	,	PUNCT
bracis-33646	283	5	\(a	\(a	NOUN
bracis-33646	283	6	\not	\not	ADV
bracis-33646	283	7	\subseteq	\subseteq	PROPN
bracis-33646	283	8	k'\	k'\	PROPN
bracis-33646	283	9	)	)	PUNCT
bracis-33646	283	10	,	,	PUNCT
bracis-33646	283	11	and	and	CCONJ
bracis-33646	283	12	\	\	PROPN
bracis-33646	283	13	(	(	PUNCT
bracis-33646	283	14	cn(k	cn(k	PUNCT
bracis-33646	283	15	'	'	PUNCT
bracis-33646	283	16	\cup	\cup	VERB
bracis-33646	283	17	a	a	PRON
bracis-33646	283	18	)	)	PUNCT
bracis-33646	283	19	=	=	SYM
bracis-33646	283	20	cn(\emptyset	cn(\emptyset	NOUN
bracis-33646	283	21	)	)	PUNCT
bracis-33646	284	1	\	\	PROPN
bracis-33646	284	2	)	)	PUNCT
bracis-33646	284	3	.	.	PUNCT
bracis-33646	285	1	in	in	ADP
bracis-33646	285	2	another	another	DET
bracis-33646	285	3	way	way	NOUN
bracis-33646	285	4	,	,	PUNCT
bracis-33646	285	5	given	give	VERB
bracis-33646	285	6	the	the	DET
bracis-33646	285	7	open	open	ADJ
bracis-33646	285	8	set	set	VERB
bracis-33646	285	9	\(x	\(x	NOUN
bracis-33646	285	10	=	=	PUNCT
bracis-33646	285	11	\llbracket	\llbracket	PROPN
bracis-33646	285	12	\lnot	\lnot	PROPN
bracis-33646	285	13	p\rrbracket	p\rrbracket	NOUN
bracis-33646	285	14	\	\	PROPN
bracis-33646	285	15	)	)	PUNCT
bracis-33646	285	16	,	,	PUNCT
bracis-33646	285	17	for	for	ADP
bracis-33646	285	18	\(y	\(y	PRON
bracis-33646	285	19	=	=	SYM
bracis-33646	285	20	\llbracket	\llbracket	PROPN
bracis-33646	285	21	p	p	PROPN
bracis-33646	285	22	\vee	\vee	PROPN
bracis-33646	285	23	\lnot	\lnot	INTJ
bracis-33646	285	24	p\rrbracket	p\rrbracket	NOUN
bracis-33646	285	25	\	\	PROPN
bracis-33646	285	26	)	)	PUNCT
bracis-33646	285	27	,	,	PUNCT
bracis-33646	285	28	there	there	PRON
bracis-33646	285	29	is	be	VERB
bracis-33646	285	30	no	no	DET
bracis-33646	285	31	b.o.s	b.o.s	NOUN
bracis-33646	285	32	.	.	PUNCT
bracis-33646	286	1	z	z	PROPN
bracis-33646	286	2	s.t	s.t	PROPN
bracis-33646	286	3	.	.	PROPN
bracis-33646	286	4	\(x\subset	\(x\subset	PROPN
bracis-33646	286	5	z	z	NOUN
bracis-33646	287	1	\subseteq	\subseteq	PROPN
bracis-33646	287	2	x	x	PART
bracis-33646	287	3	\cup	\cup	VERB
bracis-33646	287	4	\overline{y}\	\overline{y}\	NUM
bracis-33646	287	5	)	)	PUNCT
bracis-33646	287	6	,	,	PUNCT
bracis-33646	287	7	as	as	SCONJ
bracis-33646	287	8	any	any	DET
bracis-33646	287	9	such	such	ADJ
bracis-33646	287	10	element	element	NOUN
bracis-33646	287	11	would	would	AUX
bracis-33646	287	12	necessarily	necessarily	ADV
bracis-33646	287	13	include	include	VERB
bracis-33646	287	14	\(cn(p\vee	\(cn(p\vee	PROPN
bracis-33646	288	1	\lnot	\lnot	PROPN
bracis-33646	289	1	p)\not	p)\not	ADV
bracis-33646	289	2	\in	\in	PROPN
bracis-33646	289	3	x	x	PUNCT
bracis-33646	289	4	\cup	\cup	VERB
bracis-33646	289	5	\overline{y}\	\overline{y}\	NUM
bracis-33646	289	6	)	)	PUNCT
bracis-33646	289	7	.	.	PUNCT
bracis-33646	290	1	thus	thus	ADV
bracis-33646	290	2	,	,	PUNCT
bracis-33646	290	3	by	by	ADP
bracis-33646	290	4	lemma	lemma	PROPN
bracis-33646	290	5	 	 	SPACE
bracis-33646	290	6	5	5	NUM
bracis-33646	290	7	,	,	PUNCT
bracis-33646	290	8	there	there	PRON
bracis-33646	290	9	is	be	VERB
bracis-33646	290	10	no	no	DET
bracis-33646	290	11	topological	topological	ADJ
bracis-33646	290	12	semantic	semantic	ADJ
bracis-33646	290	13	selection	selection	NOUN
bracis-33646	290	14	function	function	NOUN
bracis-33646	290	15	on	on	ADP
bracis-33646	290	16	\(\llbracket	\(\llbracket	NOUN
bracis-33646	291	1	\lnot	\lnot	PROPN
bracis-33646	291	2	p\rrbracket	p\rrbracket	NOUN
bracis-33646	291	3	\	\	PROPN
bracis-33646	291	4	)	)	PUNCT
bracis-33646	291	5	.	.	PUNCT
bracis-33646	292	1	fig	fig	NOUN
bracis-33646	292	2	.	.	PUNCT
bracis-33646	293	1	1	1	X
bracis-33646	293	2	.	.	X
bracis-33646	293	3	the	the	DET
bracis-33646	293	4	rieger	rieger	PROPN
bracis-33646	293	5	-	-	PUNCT
bracis-33646	293	6	nishimura	nishimura	PROPN
bracis-33646	293	7	lattice	lattice	PROPN
bracis-33646	293	8	of	of	ADP
bracis-33646	293	9	intuitionistic	intuitionistic	ADJ
bracis-33646	293	10	basic	basic	ADJ
bracis-33646	293	11	open	open	ADJ
bracis-33646	293	12	sets	set	NOUN
bracis-33646	293	13	full	full	ADJ
bracis-33646	293	14	size	size	NOUN
bracis-33646	293	15	image	image	NOUN
bracis-33646	293	16	notice	notice	VERB
bracis-33646	293	17	that	that	SCONJ
bracis-33646	293	18	the	the	DET
bracis-33646	293	19	topological	topological	ADJ
bracis-33646	293	20	contractions	contraction	NOUN
bracis-33646	293	21	provided	provide	VERB
bracis-33646	293	22	above	above	ADV
bracis-33646	293	23	are	be	AUX
bracis-33646	293	24	defined	define	VERB
bracis-33646	293	25	to	to	PART
bracis-33646	293	26	contract	contract	VERB
bracis-33646	293	27	a	a	DET
bracis-33646	293	28	(	(	PUNCT
bracis-33646	293	29	possibly	possibly	ADV
bracis-33646	293	30	infinite	infinite	VERB
bracis-33646	293	31	)	)	PUNCT
bracis-33646	293	32	set	set	NOUN
bracis-33646	293	33	of	of	ADP
bracis-33646	293	34	formulas	formula	NOUN
bracis-33646	293	35	from	from	ADP
bracis-33646	293	36	a	a	DET
bracis-33646	293	37	theory	theory	NOUN
bracis-33646	293	38	which	which	PRON
bracis-33646	293	39	coincides	coincide	VERB
bracis-33646	293	40	with	with	ADP
bracis-33646	293	41	the	the	DET
bracis-33646	293	42	notion	notion	NOUN
bracis-33646	293	43	of	of	ADP
bracis-33646	293	44	choice	choice	NOUN
bracis-33646	293	45	multiple	multiple	ADJ
bracis-33646	293	46	contractions	contraction	NOUN
bracis-33646	293	47	 	 	SPACE
bracis-33646	294	1	[	[	X
bracis-33646	294	2	6	6	NUM
bracis-33646	294	3	]	]	PUNCT
bracis-33646	294	4	.	.	PUNCT
bracis-33646	295	1	it	it	PRON
bracis-33646	295	2	is	be	AUX
bracis-33646	295	3	useful	useful	ADJ
bracis-33646	295	4	,	,	PUNCT
bracis-33646	295	5	however	however	ADV
bracis-33646	295	6	,	,	PUNCT
bracis-33646	295	7	to	to	PART
bracis-33646	295	8	weaken	weaken	VERB
bracis-33646	295	9	our	our	PRON
bracis-33646	295	10	definition	definition	NOUN
bracis-33646	295	11	to	to	PART
bracis-33646	295	12	account	account	VERB
bracis-33646	295	13	for	for	ADP
bracis-33646	295	14	a	a	DET
bracis-33646	295	15	smaller	small	ADJ
bracis-33646	295	16	family	family	NOUN
bracis-33646	295	17	of	of	ADP
bracis-33646	295	18	theories	theory	NOUN
bracis-33646	295	19	considered	consider	VERB
bracis-33646	295	20	as	as	ADP
bracis-33646	295	21	inputs	input	NOUN
bracis-33646	295	22	to	to	ADP
bracis-33646	295	23	our	our	PRON
bracis-33646	295	24	contraction	contraction	NOUN
bracis-33646	295	25	functions	function	NOUN
bracis-33646	295	26	.	.	PUNCT
bracis-33646	296	1	for	for	ADP
bracis-33646	296	2	example	example	NOUN
bracis-33646	296	3	,	,	PUNCT
bracis-33646	296	4	we	we	PRON
bracis-33646	296	5	can	can	AUX
bracis-33646	296	6	restrict	restrict	VERB
bracis-33646	296	7	our	our	PRON
bracis-33646	296	8	analysis	analysis	NOUN
bracis-33646	296	9	to	to	ADP
bracis-33646	296	10	contracting	contract	VERB
bracis-33646	296	11	a	a	DET
bracis-33646	296	12	finite	finite	ADJ
bracis-33646	296	13	amount	amount	NOUN
bracis-33646	296	14	of	of	ADP
bracis-33646	296	15	information	information	NOUN
bracis-33646	296	16	(	(	PUNCT
bracis-33646	296	17	or	or	CCONJ
bracis-33646	296	18	equivalently	equivalently	ADV
bracis-33646	296	19	a	a	DET
bracis-33646	296	20	finitely	finitely	ADV
bracis-33646	296	21	representable	representable	ADJ
bracis-33646	296	22	theory	theory	NOUN
bracis-33646	296	23	)	)	PUNCT
bracis-33646	296	24	,	,	PUNCT
bracis-33646	296	25	as	as	SCONJ
bracis-33646	296	26	investigated	investigate	VERB
bracis-33646	296	27	by	by	ADP
bracis-33646	296	28	authors	author	NOUN
bracis-33646	296	29	such	such	ADJ
bracis-33646	296	30	as	as	ADP
bracis-33646	296	31	ribeiro	ribeiro	PROPN
bracis-33646	296	32	and	and	CCONJ
bracis-33646	296	33	wassermann	wassermann	PROPN
bracis-33646	296	34	 	 	SPACE
bracis-33646	297	1	[	[	X
bracis-33646	297	2	16	16	NUM
bracis-33646	297	3	]	]	PUNCT
bracis-33646	297	4	in	in	ADP
bracis-33646	297	5	the	the	DET
bracis-33646	297	6	context	context	NOUN
bracis-33646	297	7	of	of	ADP
bracis-33646	297	8	belief	belief	NOUN
bracis-33646	297	9	change	change	NOUN
bracis-33646	297	10	for	for	ADP
bracis-33646	297	11	description	description	NOUN
bracis-33646	297	12	logics	logic	NOUN
bracis-33646	297	13	.	.	PUNCT
bracis-33646	298	1	to	to	PART
bracis-33646	298	2	provide	provide	VERB
bracis-33646	298	3	constructions	construction	NOUN
bracis-33646	298	4	for	for	ADP
bracis-33646	298	5	rational	rational	ADJ
bracis-33646	298	6	contractions	contraction	NOUN
bracis-33646	298	7	on	on	ADP
bracis-33646	298	8	a	a	DET
bracis-33646	298	9	limited	limited	ADJ
bracis-33646	298	10	class	class	NOUN
bracis-33646	298	11	of	of	ADP
bracis-33646	298	12	inputs	input	NOUN
bracis-33646	298	13	,	,	PUNCT
bracis-33646	298	14	we	we	PRON
bracis-33646	298	15	need	need	VERB
bracis-33646	298	16	to	to	PART
bracis-33646	298	17	introduce	introduce	VERB
bracis-33646	298	18	the	the	DET
bracis-33646	298	19	notion	notion	NOUN
bracis-33646	298	20	of	of	ADP
bracis-33646	298	21	a	a	DET
bracis-33646	298	22	restricted	restricted	ADJ
bracis-33646	298	23	semantic	semantic	ADJ
bracis-33646	298	24	selection	selection	NOUN
bracis-33646	298	25	function	function	NOUN
bracis-33646	298	26	.	.	PUNCT
bracis-33646	299	1	definition	definition	NOUN
bracis-33646	299	2	13	13	NUM
bracis-33646	299	3	let	let	VERB
bracis-33646	299	4	\(mod(\mathcal	\(mod(\mathcal	PROPN
bracis-33646	299	5	{	{	PUNCT
bracis-33646	299	6	l	l	NOUN
bracis-33646	299	7	}	}	PUNCT
bracis-33646	299	8	)	)	PUNCT
bracis-33646	300	1	=	=	PUNCT
bracis-33646	300	2	\langle	\langle	PROPN
bracis-33646	300	3	m	m	PRON
bracis-33646	300	4	,	,	PUNCT
bracis-33646	300	5	\vdash	\vdash	VERB
bracis-33646	300	6	\rangle	\rangle	NOUN
bracis-33646	300	7	\	\	NOUN
bracis-33646	300	8	)	)	PUNCT
bracis-33646	300	9	be	be	AUX
bracis-33646	300	10	an	an	DET
bracis-33646	300	11	abstract	abstract	ADJ
bracis-33646	300	12	model	model	NOUN
bracis-33646	300	13	theory	theory	NOUN
bracis-33646	300	14	,	,	PUNCT
bracis-33646	300	15	\(\mathcal	\(\mathcal	ADJ
bracis-33646	300	16	{	{	PUNCT
bracis-33646	300	17	o	o	NOUN
bracis-33646	300	18	}	}	PUNCT
bracis-33646	300	19	\subseteq	\subseteq	PROPN
bracis-33646	300	20	2^m\	2^m\	NUM
bracis-33646	300	21	)	)	PUNCT
bracis-33646	300	22	a	a	DET
bracis-33646	300	23	family	family	NOUN
bracis-33646	300	24	of	of	ADP
bracis-33646	300	25	subsets	subset	NOUN
bracis-33646	300	26	of	of	ADP
bracis-33646	300	27	m	m	PROPN
bracis-33646	300	28	,	,	PUNCT
bracis-33646	300	29	\(x\in	\(x\in	PROPN
bracis-33646	300	30	\mathcal	\mathcal	PROPN
bracis-33646	300	31	{	{	PUNCT
bracis-33646	300	32	o}\	o}\	PROPN
bracis-33646	300	33	)	)	PUNCT
bracis-33646	300	34	a	a	DET
bracis-33646	300	35	set	set	NOUN
bracis-33646	300	36	of	of	ADP
bracis-33646	300	37	interpretations	interpretation	NOUN
bracis-33646	300	38	,	,	PUNCT
bracis-33646	300	39	and	and	CCONJ
bracis-33646	300	40	\(f	\(f	NUM
bracis-33646	300	41	:	:	PUNCT
bracis-33646	300	42	2^m	2^m	NUM
bracis-33646	300	43	\times	\time	NOUN
bracis-33646	300	44	2^m	2^m	NUM
bracis-33646	300	45	\rightarrow	\rightarrow	PROPN
bracis-33646	300	46	2^m\	2^m\	NUM
bracis-33646	300	47	)	)	PUNCT
bracis-33646	300	48	a	a	DET
bracis-33646	300	49	function	function	NOUN
bracis-33646	300	50	.	.	PUNCT
bracis-33646	301	1	we	we	PRON
bracis-33646	301	2	say	say	VERB
bracis-33646	301	3	f	f	PROPN
bracis-33646	301	4	is	be	AUX
bracis-33646	301	5	an	an	DET
bracis-33646	301	6	ssf	ssf	NOUN
bracis-33646	301	7	restricted	restrict	VERB
bracis-33646	301	8	to	to	ADP
bracis-33646	301	9	\(\mathcal	\(\mathcal	ADJ
bracis-33646	301	10	{	{	PUNCT
bracis-33646	301	11	o}\	o}\	NOUN
bracis-33646	301	12	)	)	PUNCT
bracis-33646	301	13	if	if	SCONJ
bracis-33646	301	14	its	its	PRON
bracis-33646	301	15	restriction	restriction	NOUN
bracis-33646	301	16	to	to	ADP
bracis-33646	301	17	\(\mathcal	\(\mathcal	NOUN
bracis-33646	301	18	{	{	PUNCT
bracis-33646	301	19	o}\	o}\	PROPN
bracis-33646	301	20	)	)	PUNCT
bracis-33646	301	21	is	be	AUX
bracis-33646	301	22	an	an	DET
bracis-33646	301	23	ssf	ssf	NOUN
bracis-33646	301	24	on	on	ADP
bracis-33646	301	25	x	x	SYM
bracis-33646	301	26	,	,	PUNCT
bracis-33646	301	27	i.e.	i.e.	X
bracis-33646	301	28	of	of	ADP
bracis-33646	301	29	the	the	DET
bracis-33646	301	30	function	function	NOUN
bracis-33646	301	31	\(f\restriction	\(f\restriction	NOUN
bracis-33646	302	1	_	_	PUNCT
bracis-33646	303	1	\mathcal	\mathcal	X
bracis-33646	303	2	{	{	PUNCT
bracis-33646	303	3	o}\	o}\	NOUN
bracis-33646	303	4	)	)	PUNCT
bracis-33646	303	5	satisfies	satisfy	VERB
bracis-33646	303	6	the	the	DET
bracis-33646	303	7	conditions	condition	NOUN
bracis-33646	303	8	in	in	ADP
bracis-33646	303	9	definition	definition	NOUN
bracis-33646	303	10	 	 	SPACE
bracis-33646	303	11	10	10	NUM
bracis-33646	303	12	.	.	PUNCT
bracis-33646	304	1	notice	notice	VERB
bracis-33646	304	2	the	the	DET
bracis-33646	304	3	above	above	ADJ
bracis-33646	304	4	definition	definition	NOUN
bracis-33646	304	5	is	be	AUX
bracis-33646	304	6	akin	akin	ADJ
bracis-33646	304	7	to	to	ADP
bracis-33646	304	8	defining	define	VERB
bracis-33646	304	9	selection	selection	NOUN
bracis-33646	304	10	functions	function	NOUN
bracis-33646	304	11	on	on	ADP
bracis-33646	304	12	the	the	DET
bracis-33646	304	13	sublogic	sublogic	NOUN
bracis-33646	304	14	defined	define	VERB
bracis-33646	304	15	by	by	ADP
bracis-33646	304	16	the	the	DET
bracis-33646	304	17	family	family	NOUN
bracis-33646	304	18	\(\mathcal	\(\mathcal	ADJ
bracis-33646	304	19	{	{	PUNCT
bracis-33646	304	20	o}\	o}\	PROPN
bracis-33646	304	21	)	)	PUNCT
bracis-33646	304	22	.	.	PUNCT
bracis-33646	305	1	furthermore	furthermore	ADV
bracis-33646	305	2	,	,	PUNCT
bracis-33646	305	3	we	we	PRON
bracis-33646	305	4	say	say	VERB
bracis-33646	305	5	an	an	DET
bracis-33646	305	6	operator	operator	NOUN
bracis-33646	305	7	is	be	AUX
bracis-33646	305	8	a	a	DET
bracis-33646	305	9	semantic	semantic	ADJ
bracis-33646	305	10	contraction	contraction	NOUN
bracis-33646	305	11	operator	operator	NOUN
bracis-33646	305	12	on	on	ADP
bracis-33646	305	13	a	a	DET
bracis-33646	305	14	set	set	NOUN
bracis-33646	305	15	of	of	ADP
bracis-33646	305	16	sentences	sentence	NOUN
bracis-33646	305	17	b	b	NUM
bracis-33646	305	18	,	,	PUNCT
bracis-33646	305	19	restricted	restrict	VERB
bracis-33646	305	20	to	to	ADP
bracis-33646	305	21	a	a	DET
bracis-33646	305	22	family	family	NOUN
bracis-33646	305	23	of	of	ADP
bracis-33646	305	24	theories	theory	NOUN
bracis-33646	305	25	\(\mathcal	\(\mathcal	ADJ
bracis-33646	305	26	{	{	PUNCT
bracis-33646	305	27	t}\	t}\	NUM
bracis-33646	305	28	)	)	PUNCT
bracis-33646	305	29	,	,	PUNCT
bracis-33646	305	30	if	if	SCONJ
bracis-33646	305	31	there	there	PRON
bracis-33646	305	32	is	be	VERB
bracis-33646	305	33	an	an	DET
bracis-33646	305	34	ssf	ssf	NOUN
bracis-33646	305	35	on	on	ADP
bracis-33646	305	36	\(\llbracket	\(\llbracket	NOUN
bracis-33646	305	37	b\rrbracket	b\rrbracket	X
bracis-33646	305	38	\	\	PROPN
bracis-33646	305	39	)	)	PUNCT
bracis-33646	305	40	restricted	restrict	VERB
bracis-33646	305	41	to	to	PART
bracis-33646	305	42	\(\overline{\llbracket	\(\overline{\llbracket	VERB
bracis-33646	305	43	\mathcal	\mathcal	PROPN
bracis-33646	305	44	{	{	PUNCT
bracis-33646	305	45	t}\rrbracket	t}\rrbracket	NOUN
bracis-33646	305	46	}	}	PUNCT
bracis-33646	305	47	=	=	PUNCT
bracis-33646	306	1	\{\overline{\llbracket	\{\overline{\llbracket	ADP
bracis-33646	306	2	k\rrbracket	k\rrbracket	NOUN
bracis-33646	306	3	}	}	PUNCT
bracis-33646	306	4	~|~	~|~	X
bracis-33646	306	5	k\in	k\in	PROPN
bracis-33646	306	6	\mathcal	\mathcal	PROPN
bracis-33646	306	7	{	{	PUNCT
bracis-33646	306	8	t}\}\	t}\}\	NOUN
bracis-33646	306	9	)	)	PUNCT
bracis-33646	306	10	,	,	PUNCT
bracis-33646	306	11	satisfying	satisfy	VERB
bracis-33646	306	12	the	the	DET
bracis-33646	306	13	condition	condition	NOUN
bracis-33646	306	14	in	in	ADP
bracis-33646	306	15	definition	definition	NOUN
bracis-33646	306	16	 	 	SPACE
bracis-33646	306	17	11	11	NUM
bracis-33646	306	18	for	for	ADP
bracis-33646	306	19	any	any	DET
bracis-33646	306	20	\(a	\(a	NOUN
bracis-33646	306	21	\subseteq	\subseteq	PROPN
bracis-33646	306	22	\mathcal	\mathcal	PROPN
bracis-33646	306	23	{	{	PUNCT
bracis-33646	306	24	t}\	t}\	NUM
bracis-33646	306	25	)	)	PUNCT
bracis-33646	306	26	.	.	PUNCT
bracis-33646	307	1	with	with	ADP
bracis-33646	307	2	that	that	PRON
bracis-33646	307	3	,	,	PUNCT
bracis-33646	307	4	it	it	PRON
bracis-33646	307	5	is	be	AUX
bracis-33646	307	6	easy	easy	ADJ
bracis-33646	307	7	to	to	PART
bracis-33646	307	8	see	see	VERB
bracis-33646	307	9	that	that	SCONJ
bracis-33646	307	10	the	the	DET
bracis-33646	307	11	following	follow	VERB
bracis-33646	307	12	holds	hold	NOUN
bracis-33646	307	13	.	.	PUNCT
bracis-33646	308	1	corollary	corollary	ADJ
bracis-33646	308	2	1	1	NUM
bracis-33646	308	3	let	let	VERB
bracis-33646	308	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	308	5	{	{	PUNCT
bracis-33646	308	6	l}\	l}\	PROPN
bracis-33646	308	7	)	)	PUNCT
bracis-33646	308	8	be	be	AUX
bracis-33646	308	9	a	a	DET
bracis-33646	308	10	logic	logic	NOUN
bracis-33646	308	11	,	,	PUNCT
bracis-33646	308	12	\(k\in	\(k\in	PROPN
bracis-33646	308	13	th_\mathcal	th_\mathcal	PROPN
bracis-33646	308	14	{	{	PUNCT
bracis-33646	308	15	l}\	l}\	PROPN
bracis-33646	308	16	)	)	PUNCT
bracis-33646	308	17	be	be	AUX
bracis-33646	308	18	a	a	DET
bracis-33646	308	19	theory	theory	NOUN
bracis-33646	308	20	,	,	PUNCT
bracis-33646	308	21	\(\mathcal	\(\mathcal	ADJ
bracis-33646	308	22	{	{	PUNCT
bracis-33646	308	23	t}\subseteq	t}\subseteq	ADJ
bracis-33646	308	24	th_\mathcal	th_\mathcal	PROPN
bracis-33646	308	25	{	{	PUNCT
bracis-33646	308	26	l}\	l}\	PROPN
bracis-33646	308	27	)	)	PUNCT
bracis-33646	308	28	be	be	VERB
bracis-33646	308	29	a	a	DET
bracis-33646	308	30	family	family	NOUN
bracis-33646	308	31	of	of	ADP
bracis-33646	308	32	theories	theory	NOUN
bracis-33646	308	33	of	of	ADP
bracis-33646	308	34	\(\mathcal	\(\mathcal	ADJ
bracis-33646	308	35	{	{	PUNCT
bracis-33646	308	36	l}\	l}\	PROPN
bracis-33646	308	37	)	)	PUNCT
bracis-33646	308	38	,	,	PUNCT
bracis-33646	308	39	and	and	CCONJ
bracis-33646	308	40	\(\dot{-	\(\dot{-	NOUN
bracis-33646	308	41	}	}	PUNCT
bracis-33646	308	42	:	:	PUNCT
bracis-33646	309	1	2^l	2^l	NUM
bracis-33646	309	2	\times	\time	VERB
bracis-33646	309	3	2^l	2^l	NUM
bracis-33646	309	4	\rightarrow	\rightarrow	PROPN
bracis-33646	309	5	2^l\	2^l\	NUM
bracis-33646	309	6	)	)	PUNCT
bracis-33646	309	7	be	be	AUX
bracis-33646	309	8	a	a	DET
bracis-33646	309	9	semantic	semantic	ADJ
bracis-33646	309	10	selection	selection	NOUN
bracis-33646	309	11	contraction	contraction	NOUN
bracis-33646	309	12	on	on	ADP
bracis-33646	309	13	k	k	PROPN
bracis-33646	309	14	restricted	restrict	VERB
bracis-33646	309	15	to	to	ADP
bracis-33646	309	16	\(\mathcal	\(\mathcal	ADJ
bracis-33646	309	17	{	{	PUNCT
bracis-33646	309	18	t}\	t}\	NUM
bracis-33646	309	19	)	)	PUNCT
bracis-33646	309	20	.	.	PUNCT
bracis-33646	310	1	then	then	ADV
bracis-33646	310	2	,	,	PUNCT
bracis-33646	310	3	\(\dot{-}\	\(\dot{-}\	PROPN
bracis-33646	310	4	)	)	PUNCT
bracis-33646	310	5	satisfies	satisfie	NOUN
bracis-33646	310	6	(	(	PUNCT
bracis-33646	310	7	closure	closure	NOUN
bracis-33646	310	8	)	)	PUNCT
bracis-33646	310	9	,	,	PUNCT
bracis-33646	310	10	(	(	PUNCT
bracis-33646	310	11	success),(inclusion	success),(inclusion	NOUN
bracis-33646	310	12	)	)	PUNCT
bracis-33646	310	13	,	,	PUNCT
bracis-33646	310	14	(	(	PUNCT
bracis-33646	310	15	vacuity),(recovery	vacuity),(recovery	NOUN
bracis-33646	310	16	)	)	PUNCT
bracis-33646	310	17	,	,	PUNCT
bracis-33646	310	18	and	and	CCONJ
bracis-33646	310	19	(	(	PUNCT
bracis-33646	310	20	extensionality	extensionality	NOUN
bracis-33646	310	21	)	)	PUNCT
bracis-33646	310	22	for	for	ADP
bracis-33646	310	23	all	all	DET
bracis-33646	310	24	\(a\subseteq	\(a\subseteq	PROPN
bracis-33646	310	25	l\	l\	PROPN
bracis-33646	310	26	)	)	PUNCT
bracis-33646	310	27	with	with	ADP
bracis-33646	310	28	\(cn(a	\(cn(a	PROPN
bracis-33646	310	29	)	)	PUNCT
bracis-33646	310	30	\in	\in	PROPN
bracis-33646	310	31	\mathcal	\mathcal	PROPN
bracis-33646	310	32	{	{	PUNCT
bracis-33646	310	33	t}\	t}\	NUM
bracis-33646	310	34	)	)	PUNCT
bracis-33646	310	35	,	,	PUNCT
bracis-33646	310	36	if	if	SCONJ
bracis-33646	310	37	,	,	PUNCT
bracis-33646	310	38	and	and	CCONJ
bracis-33646	310	39	only	only	ADV
bracis-33646	310	40	if	if	SCONJ
bracis-33646	310	41	,	,	PUNCT
bracis-33646	310	42	it	it	PRON
bracis-33646	310	43	is	be	AUX
bracis-33646	310	44	topological	topological	ADJ
bracis-33646	310	45	on	on	ADP
bracis-33646	310	46	\(\mathcal	\(\mathcal	ADJ
bracis-33646	310	47	{	{	PUNCT
bracis-33646	310	48	t}\	t}\	NUM
bracis-33646	310	49	)	)	PUNCT
bracis-33646	310	50	.	.	PUNCT
bracis-33646	311	1	we	we	PRON
bracis-33646	311	2	employ	employ	VERB
bracis-33646	311	3	the	the	DET
bracis-33646	311	4	result	result	NOUN
bracis-33646	311	5	above	above	ADV
bracis-33646	311	6	to	to	PART
bracis-33646	311	7	show	show	VERB
bracis-33646	311	8	that	that	SCONJ
bracis-33646	311	9	our	our	PRON
bracis-33646	311	10	construction	construction	NOUN
bracis-33646	311	11	subsumes	subsume	VERB
bracis-33646	311	12	those	those	PRON
bracis-33646	311	13	proposed	propose	VERB
bracis-33646	311	14	by	by	ADP
bracis-33646	311	15	authors	author	NOUN
bracis-33646	311	16	such	such	ADJ
bracis-33646	311	17	as	as	ADP
bracis-33646	311	18	ribeiro	ribeiro	PROPN
bracis-33646	311	19	et	et	PROPN
bracis-33646	311	20	al	al	PROPN
bracis-33646	311	21	.	.	PUNCT
bracis-33646	311	22	 	 	SPACE
bracis-33646	312	1	[	[	X
bracis-33646	312	2	15	15	NUM
bracis-33646	312	3	]	]	X
bracis-33646	312	4	for	for	ADP
bracis-33646	312	5	rational	rational	ADJ
bracis-33646	312	6	contractions	contraction	NOUN
bracis-33646	312	7	of	of	ADP
bracis-33646	312	8	finitely	finitely	ADV
bracis-33646	312	9	representable	representable	ADJ
bracis-33646	312	10	theories	theory	NOUN
bracis-33646	312	11	on	on	ADP
bracis-33646	312	12	boolean	boolean	ADJ
bracis-33646	312	13	non	non	ADJ
bracis-33646	312	14	-	-	ADJ
bracis-33646	312	15	compact	compact	ADJ
bracis-33646	312	16	logics	logic	NOUN
bracis-33646	312	17	.	.	PUNCT
bracis-33646	313	1	let	let	VERB
bracis-33646	313	2	us	we	PRON
bracis-33646	313	3	first	first	ADV
bracis-33646	313	4	define	define	VERB
bracis-33646	313	5	an	an	DET
bracis-33646	313	6	appropriate	appropriate	ADJ
bracis-33646	313	7	property	property	NOUN
bracis-33646	313	8	of	of	ADP
bracis-33646	313	9	this	this	DET
bracis-33646	313	10	family	family	NOUN
bracis-33646	313	11	of	of	ADP
bracis-33646	313	12	theories	theory	NOUN
bracis-33646	313	13	that	that	PRON
bracis-33646	313	14	is	be	AUX
bracis-33646	313	15	appropriate	appropriate	ADJ
bracis-33646	313	16	for	for	ADP
bracis-33646	313	17	the	the	DET
bracis-33646	313	18	construction	construction	NOUN
bracis-33646	313	19	of	of	ADP
bracis-33646	313	20	a	a	DET
bracis-33646	313	21	topological	topological	ADJ
bracis-33646	313	22	function	function	NOUN
bracis-33646	313	23	.	.	PUNCT
bracis-33646	314	1	definition	definition	NOUN
bracis-33646	314	2	14	14	NUM
bracis-33646	314	3	let	let	VERB
bracis-33646	314	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	314	5	{	{	PUNCT
bracis-33646	314	6	l}\	l}\	PROPN
bracis-33646	314	7	)	)	PUNCT
bracis-33646	314	8	be	be	AUX
bracis-33646	314	9	a	a	DET
bracis-33646	314	10	logic	logic	NOUN
bracis-33646	314	11	and	and	CCONJ
bracis-33646	314	12	\(\mathcal	\(\mathcal	ADJ
bracis-33646	314	13	{	{	PUNCT
bracis-33646	314	14	t	t	PROPN
bracis-33646	314	15	}	}	PUNCT
bracis-33646	314	16	\subseteq	\subseteq	PROPN
bracis-33646	314	17	th_\mathcal	th_\mathcal	PROPN
bracis-33646	314	18	{	{	PUNCT
bracis-33646	314	19	l}\	l}\	PROPN
bracis-33646	314	20	)	)	PUNCT
bracis-33646	314	21	be	be	VERB
bracis-33646	314	22	a	a	DET
bracis-33646	314	23	family	family	NOUN
bracis-33646	314	24	of	of	ADP
bracis-33646	314	25	\(\mathcal	\(\mathcal	ADJ
bracis-33646	314	26	{	{	PUNCT
bracis-33646	314	27	l}\)-theories	l}\)-theorie	NOUN
bracis-33646	314	28	.	.	PUNCT
bracis-33646	315	1	we	we	PRON
bracis-33646	315	2	say	say	VERB
bracis-33646	315	3	\(\mathcal	\(\mathcal	ADJ
bracis-33646	315	4	{	{	PUNCT
bracis-33646	315	5	t}\	t}\	NUM
bracis-33646	315	6	)	)	PUNCT
bracis-33646	315	7	is	be	AUX
bracis-33646	315	8	closed	close	VERB
bracis-33646	315	9	under	under	ADP
bracis-33646	315	10	classical	classical	ADJ
bracis-33646	315	11	negation	negation	NOUN
bracis-33646	315	12	if	if	SCONJ
bracis-33646	315	13	for	for	ADP
bracis-33646	315	14	any	any	DET
bracis-33646	315	15	\(\vargamma	\(\vargamma	PROPN
bracis-33646	315	16	\in	\in	PROPN
bracis-33646	315	17	\mathcal	\mathcal	PROPN
bracis-33646	315	18	{	{	PUNCT
bracis-33646	315	19	t}\	t}\	NUM
bracis-33646	315	20	)	)	PUNCT
bracis-33646	315	21	,	,	PUNCT
bracis-33646	315	22	there	there	PRON
bracis-33646	315	23	is	be	VERB
bracis-33646	315	24	some	some	DET
bracis-33646	315	25	\(neg(\vargamma	\(neg(\vargamma	PROPN
bracis-33646	315	26	)	)	PUNCT
bracis-33646	315	27	\in	\in	PROPN
bracis-33646	315	28	\mathcal	\mathcal	PROPN
bracis-33646	315	29	{	{	PUNCT
bracis-33646	315	30	t}\	t}\	NOUN
bracis-33646	315	31	)	)	PUNCT
bracis-33646	315	32	s.t	s.t	PROPN
bracis-33646	315	33	.	.	PUNCT
bracis-33646	316	1	\(neg(\vargamma	\(neg(\vargamma	PROPN
bracis-33646	316	2	)	)	PUNCT
bracis-33646	316	3	\cap	\cap	PROPN
bracis-33646	316	4	\vargamma	\vargamma	PROPN
bracis-33646	316	5	=	=	PUNCT
bracis-33646	316	6	cn(\emptyset	cn(\emptyset	PROPN
bracis-33646	316	7	)	)	PUNCT
bracis-33646	316	8	\	\	NOUN
bracis-33646	316	9	)	)	PUNCT
bracis-33646	316	10	and	and	CCONJ
bracis-33646	316	11	\(cn(\vargamma	\(cn(\vargamma	PROPN
bracis-33646	316	12	\cup	\cup	VERB
bracis-33646	316	13	neg(\vargamma	neg(\vargamma	PROPN
bracis-33646	316	14	)	)	PUNCT
bracis-33646	316	15	)	)	PUNCT
bracis-33646	317	1	=	=	PUNCT
bracis-33646	318	1	l\	l\	NOUN
bracis-33646	318	2	)	)	PUNCT
bracis-33646	318	3	.	.	PUNCT
bracis-33646	319	1	it	it	PRON
bracis-33646	319	2	is	be	AUX
bracis-33646	319	3	easy	easy	ADJ
bracis-33646	319	4	to	to	PART
bracis-33646	319	5	see	see	VERB
bracis-33646	319	6	that	that	SCONJ
bracis-33646	319	7	we	we	PRON
bracis-33646	319	8	can	can	AUX
bracis-33646	319	9	always	always	ADV
bracis-33646	319	10	construct	construct	VERB
bracis-33646	319	11	topological	topological	ADJ
bracis-33646	319	12	functions	function	NOUN
bracis-33646	319	13	restricted	restrict	VERB
bracis-33646	319	14	to	to	ADP
bracis-33646	319	15	a	a	DET
bracis-33646	319	16	family	family	NOUN
bracis-33646	319	17	of	of	ADP
bracis-33646	319	18	theories	theory	NOUN
bracis-33646	319	19	which	which	PRON
bracis-33646	319	20	is	be	AUX
bracis-33646	319	21	closed	close	VERB
bracis-33646	319	22	under	under	ADP
bracis-33646	319	23	classical	classical	ADJ
bracis-33646	319	24	negation	negation	NOUN
bracis-33646	319	25	.	.	PUNCT
bracis-33646	320	1	proposition	proposition	NOUN
bracis-33646	320	2	6	6	NUM
bracis-33646	320	3	let	let	VERB
bracis-33646	320	4	\(\mathcal	\(\mathcal	ADJ
bracis-33646	320	5	{	{	PUNCT
bracis-33646	320	6	l}\	l}\	PROPN
bracis-33646	320	7	)	)	PUNCT
bracis-33646	320	8	be	be	AUX
bracis-33646	320	9	a	a	DET
bracis-33646	320	10	logic	logic	NOUN
bracis-33646	320	11	and	and	CCONJ
bracis-33646	320	12	\(\mathcal	\(\mathcal	ADJ
bracis-33646	320	13	{	{	PUNCT
bracis-33646	320	14	t	t	PROPN
bracis-33646	320	15	}	}	PUNCT
bracis-33646	320	16	\subseteq	\subseteq	PROPN
bracis-33646	320	17	th_\mathcal	th_\mathcal	PROPN
bracis-33646	320	18	{	{	PUNCT
bracis-33646	320	19	l}\	l}\	PROPN
bracis-33646	320	20	)	)	PUNCT
bracis-33646	320	21	a	a	DET
bracis-33646	320	22	family	family	NOUN
bracis-33646	320	23	of	of	ADP
bracis-33646	320	24	theories	theory	NOUN
bracis-33646	320	25	closed	close	VERB
bracis-33646	320	26	under	under	ADP
bracis-33646	320	27	classical	classical	ADJ
bracis-33646	320	28	negation	negation	NOUN
bracis-33646	320	29	,	,	PUNCT
bracis-33646	320	30	there	there	PRON
bracis-33646	320	31	is	be	VERB
bracis-33646	320	32	a	a	DET
bracis-33646	320	33	topological	topological	ADJ
bracis-33646	320	34	selection	selection	NOUN
bracis-33646	320	35	function	function	NOUN
bracis-33646	320	36	f	f	PROPN
bracis-33646	320	37	restricted	restrict	VERB
bracis-33646	320	38	to	to	ADP
bracis-33646	320	39	the	the	DET
bracis-33646	320	40	set	set	ADJ
bracis-33646	320	41	\(\llbracket	\(\llbracket	NOUN
bracis-33646	320	42	\mathcal	\mathcal	PROPN
bracis-33646	320	43	{	{	PUNCT
bracis-33646	320	44	t}\rrbracket	t}\rrbracket	NOUN
bracis-33646	320	45	=	=	SYM
bracis-33646	320	46	\{\llbracket	\{\llbracket	NOUN
bracis-33646	320	47	\vargamma	\vargamma	NOUN
bracis-33646	320	48	\rrbracket	\rrbracket	VERB
bracis-33646	320	49	~|~\vargamma	~|~\vargamma	PROPN
bracis-33646	320	50	\in	\in	PROPN
bracis-33646	320	51	\mathcal	\mathcal	PROPN
bracis-33646	320	52	{	{	PUNCT
bracis-33646	320	53	t}\}\	t}\}\	NOUN
bracis-33646	320	54	)	)	PUNCT
bracis-33646	320	55	.	.	PUNCT
bracis-33646	321	1	proof	proof	NOUN
bracis-33646	321	2	it	it	PRON
bracis-33646	321	3	suffices	suffice	VERB
bracis-33646	321	4	to	to	PART
bracis-33646	321	5	see	see	VERB
bracis-33646	321	6	that	that	PRON
bracis-33646	321	7	for	for	ADP
bracis-33646	321	8	any	any	DET
bracis-33646	321	9	family	family	NOUN
bracis-33646	321	10	of	of	ADP
bracis-33646	321	11	theories	theory	NOUN
bracis-33646	321	12	\(\mathcal	\(\mathcal	ADJ
bracis-33646	321	13	{	{	PUNCT
bracis-33646	321	14	t}\	t}\	NUM
bracis-33646	321	15	)	)	PUNCT
bracis-33646	321	16	closed	close	VERB
bracis-33646	321	17	under	under	ADP
bracis-33646	321	18	classical	classical	ADJ
bracis-33646	321	19	negation	negation	NOUN
bracis-33646	321	20	,	,	PUNCT
bracis-33646	321	21	if	if	SCONJ
bracis-33646	321	22	\(\vargamma	\(\vargamma	PROPN
bracis-33646	321	23	\in	\in	PROPN
bracis-33646	321	24	\mathcal	\mathcal	PROPN
bracis-33646	321	25	{	{	PUNCT
bracis-33646	321	26	t}\	t}\	NUM
bracis-33646	321	27	)	)	PUNCT
bracis-33646	321	28	,	,	PUNCT
bracis-33646	321	29	there	there	PRON
bracis-33646	321	30	is	be	VERB
bracis-33646	321	31	some	some	DET
bracis-33646	321	32	theory	theory	NOUN
bracis-33646	321	33	\(neg(\vargamma	\(neg(\vargamma	PROPN
bracis-33646	321	34	)	)	PUNCT
bracis-33646	321	35	\in	\in	PROPN
bracis-33646	321	36	\mathcal	\mathcal	PROPN
bracis-33646	321	37	{	{	PUNCT
bracis-33646	321	38	t}\	t}\	NOUN
bracis-33646	321	39	)	)	PUNCT
bracis-33646	321	40	s.t	s.t	PROPN
bracis-33646	321	41	.	.	PUNCT
bracis-33646	321	42	\(neg(\vargamma	\(neg(\vargamma	PROPN
bracis-33646	321	43	)	)	PUNCT
bracis-33646	322	1	\cap	\cap	PROPN
bracis-33646	322	2	\vargamma	\vargamma	PROPN
bracis-33646	322	3	=	=	PUNCT
bracis-33646	322	4	cn(\emptyset	cn(\emptyset	PROPN
bracis-33646	322	5	)	)	PUNCT
bracis-33646	322	6	\	\	NOUN
bracis-33646	322	7	)	)	PUNCT
bracis-33646	322	8	and	and	CCONJ
bracis-33646	322	9	\(cn(neg(\vargamma	\(cn(neg(\vargamma	PROPN
bracis-33646	322	10	)	)	PUNCT
bracis-33646	322	11	\cup	\cup	VERB
bracis-33646	322	12	\vargamma	\vargamma	PROPN
bracis-33646	322	13	)	)	PUNCT
bracis-33646	322	14	=	=	PUNCT
bracis-33646	323	1	l\	l\	NOUN
bracis-33646	323	2	)	)	PUNCT
bracis-33646	323	3	.	.	PUNCT
bracis-33646	324	1	as	as	ADP
bracis-33646	324	2	such	such	ADJ
bracis-33646	324	3	,	,	PUNCT
bracis-33646	324	4	\(\overline{\llbracket	\(\overline{\llbracket	ADJ
bracis-33646	324	5	\vargamma	\vargamma	NOUN
bracis-33646	324	6	\rrbracket	\rrbracket	PROPN
bracis-33646	324	7	}	}	PUNCT
bracis-33646	324	8	\	\	NOUN
bracis-33646	324	9	)	)	PUNCT
bracis-33646	324	10	is	be	AUX
bracis-33646	324	11	a	a	DET
bracis-33646	324	12	b.o.s	b.o.s	NOUN
bracis-33646	324	13	.	.	PUNCT
bracis-33646	325	1	and	and	CCONJ
bracis-33646	325	2	,	,	PUNCT
bracis-33646	325	3	thus	thus	ADV
bracis-33646	325	4	,	,	PUNCT
bracis-33646	325	5	there	there	PRON
bracis-33646	325	6	is	be	VERB
bracis-33646	325	7	a	a	DET
bracis-33646	325	8	function	function	NOUN
bracis-33646	325	9	\(f(x	\(f(x	PROPN
bracis-33646	325	10	,	,	PUNCT
bracis-33646	325	11	y	y	NOUN
bracis-33646	325	12	)	)	PUNCT
bracis-33646	325	13	=	=	PUNCT
bracis-33646	326	1	x\	x\	NOUN
bracis-33646	326	2	)	)	PUNCT
bracis-33646	326	3	if	if	SCONJ
bracis-33646	326	4	\(x\cap	\(x\cap	VERB
bracis-33646	326	5	y\ne	y\ne	PROPN
bracis-33646	326	6	\emptyset	\emptyset	PROPN
bracis-33646	326	7	\	\	PROPN
bracis-33646	326	8	)	)	PUNCT
bracis-33646	326	9	and	and	CCONJ
bracis-33646	326	10	\(f(x	\(f(x	PROPN
bracis-33646	326	11	,	,	PUNCT
bracis-33646	326	12	y	y	PROPN
bracis-33646	326	13	)	)	PUNCT
bracis-33646	326	14	=	=	PUNCT
bracis-33646	327	1	x\cup	x\cup	PUNCT
bracis-33646	328	1	y\	y\	NOUN
bracis-33646	328	2	)	)	PUNCT
bracis-33646	328	3	,	,	PUNCT
bracis-33646	328	4	which	which	PRON
bracis-33646	328	5	is	be	AUX
bracis-33646	328	6	topological	topological	ADJ
bracis-33646	328	7	for	for	ADP
bracis-33646	328	8	all	all	DET
bracis-33646	328	9	\(y	\(y	NUM
bracis-33646	328	10	=	=	SYM
bracis-33646	328	11	\overline{\llbracket	\overline{\llbracket	NOUN
bracis-33646	328	12	\vargamma	\vargamma	NOUN
bracis-33646	328	13	\rrbracket	\rrbracket	NOUN
bracis-33646	328	14	}	}	PUNCT
bracis-33646	328	15	=	=	SYM
bracis-33646	328	16	\llbracket	\llbracket	PROPN
bracis-33646	328	17	neg(\vargamma	neg(\vargamma	NOUN
bracis-33646	328	18	)	)	PUNCT
bracis-33646	328	19	\rrbracket	\rrbracket	VERB
bracis-33646	328	20	\	\	NOUN
bracis-33646	328	21	)	)	PUNCT
bracis-33646	328	22	with	with	ADP
bracis-33646	328	23	\(\vargamma	\(\vargamma	PROPN
bracis-33646	328	24	\in	\in	PROPN
bracis-33646	328	25	\mathcal	\mathcal	PROPN
bracis-33646	328	26	{	{	PUNCT
bracis-33646	328	27	t}\	t}\	NUM
bracis-33646	328	28	)	)	PUNCT
bracis-33646	328	29	.	.	PUNCT
bracis-33646	328	30	   	   	SPACE
bracis-33646	329	1	\(\square	\(\square	VERB
bracis-33646	329	2	\	\	NOUN
bracis-33646	329	3	)	)	PUNCT
bracis-33646	330	1	the	the	DET
bracis-33646	330	2	above	above	ADJ
bracis-33646	330	3	result	result	NOUN
bracis-33646	330	4	generalises	generalise	VERB
bracis-33646	330	5	ribeiro	ribeiro	PROPN
bracis-33646	330	6	et	et	PROPN
bracis-33646	330	7	al	al	PROPN
bracis-33646	330	8	.	.	PUNCT
bracis-33646	330	9	 	 	SPACE
bracis-33646	331	1	[	[	X
bracis-33646	331	2	15	15	NUM
bracis-33646	331	3	]	]	X
bracis-33646	331	4	construction	construction	NOUN
bracis-33646	331	5	for	for	ADP
bracis-33646	331	6	non	non	ADJ
bracis-33646	331	7	-	-	ADJ
bracis-33646	331	8	compact	compact	ADJ
bracis-33646	331	9	logics	logic	NOUN
bracis-33646	331	10	,	,	PUNCT
bracis-33646	331	11	showing	show	VERB
bracis-33646	331	12	that	that	SCONJ
bracis-33646	331	13	we	we	PRON
bracis-33646	331	14	can	can	AUX
bracis-33646	331	15	extend	extend	VERB
bracis-33646	331	16	their	their	PRON
bracis-33646	331	17	construction	construction	NOUN
bracis-33646	331	18	to	to	PART
bracis-33646	331	19	consider	consider	VERB
bracis-33646	331	20	other	other	ADJ
bracis-33646	331	21	logics	logic	NOUN
bracis-33646	331	22	and	and	CCONJ
bracis-33646	331	23	inputs	input	NOUN
bracis-33646	331	24	as	as	ADV
bracis-33646	331	25	long	long	ADV
bracis-33646	331	26	as	as	SCONJ
bracis-33646	331	27	we	we	PRON
bracis-33646	331	28	restrict	restrict	VERB
bracis-33646	331	29	the	the	DET
bracis-33646	331	30	input	input	NOUN
bracis-33646	331	31	to	to	ADP
bracis-33646	331	32	cases	case	NOUN
bracis-33646	331	33	in	in	ADP
bracis-33646	331	34	which	which	PRON
bracis-33646	331	35	the	the	DET
bracis-33646	331	36	logic	logic	NOUN
bracis-33646	331	37	admits	admit	VERB
bracis-33646	331	38	classical	classical	ADJ
bracis-33646	331	39	negation	negation	NOUN
bracis-33646	331	40	.	.	PUNCT
bracis-33646	332	1	corollary	corollary	ADJ
bracis-33646	332	2	2	2	NUM
bracis-33646	333	1	[	[	X
bracis-33646	333	2	15	15	NUM
bracis-33646	333	3	]	]	PUNCT
bracis-33646	333	4	let	let	VERB
bracis-33646	333	5	\(\mathcal	\(\mathcal	ADJ
bracis-33646	333	6	{	{	PUNCT
bracis-33646	333	7	l}\	l}\	PROPN
bracis-33646	333	8	)	)	PUNCT
bracis-33646	333	9	be	be	VERB
bracis-33646	333	10	a	a	DET
bracis-33646	333	11	logic	logic	NOUN
bracis-33646	333	12	closed	close	VERB
bracis-33646	333	13	under	under	ADP
bracis-33646	333	14	disjunction	disjunction	NOUN
bracis-33646	333	15	and	and	CCONJ
bracis-33646	333	16	classical	classical	ADJ
bracis-33646	333	17	negation	negation	NOUN
bracis-33646	333	18	,	,	PUNCT
bracis-33646	333	19	there	there	PRON
bracis-33646	333	20	is	be	VERB
bracis-33646	333	21	a	a	DET
bracis-33646	333	22	topological	topological	ADJ
bracis-33646	333	23	semantic	semantic	ADJ
bracis-33646	333	24	selection	selection	NOUN
bracis-33646	333	25	contraction	contraction	NOUN
bracis-33646	333	26	\(\dot{-}\	\(\dot{-}\	NOUN
bracis-33646	333	27	)	)	PUNCT
bracis-33646	333	28	restricted	restrict	VERB
bracis-33646	333	29	to	to	ADP
bracis-33646	333	30	finitely	finitely	ADV
bracis-33646	333	31	representable	representable	ADJ
bracis-33646	333	32	theories	theory	NOUN
bracis-33646	333	33	.	.	PUNCT
bracis-33646	334	1	5	5	NUM
bracis-33646	334	2	related	relate	VERB
bracis-33646	334	3	work	work	NOUN
bracis-33646	334	4	work	work	NOUN
bracis-33646	334	5	on	on	ADP
bracis-33646	334	6	the	the	DET
bracis-33646	334	7	definability	definability	NOUN
bracis-33646	334	8	of	of	ADP
bracis-33646	334	9	belief	belief	NOUN
bracis-33646	334	10	change	change	NOUN
bracis-33646	334	11	operators	operator	NOUN
bracis-33646	334	12	in	in	ADP
bracis-33646	334	13	non	non	ADJ
bracis-33646	334	14	-	-	ADJ
bracis-33646	334	15	classical	classical	ADJ
bracis-33646	334	16	logics	logic	NOUN
bracis-33646	334	17	remounts	remount	NOUN
bracis-33646	334	18	at	at	ADP
bracis-33646	334	19	least	least	ADJ
bracis-33646	334	20	to	to	ADP
bracis-33646	334	21	the	the	DET
bracis-33646	334	22	work	work	NOUN
bracis-33646	334	23	of	of	ADP
bracis-33646	334	24	hansson	hansson	PROPN
bracis-33646	334	25	and	and	CCONJ
bracis-33646	334	26	wassermann	wassermann	PROPN
bracis-33646	334	27	 	 	SPACE
bracis-33646	335	1	[	[	X
bracis-33646	335	2	9	9	NUM
bracis-33646	335	3	]	]	PUNCT
bracis-33646	335	4	,	,	PUNCT
bracis-33646	335	5	in	in	ADP
bracis-33646	335	6	which	which	PRON
bracis-33646	335	7	the	the	DET
bracis-33646	335	8	authors	author	NOUN
bracis-33646	335	9	show	show	VERB
bracis-33646	335	10	that	that	SCONJ
bracis-33646	335	11	partial	partial	ADJ
bracis-33646	335	12	meet	meet	NOUN
bracis-33646	335	13	contractions	contraction	NOUN
bracis-33646	335	14	are	be	AUX
bracis-33646	335	15	definable	definable	ADJ
bracis-33646	335	16	for	for	ADP
bracis-33646	335	17	any	any	DET
bracis-33646	335	18	monotonic	monotonic	ADJ
bracis-33646	335	19	and	and	CCONJ
bracis-33646	335	20	compact	compact	ADJ
bracis-33646	335	21	logic	logic	NOUN
bracis-33646	335	22	.	.	PUNCT
bracis-33646	336	1	while	while	SCONJ
bracis-33646	336	2	most	most	ADJ
bracis-33646	336	3	work	work	VERB
bracis-33646	336	4	on	on	ADP
bracis-33646	336	5	belief	belief	NOUN
bracis-33646	336	6	change	change	NOUN
bracis-33646	336	7	for	for	ADP
bracis-33646	336	8	non	non	ADJ
bracis-33646	336	9	-	-	ADJ
bracis-33646	336	10	classical	classical	ADJ
bracis-33646	336	11	logics	logic	NOUN
bracis-33646	336	12	,	,	PUNCT
bracis-33646	336	13	such	such	ADJ
bracis-33646	336	14	as	as	ADP
bracis-33646	336	15	that	that	PRON
bracis-33646	336	16	of	of	ADP
bracis-33646	336	17	delgrande	delgrande	NOUN
bracis-33646	336	18	 	 	SPACE
bracis-33646	336	19	[	[	X
bracis-33646	336	20	4	4	NUM
bracis-33646	336	21	]	]	PUNCT
bracis-33646	336	22	or	or	CCONJ
bracis-33646	336	23	girard	girard	NOUN
bracis-33646	336	24	and	and	CCONJ
bracis-33646	336	25	tanaka	tanaka	PROPN
bracis-33646	336	26	 	 	SPACE
bracis-33646	337	1	[	[	X
bracis-33646	337	2	7	7	NUM
bracis-33646	337	3	]	]	PUNCT
bracis-33646	337	4	,	,	PUNCT
bracis-33646	337	5	focused	focus	VERB
bracis-33646	337	6	on	on	ADP
bracis-33646	337	7	defining	define	VERB
bracis-33646	337	8	appropriate	appropriate	ADJ
bracis-33646	337	9	operations	operation	NOUN
bracis-33646	337	10	in	in	ADP
bracis-33646	337	11	these	these	DET
bracis-33646	337	12	logics	logic	NOUN
bracis-33646	337	13	,	,	PUNCT
bracis-33646	337	14	only	only	ADV
bracis-33646	337	15	recent	recent	ADJ
bracis-33646	337	16	work	work	NOUN
bracis-33646	337	17	in	in	ADP
bracis-33646	337	18	the	the	DET
bracis-33646	337	19	literature	literature	NOUN
bracis-33646	337	20	has	have	AUX
bracis-33646	337	21	focused	focus	VERB
bracis-33646	337	22	on	on	ADP
bracis-33646	337	23	investigating	investigate	VERB
bracis-33646	337	24	which	which	DET
bracis-33646	337	25	classes	class	NOUN
bracis-33646	337	26	of	of	ADP
bracis-33646	337	27	logics	logic	NOUN
bracis-33646	337	28	allow	allow	VERB
bracis-33646	337	29	the	the	DET
bracis-33646	337	30	definition	definition	NOUN
bracis-33646	337	31	of	of	ADP
bracis-33646	337	32	a	a	DET
bracis-33646	337	33	given	give	VERB
bracis-33646	337	34	operator	operator	NOUN
bracis-33646	337	35	.	.	PUNCT
bracis-33646	338	1	famously	famously	ADV
bracis-33646	338	2	,	,	PUNCT
bracis-33646	338	3	flouris	flouris	PROPN
bracis-33646	338	4	 	 	SPACE
bracis-33646	339	1	[	[	X
bracis-33646	339	2	5	5	NUM
bracis-33646	339	3	]	]	PUNCT
bracis-33646	339	4	has	have	AUX
bracis-33646	339	5	shown	show	VERB
bracis-33646	339	6	a	a	DET
bracis-33646	339	7	characterisation	characterisation	NOUN
bracis-33646	339	8	of	of	ADP
bracis-33646	339	9	the	the	DET
bracis-33646	339	10	definability	definability	NOUN
bracis-33646	339	11	of	of	ADP
bracis-33646	339	12	agm	agm	PROPN
bracis-33646	339	13	rational	rational	ADJ
bracis-33646	339	14	contractions	contraction	NOUN
bracis-33646	339	15	employing	employ	VERB
bracis-33646	339	16	the	the	DET
bracis-33646	339	17	framework	framework	NOUN
bracis-33646	339	18	of	of	ADP
bracis-33646	339	19	order	order	NOUN
bracis-33646	339	20	theory	theory	NOUN
bracis-33646	339	21	and	and	CCONJ
bracis-33646	339	22	its	its	PRON
bracis-33646	339	23	connections	connection	NOUN
bracis-33646	339	24	to	to	ADP
bracis-33646	339	25	abstract	abstract	ADJ
bracis-33646	339	26	logic	logic	NOUN
bracis-33646	339	27	.	.	PUNCT
bracis-33646	340	1	this	this	DET
bracis-33646	340	2	study	study	NOUN
bracis-33646	340	3	has	have	AUX
bracis-33646	340	4	been	be	AUX
bracis-33646	340	5	explored	explore	VERB
bracis-33646	340	6	further	far	ADV
bracis-33646	340	7	by	by	ADP
bracis-33646	340	8	ribeiro	ribeiro	PROPN
bracis-33646	340	9	et	et	PROPN
bracis-33646	340	10	al	al	PROPN
bracis-33646	340	11	.	.	PUNCT
bracis-33646	340	12	 	 	SPACE
bracis-33646	341	1	[	[	X
bracis-33646	341	2	15	15	NUM
bracis-33646	341	3	]	]	X
bracis-33646	341	4	showing	show	VERB
bracis-33646	341	5	constructions	construction	NOUN
bracis-33646	341	6	of	of	ADP
bracis-33646	341	7	agm	agm	PROPN
bracis-33646	341	8	rational	rational	ADJ
bracis-33646	341	9	contractions	contraction	NOUN
bracis-33646	341	10	for	for	ADP
bracis-33646	341	11	non	non	ADJ
bracis-33646	341	12	-	-	ADJ
bracis-33646	341	13	compact	compact	ADJ
bracis-33646	341	14	logics	logic	NOUN
bracis-33646	341	15	,	,	PUNCT
bracis-33646	341	16	and	and	CCONJ
bracis-33646	341	17	by	by	ADP
bracis-33646	341	18	souza	souza	NOUN
bracis-33646	341	19	and	and	CCONJ
bracis-33646	341	20	wassermann	wassermann	PROPN
bracis-33646	341	21	 	 	SPACE
bracis-33646	342	1	[	[	X
bracis-33646	342	2	18	18	NUM
bracis-33646	342	3	]	]	PUNCT
bracis-33646	342	4	showing	show	VERB
bracis-33646	342	5	that	that	SCONJ
bracis-33646	342	6	a	a	DET
bracis-33646	342	7	semantically	semantically	ADV
bracis-33646	342	8	motivated	motivated	ADJ
bracis-33646	342	9	framework	framework	NOUN
bracis-33646	342	10	,	,	PUNCT
bracis-33646	342	11	which	which	PRON
bracis-33646	342	12	they	they	PRON
bracis-33646	342	13	employ	employ	VERB
bracis-33646	342	14	to	to	PART
bracis-33646	342	15	study	study	VERB
bracis-33646	342	16	hyperintensional	hyperintensional	ADJ
bracis-33646	342	17	belief	belief	NOUN
bracis-33646	342	18	change	change	NOUN
bracis-33646	342	19	,	,	PUNCT
bracis-33646	342	20	provides	provide	VERB
bracis-33646	342	21	a	a	DET
bracis-33646	342	22	rich	rich	ADJ
bracis-33646	342	23	foundation	foundation	NOUN
bracis-33646	342	24	to	to	PART
bracis-33646	342	25	encode	encode	VERB
bracis-33646	342	26	and	and	CCONJ
bracis-33646	342	27	study	study	VERB
bracis-33646	342	28	different	different	ADJ
bracis-33646	342	29	notions	notion	NOUN
bracis-33646	342	30	of	of	ADP
bracis-33646	342	31	belief	belief	NOUN
bracis-33646	342	32	change	change	NOUN
bracis-33646	342	33	.	.	PUNCT
bracis-33646	343	1	our	our	PRON
bracis-33646	343	2	work	work	NOUN
bracis-33646	343	3	develops	develop	VERB
bracis-33646	343	4	on	on	ADP
bracis-33646	343	5	these	these	DET
bracis-33646	343	6	ideas	idea	NOUN
bracis-33646	343	7	,	,	PUNCT
bracis-33646	343	8	connecting	connect	VERB
bracis-33646	343	9	the	the	DET
bracis-33646	343	10	work	work	NOUN
bracis-33646	343	11	on	on	ADP
bracis-33646	343	12	conditional	conditional	ADJ
bracis-33646	343	13	logics	logic	NOUN
bracis-33646	343	14	,	,	PUNCT
bracis-33646	343	15	abstract	abstract	ADJ
bracis-33646	343	16	model	model	NOUN
bracis-33646	343	17	theory	theory	NOUN
bracis-33646	343	18	and	and	CCONJ
bracis-33646	343	19	belief	belief	NOUN
bracis-33646	343	20	change	change	NOUN
bracis-33646	343	21	to	to	PART
bracis-33646	343	22	investigate	investigate	VERB
bracis-33646	343	23	a	a	DET
bracis-33646	343	24	general	general	ADJ
bracis-33646	343	25	notion	notion	NOUN
bracis-33646	343	26	of	of	ADP
bracis-33646	343	27	belief	belief	NOUN
bracis-33646	343	28	contraction	contraction	NOUN
bracis-33646	343	29	,	,	PUNCT
bracis-33646	343	30	namely	namely	ADV
bracis-33646	343	31	semantic	semantic	ADJ
bracis-33646	343	32	selection	selection	NOUN
bracis-33646	343	33	contraction	contraction	NOUN
bracis-33646	343	34	,	,	PUNCT
bracis-33646	343	35	which	which	PRON
bracis-33646	343	36	can	can	AUX
bracis-33646	343	37	be	be	AUX
bracis-33646	343	38	used	use	VERB
bracis-33646	343	39	to	to	PART
bracis-33646	343	40	unify	unify	VERB
bracis-33646	343	41	different	different	ADJ
bracis-33646	343	42	results	result	NOUN
bracis-33646	343	43	in	in	ADP
bracis-33646	343	44	the	the	DET
bracis-33646	343	45	area	area	NOUN
bracis-33646	343	46	.	.	PUNCT
bracis-33646	344	1	6	6	NUM
bracis-33646	344	2	final	final	ADJ
bracis-33646	344	3	considerations	consideration	NOUN
bracis-33646	344	4	in	in	ADP
bracis-33646	344	5	this	this	DET
bracis-33646	344	6	work	work	NOUN
bracis-33646	344	7	,	,	PUNCT
bracis-33646	344	8	we	we	PRON
bracis-33646	344	9	investigated	investigate	VERB
bracis-33646	344	10	the	the	DET
bracis-33646	344	11	use	use	NOUN
bracis-33646	344	12	of	of	ADP
bracis-33646	344	13	abstract	abstract	ADJ
bracis-33646	344	14	model	model	NOUN
bracis-33646	344	15	theory	theory	NOUN
bracis-33646	344	16	and	and	CCONJ
bracis-33646	344	17	topology	topology	NOUN
bracis-33646	344	18	to	to	PART
bracis-33646	344	19	describe	describe	VERB
bracis-33646	344	20	belief	belief	NOUN
bracis-33646	344	21	change	change	NOUN
bracis-33646	344	22	operators	operator	NOUN
bracis-33646	344	23	,	,	PUNCT
bracis-33646	344	24	showing	show	VERB
bracis-33646	344	25	that	that	SCONJ
bracis-33646	344	26	our	our	PRON
bracis-33646	344	27	notion	notion	NOUN
bracis-33646	344	28	subsumes	subsume	VERB
bracis-33646	344	29	different	different	ADJ
bracis-33646	344	30	operations	operation	NOUN
bracis-33646	344	31	in	in	ADP
bracis-33646	344	32	the	the	DET
bracis-33646	344	33	literature	literature	NOUN
bracis-33646	344	34	,	,	PUNCT
bracis-33646	344	35	such	such	ADJ
bracis-33646	344	36	as	as	ADP
bracis-33646	344	37	partial	partial	ADJ
bracis-33646	344	38	meet	meet	NOUN
bracis-33646	344	39	contractions	contraction	NOUN
bracis-33646	344	40	and	and	CCONJ
bracis-33646	344	41	agm	agm	PROPN
bracis-33646	344	42	rational	rational	ADJ
bracis-33646	344	43	contractions	contraction	NOUN
bracis-33646	344	44	.	.	PUNCT
bracis-33646	345	1	furthermore	furthermore	ADV
bracis-33646	345	2	,	,	PUNCT
bracis-33646	345	3	we	we	PRON
bracis-33646	345	4	characterise	characterise	VERB
bracis-33646	345	5	rational	rational	ADJ
bracis-33646	345	6	contractions	contraction	NOUN
bracis-33646	345	7	within	within	ADP
bracis-33646	345	8	our	our	PRON
bracis-33646	345	9	framework	framework	NOUN
bracis-33646	345	10	and	and	CCONJ
bracis-33646	345	11	show	show	VERB
bracis-33646	345	12	that	that	SCONJ
bracis-33646	345	13	other	other	ADJ
bracis-33646	345	14	characterisation	characterisation	NOUN
bracis-33646	345	15	results	result	NOUN
bracis-33646	345	16	,	,	PUNCT
bracis-33646	345	17	such	such	ADJ
bracis-33646	345	18	as	as	ADP
bracis-33646	345	19	that	that	PRON
bracis-33646	345	20	of	of	ADP
bracis-33646	345	21	flouris	flouris	PROPN
bracis-33646	345	22	 	 	SPACE
bracis-33646	346	1	[	[	X
bracis-33646	346	2	5	5	NUM
bracis-33646	346	3	]	]	PUNCT
bracis-33646	346	4	and	and	CCONJ
bracis-33646	346	5	ribeiro	ribeiro	PROPN
bracis-33646	346	6	et	et	PROPN
bracis-33646	346	7	al	al	PROPN
bracis-33646	346	8	.	.	PUNCT
bracis-33646	346	9	 	 	SPACE
bracis-33646	347	1	[	[	X
bracis-33646	347	2	15	15	NUM
bracis-33646	347	3	]	]	PUNCT
bracis-33646	347	4	,	,	PUNCT
bracis-33646	347	5	are	be	AUX
bracis-33646	347	6	captured	capture	VERB
bracis-33646	347	7	within	within	ADP
bracis-33646	347	8	it	it	PRON
bracis-33646	347	9	.	.	PUNCT
bracis-33646	348	1	this	this	DET
bracis-33646	348	2	investigation	investigation	NOUN
bracis-33646	348	3	provides	provide	VERB
bracis-33646	348	4	greater	great	ADJ
bracis-33646	348	5	evidence	evidence	NOUN
bracis-33646	348	6	to	to	ADP
bracis-33646	348	7	the	the	DET
bracis-33646	348	8	conjecture	conjecture	NOUN
bracis-33646	348	9	raised	raise	VERB
bracis-33646	348	10	by	by	ADP
bracis-33646	348	11	souza	souza	PROPN
bracis-33646	348	12	and	and	CCONJ
bracis-33646	348	13	wassermann	wassermann	PROPN
bracis-33646	348	14	 	 	SPACE
bracis-33646	349	1	[	[	X
bracis-33646	349	2	19	19	NUM
bracis-33646	349	3	]	]	PUNCT
bracis-33646	349	4	that	that	SCONJ
bracis-33646	349	5	“	"	PUNCT
bracis-33646	349	6	different	different	ADJ
bracis-33646	349	7	notions	notion	NOUN
bracis-33646	349	8	of	of	ADP
bracis-33646	349	9	minimality	minimality	NOUN
bracis-33646	349	10	arise	arise	VERB
bracis-33646	349	11	as	as	ADP
bracis-33646	349	12	the	the	DET
bracis-33646	349	13	reflection	reflection	NOUN
bracis-33646	349	14	of	of	ADP
bracis-33646	349	15	topological	topological	ADJ
bracis-33646	349	16	properties	property	NOUN
bracis-33646	349	17	of	of	ADP
bracis-33646	349	18	the	the	DET
bracis-33646	349	19	model	model	NOUN
bracis-33646	349	20	space	space	NOUN
bracis-33646	349	21	”	"	PUNCT
bracis-33646	349	22	,	,	PUNCT
bracis-33646	349	23	not	not	PART
bracis-33646	349	24	necessarily	necessarily	ADV
bracis-33646	349	25	as	as	ADP
bracis-33646	349	26	intrinsic	intrinsic	ADJ
bracis-33646	349	27	distinction	distinction	NOUN
bracis-33646	349	28	in	in	ADP
bracis-33646	349	29	their	their	PRON
bracis-33646	349	30	constructions	construction	NOUN
bracis-33646	349	31	.	.	PUNCT
bracis-33646	350	1	for	for	ADP
bracis-33646	350	2	future	future	ADJ
bracis-33646	350	3	work	work	NOUN
bracis-33646	350	4	,	,	PUNCT
bracis-33646	350	5	we	we	PRON
bracis-33646	350	6	intend	intend	VERB
bracis-33646	350	7	to	to	PART
bracis-33646	350	8	study	study	VERB
bracis-33646	350	9	different	different	ADJ
bracis-33646	350	10	belief	belief	NOUN
bracis-33646	350	11	change	change	NOUN
bracis-33646	350	12	operations	operation	NOUN
bracis-33646	350	13	in	in	ADP
bracis-33646	350	14	this	this	DET
bracis-33646	350	15	framework	framework	NOUN
bracis-33646	350	16	,	,	PUNCT
bracis-33646	350	17	such	such	ADJ
bracis-33646	350	18	as	as	ADP
bracis-33646	350	19	partial	partial	ADJ
bracis-33646	350	20	meet	meet	NOUN
bracis-33646	350	21	contractions	contraction	NOUN
bracis-33646	350	22	,	,	PUNCT
bracis-33646	350	23	revisions	revision	NOUN
bracis-33646	350	24	and	and	CCONJ
bracis-33646	350	25	semi	semi	NOUN
bracis-33646	350	26	-	-	NOUN
bracis-33646	350	27	revisions	revision	NOUN
bracis-33646	350	28	and	and	CCONJ
bracis-33646	350	29	their	their	PRON
bracis-33646	350	30	relations	relation	NOUN
bracis-33646	350	31	,	,	PUNCT
bracis-33646	350	32	aiming	aim	VERB
bracis-33646	350	33	to	to	PART
bracis-33646	350	34	provide	provide	VERB
bracis-33646	350	35	a	a	DET
bracis-33646	350	36	unified	unified	ADJ
bracis-33646	350	37	view	view	NOUN
bracis-33646	350	38	of	of	ADP
bracis-33646	350	39	definability	definability	NOUN
bracis-33646	350	40	and	and	CCONJ
bracis-33646	350	41	constructibility	constructibility	NOUN
bracis-33646	350	42	of	of	ADP
bracis-33646	350	43	these	these	DET
bracis-33646	350	44	operations	operation	NOUN
bracis-33646	350	45	based	base	VERB
bracis-33646	350	46	on	on	ADP
bracis-33646	350	47	a	a	DET
bracis-33646	350	48	single	single	ADJ
bracis-33646	350	49	semantic	semantic	ADJ
bracis-33646	350	50	framework	framework	NOUN
bracis-33646	350	51	.	.	PUNCT
bracis-33646	351	1	notes	note	VERB
bracis-33646	351	2	1.such	1.such	NUM
bracis-33646	351	3	logics	logic	NOUN
bracis-33646	351	4	are	be	AUX
bracis-33646	351	5	called	call	VERB
bracis-33646	351	6	tarskian	tarskian	NOUN
bracis-33646	351	7	,	,	PUNCT
bracis-33646	351	8	due	due	ADJ
bracis-33646	351	9	to	to	ADP
bracis-33646	351	10	polish	polish	ADJ
bracis-33646	351	11	logician	logician	ADJ
bracis-33646	351	12	alfred	alfre	VERB
bracis-33646	351	13	tarski	tarski	PROPN
bracis-33646	351	14	.	.	PUNCT
bracis-33646	352	1	non	non	ADJ
bracis-33646	352	2	-	-	ADJ
bracis-33646	352	3	tarskian	tarskian	ADJ
bracis-33646	352	4	logics	logic	NOUN
bracis-33646	352	5	exist	exist	VERB
bracis-33646	352	6	in	in	ADP
bracis-33646	352	7	the	the	DET
bracis-33646	352	8	literature	literature	NOUN
bracis-33646	352	9	but	but	CCONJ
bracis-33646	352	10	will	will	AUX
bracis-33646	352	11	not	not	PART
bracis-33646	352	12	be	be	AUX
bracis-33646	352	13	studied	study	VERB
bracis-33646	352	14	in	in	ADP
bracis-33646	352	15	this	this	DET
bracis-33646	352	16	work	work	NOUN
bracis-33646	352	17	.	.	PUNCT
bracis-33646	353	1	2.in	2.in	NUM
bracis-33646	353	2	the	the	DET
bracis-33646	353	3	following	following	NOUN
bracis-33646	353	4	we	we	PRON
bracis-33646	353	5	will	will	AUX
bracis-33646	353	6	often	often	ADV
bracis-33646	353	7	refer	refer	VERB
bracis-33646	353	8	to	to	ADP
bracis-33646	353	9	closed	closed	ADJ
bracis-33646	353	10	sets	set	NOUN
bracis-33646	353	11	by	by	ADP
bracis-33646	353	12	the	the	DET
bracis-33646	353	13	letter	letter	NOUN
bracis-33646	353	14	k	k	PROPN
bracis-33646	353	15	(	(	PUNCT
bracis-33646	353	16	\(k'\),\(k''\	\(k'\),\(k''\	PROPN
bracis-33646	353	17	)	)	PUNCT
bracis-33646	353	18	,	,	PUNCT
bracis-33646	353	19	etc	etc	X
bracis-33646	353	20	.	.	X
bracis-33646	353	21	)	)	PUNCT
bracis-33646	353	22	,	,	PUNCT
bracis-33646	353	23	arbitrary	arbitrary	ADJ
bracis-33646	353	24	sets	set	NOUN
bracis-33646	353	25	of	of	ADP
bracis-33646	353	26	formulas	formula	NOUN
bracis-33646	353	27	by	by	ADP
bracis-33646	353	28	the	the	DET
bracis-33646	353	29	letter	letter	NOUN
bracis-33646	353	30	b	b	PROPN
bracis-33646	353	31	(	(	PUNCT
bracis-33646	353	32	\(b'\),\(b''\	\(b'\),\(b''\	PROPN
bracis-33646	353	33	)	)	PUNCT
bracis-33646	353	34	,	,	PUNCT
bracis-33646	353	35	etc	etc	X
bracis-33646	353	36	.	.	X
bracis-33646	353	37	)	)	PUNCT
bracis-33646	353	38	.	.	PUNCT
bracis-33646	354	1	references	reference	NOUN
bracis-33646	354	2	alchourrón	alchourrón	PROPN
bracis-33646	354	3	,	,	PUNCT
bracis-33646	354	4	c.e	c.e	PROPN
bracis-33646	354	5	.	.	PROPN
bracis-33646	354	6	,	,	PUNCT
bracis-33646	354	7	gärdenfors	gärdenfor	NOUN
bracis-33646	354	8	,	,	PUNCT
bracis-33646	354	9	p.	p.	PROPN
bracis-33646	354	10	,	,	PUNCT
bracis-33646	354	11	makinson	makinson	PROPN
bracis-33646	354	12	,	,	PUNCT
bracis-33646	354	13	d.	d.	PROPN
bracis-33646	354	14	:	:	PUNCT
bracis-33646	354	15	on	on	ADP
bracis-33646	354	16	the	the	DET
bracis-33646	354	17	logic	logic	NOUN
bracis-33646	354	18	of	of	ADP
bracis-33646	354	19	theory	theory	NOUN
bracis-33646	354	20	change	change	NOUN
bracis-33646	354	21	:	:	PUNCT
bracis-33646	354	22	partial	partial	ADJ
bracis-33646	354	23	meet	meet	NOUN
bracis-33646	354	24	contraction	contraction	NOUN
bracis-33646	354	25	and	and	CCONJ
bracis-33646	354	26	revision	revision	NOUN
bracis-33646	354	27	functions	function	NOUN
bracis-33646	354	28	.	.	PUNCT
bracis-33646	355	1	j.	j.	PROPN
bracis-33646	355	2	symb	symb	PROPN
bracis-33646	355	3	.	.	PUNCT
bracis-33646	356	1	log	log	PROPN
bracis-33646	356	2	.	.	PUNCT
bracis-33646	357	1	50(2	50(2	NUM
bracis-33646	357	2	)	)	PUNCT
bracis-33646	357	3	,	,	PUNCT
bracis-33646	357	4	510–530	510–530	NUM
bracis-33646	357	5	(	(	PUNCT
bracis-33646	357	6	1985	1985	NUM
bracis-33646	357	7	)	)	PUNCT
bracis-33646	357	8	google	google	PROPN
bracis-33646	357	9	scholar	scholar	NOUN
bracis-33646	357	10	  	  	SPACE
bracis-33646	357	11	baltag	baltag	NOUN
bracis-33646	357	12	,	,	PUNCT
bracis-33646	357	13	a.	a.	NOUN
bracis-33646	357	14	,	,	PUNCT
bracis-33646	357	15	bezhanishvili	bezhanishvili	NOUN
bracis-33646	357	16	,	,	PUNCT
bracis-33646	357	17	n.	n.	NOUN
bracis-33646	357	18	,	,	PUNCT
bracis-33646	357	19	özgün	özgün	NOUN
bracis-33646	357	20	,	,	PUNCT
bracis-33646	357	21	a.	a.	NOUN
bracis-33646	357	22	,	,	PUNCT
bracis-33646	357	23	smets	smet	NOUN
bracis-33646	357	24	,	,	PUNCT
bracis-33646	357	25	s.	s.	PROPN
bracis-33646	357	26	:	:	PUNCT
bracis-33646	357	27	the	the	DET
bracis-33646	357	28	topology	topology	NOUN
bracis-33646	357	29	of	of	ADP
bracis-33646	357	30	belief	belief	NOUN
bracis-33646	357	31	,	,	PUNCT
bracis-33646	357	32	belief	belief	NOUN
bracis-33646	357	33	revision	revision	NOUN
bracis-33646	357	34	and	and	CCONJ
bracis-33646	357	35	defeasible	defeasible	ADJ
bracis-33646	357	36	knowledge	knowledge	NOUN
bracis-33646	357	37	.	.	PUNCT
bracis-33646	358	1	in	in	ADP
bracis-33646	358	2	:	:	PUNCT
bracis-33646	358	3	logic	logic	NOUN
bracis-33646	358	4	,	,	PUNCT
bracis-33646	358	5	rationality	rationality	NOUN
bracis-33646	358	6	,	,	PUNCT
bracis-33646	358	7	and	and	CCONJ
bracis-33646	358	8	interaction	interaction	NOUN
bracis-33646	358	9	,	,	PUNCT
bracis-33646	358	10	pp	pp	ADJ
bracis-33646	358	11	.	.	PUNCT
bracis-33646	359	1	27–40	27–40	NUM
bracis-33646	359	2	.	.	PUNCT
bracis-33646	359	3	springer	springer	NOUN
bracis-33646	359	4	,	,	PUNCT
bracis-33646	359	5	new	new	PROPN
bracis-33646	359	6	york	york	PROPN
bracis-33646	359	7	(	(	PUNCT
bracis-33646	359	8	2013	2013	NUM
bracis-33646	359	9	)	)	PUNCT
bracis-33646	359	10	google	google	PROPN
bracis-33646	359	11	scholar	scholar	NOUN
bracis-33646	359	12	  	  	SPACE
bracis-33646	359	13	bjorndahl	bjorndahl	ADV
bracis-33646	359	14	,	,	PUNCT
bracis-33646	359	15	a.	a.	NOUN
bracis-33646	359	16	,	,	PUNCT
bracis-33646	359	17	özgün	özgün	NOUN
bracis-33646	359	18	,	,	PUNCT
bracis-33646	359	19	a.	a.	NOUN
bracis-33646	359	20	,	,	PUNCT
bracis-33646	359	21	et	et	PROPN
bracis-33646	359	22	 	 	SPACE
bracis-33646	359	23	al	al	PROPN
bracis-33646	359	24	.	.	PUNCT
bracis-33646	359	25	:	:	PUNCT
bracis-33646	360	1	logic	logic	NOUN
bracis-33646	360	2	and	and	CCONJ
bracis-33646	360	3	topology	topology	NOUN
bracis-33646	360	4	for	for	ADP
bracis-33646	360	5	knowledge	knowledge	NOUN
bracis-33646	360	6	,	,	PUNCT
bracis-33646	360	7	knowability	knowability	NOUN
bracis-33646	360	8	,	,	PUNCT
bracis-33646	360	9	and	and	CCONJ
bracis-33646	360	10	belief	belief	NOUN
bracis-33646	360	11	.	.	PUNCT
bracis-33646	361	1	electron	electron	PROPN
bracis-33646	361	2	.	.	PUNCT
bracis-33646	362	1	proc	proc	PROPN
bracis-33646	362	2	.	.	PUNCT
bracis-33646	363	1	theor	theor	PROPN
bracis-33646	363	2	.	.	PUNCT
bracis-33646	364	1	comput	comput	PROPN
bracis-33646	364	2	.	.	PUNCT
bracis-33646	365	1	sci	sci	PROPN
bracis-33646	365	2	.	.	PROPN
bracis-33646	366	1	251	251	NUM
bracis-33646	366	2	(	(	PUNCT
bracis-33646	366	3	2017	2017	NUM
bracis-33646	366	4	)	)	PUNCT
bracis-33646	366	5	google	google	NOUN
bracis-33646	366	6	scholar	scholar	NOUN
bracis-33646	366	7	  	  	SPACE
bracis-33646	366	8	delgrande	delgrande	NOUN
bracis-33646	366	9	,	,	PUNCT
bracis-33646	366	10	j.p	j.p	PROPN
bracis-33646	366	11	.	.	PROPN
bracis-33646	366	12	:	:	PUNCT
bracis-33646	367	1	horn	horn	NOUN
bracis-33646	367	2	clause	clause	NOUN
bracis-33646	367	3	belief	belief	NOUN
bracis-33646	367	4	change	change	NOUN
bracis-33646	367	5	:	:	PUNCT
bracis-33646	367	6	contraction	contraction	NOUN
bracis-33646	367	7	functions	function	NOUN
bracis-33646	367	8	.	.	PUNCT
bracis-33646	368	1	in	in	ADP
bracis-33646	368	2	:	:	PUNCT
bracis-33646	368	3	proceedings	proceeding	NOUN
bracis-33646	368	4	of	of	ADP
bracis-33646	368	5	the	the	DET
bracis-33646	368	6	eleventh	eleventh	ADJ
bracis-33646	368	7	international	international	ADJ
bracis-33646	368	8	conference	conference	NOUN
bracis-33646	368	9	on	on	ADP
bracis-33646	368	10	principles	principle	NOUN
bracis-33646	368	11	of	of	ADP
bracis-33646	368	12	knowledge	knowledge	NOUN
bracis-33646	368	13	representation	representation	NOUN
bracis-33646	368	14	and	and	CCONJ
bracis-33646	368	15	reasoning	reasoning	NOUN
bracis-33646	368	16	,	,	PUNCT
bracis-33646	368	17	pp	pp	ADP
bracis-33646	368	18	.	.	PUNCT
bracis-33646	369	1	156–165	156–165	NUM
bracis-33646	369	2	(	(	PUNCT
bracis-33646	369	3	2008	2008	NUM
bracis-33646	369	4	)	)	PUNCT
bracis-33646	369	5	google	google	PROPN
bracis-33646	369	6	scholar	scholar	NOUN
bracis-33646	369	7	  	  	SPACE
bracis-33646	369	8	flouris	flouris	NOUN
bracis-33646	369	9	,	,	PUNCT
bracis-33646	369	10	g.	g.	NOUN
bracis-33646	369	11	:	:	PUNCT
bracis-33646	369	12	on	on	ADP
bracis-33646	369	13	belief	belief	NOUN
bracis-33646	369	14	change	change	NOUN
bracis-33646	369	15	and	and	CCONJ
bracis-33646	369	16	ontology	ontology	NOUN
bracis-33646	369	17	evolution	evolution	NOUN
bracis-33646	369	18	.	.	PUNCT
bracis-33646	370	1	ph.d	ph.d	PROPN
bracis-33646	370	2	.	.	PUNCT
bracis-33646	371	1	thesis	thesis	NOUN
bracis-33646	371	2	,	,	PUNCT
bracis-33646	371	3	university	university	NOUN
bracis-33646	371	4	of	of	ADP
bracis-33646	371	5	crete	crete	PROPN
bracis-33646	371	6	(	(	PUNCT
bracis-33646	371	7	2006	2006	NUM
bracis-33646	371	8	)	)	PUNCT
bracis-33646	371	9	google	google	PROPN
bracis-33646	371	10	scholar	scholar	NOUN
bracis-33646	371	11	  	  	SPACE
bracis-33646	371	12	fuhrmann	fuhrmann	NOUN
bracis-33646	371	13	,	,	PUNCT
bracis-33646	371	14	a.	a.	PROPN
bracis-33646	371	15	,	,	PUNCT
bracis-33646	371	16	hansson	hansson	PROPN
bracis-33646	371	17	,	,	PUNCT
bracis-33646	371	18	s.o	s.o	PROPN
bracis-33646	371	19	.	.	PROPN
bracis-33646	371	20	:	:	PUNCT
bracis-33646	372	1	a	a	DET
bracis-33646	372	2	survey	survey	NOUN
bracis-33646	372	3	of	of	ADP
bracis-33646	372	4	multiple	multiple	ADJ
bracis-33646	372	5	contractions	contraction	NOUN
bracis-33646	372	6	.	.	PUNCT
bracis-33646	373	1	j.	j.	PROPN
bracis-33646	373	2	logic	logic	PROPN
bracis-33646	373	3	lang	lang	PROPN
bracis-33646	373	4	.	.	PUNCT
bracis-33646	374	1	inform	inform	NOUN
bracis-33646	374	2	.	.	PUNCT
bracis-33646	375	1	3	3	NUM
bracis-33646	375	2	,	,	PUNCT
bracis-33646	375	3	39–75	39–75	NUM
bracis-33646	375	4	(	(	PUNCT
bracis-33646	375	5	1994	1994	NUM
bracis-33646	375	6	)	)	PUNCT
bracis-33646	375	7	article	article	NOUN
bracis-33646	375	8	  	  	SPACE
bracis-33646	375	9	mathscinet	mathscinet	NOUN
bracis-33646	375	10	  	  	SPACE
bracis-33646	375	11	math	math	NOUN
bracis-33646	375	12	  	  	SPACE
bracis-33646	375	13	google	google	PROPN
bracis-33646	375	14	scholar	scholar	NOUN
bracis-33646	375	15	  	  	SPACE
bracis-33646	375	16	girard	girard	NOUN
bracis-33646	375	17	,	,	PUNCT
bracis-33646	375	18	p.	p.	PROPN
bracis-33646	375	19	,	,	PUNCT
bracis-33646	375	20	tanaka	tanaka	PROPN
bracis-33646	375	21	,	,	PUNCT
bracis-33646	375	22	k.	k.	PROPN
bracis-33646	375	23	:	:	PUNCT
bracis-33646	375	24	paraconsistent	paraconsistent	NOUN
bracis-33646	375	25	dynamics	dynamic	NOUN
bracis-33646	375	26	.	.	PUNCT
bracis-33646	376	1	synthese	synthese	ADJ
bracis-33646	376	2	193(1	193(1	NUM
bracis-33646	376	3	)	)	PUNCT
bracis-33646	376	4	,	,	PUNCT
bracis-33646	376	5	1–14	1–14	PROPN
bracis-33646	376	6	(	(	PUNCT
bracis-33646	376	7	2016	2016	NUM
bracis-33646	376	8	)	)	PUNCT
bracis-33646	376	9	article	article	NOUN
bracis-33646	376	10	  	  	SPACE
bracis-33646	376	11	mathscinet	mathscinet	NOUN
bracis-33646	376	12	  	  	SPACE
bracis-33646	376	13	math	math	NOUN
bracis-33646	376	14	  	  	SPACE
bracis-33646	376	15	google	google	PROPN
bracis-33646	376	16	scholar	scholar	NOUN
bracis-33646	376	17	  	  	SPACE
bracis-33646	376	18	hansson	hansson	PROPN
bracis-33646	376	19	,	,	PUNCT
bracis-33646	376	20	s.o	s.o	PROPN
bracis-33646	376	21	.	.	PROPN
bracis-33646	376	22	:	:	PUNCT
bracis-33646	377	1	in	in	ADP
bracis-33646	377	2	defense	defense	NOUN
bracis-33646	377	3	of	of	ADP
bracis-33646	377	4	base	base	NOUN
bracis-33646	377	5	contraction	contraction	NOUN
bracis-33646	377	6	.	.	PUNCT
bracis-33646	378	1	synthese	synthese	ADJ
bracis-33646	378	2	91(3	91(3	NUM
bracis-33646	378	3	)	)	PUNCT
bracis-33646	378	4	,	,	PUNCT
bracis-33646	378	5	239–245	239–245	NUM
bracis-33646	378	6	(	(	PUNCT
bracis-33646	378	7	1992	1992	NUM
bracis-33646	378	8	)	)	PUNCT
bracis-33646	378	9	article	article	NOUN
bracis-33646	378	10	  	  	SPACE
bracis-33646	378	11	mathscinet	mathscinet	NOUN
bracis-33646	378	12	  	  	SPACE
bracis-33646	378	13	math	math	NOUN
bracis-33646	378	14	  	  	SPACE
bracis-33646	378	15	google	google	PROPN
bracis-33646	378	16	scholar	scholar	NOUN
bracis-33646	378	17	  	  	SPACE
bracis-33646	378	18	hansson	hansson	PROPN
bracis-33646	378	19	,	,	PUNCT
bracis-33646	378	20	s.o	s.o	PROPN
bracis-33646	378	21	.	.	PROPN
bracis-33646	378	22	,	,	PUNCT
bracis-33646	378	23	wassermann	wassermann	PROPN
bracis-33646	378	24	,	,	PUNCT
bracis-33646	378	25	r.	r.	PROPN
bracis-33646	378	26	:	:	PUNCT
bracis-33646	378	27	local	local	ADJ
bracis-33646	378	28	change	change	NOUN
bracis-33646	378	29	.	.	PUNCT
bracis-33646	379	1	stud	stud	NOUN
bracis-33646	379	2	.	.	PUNCT
bracis-33646	380	1	logica	logica	PROPN
bracis-33646	380	2	.	.	PUNCT
bracis-33646	381	1	70(1	70(1	NUM
bracis-33646	381	2	)	)	PUNCT
bracis-33646	381	3	,	,	PUNCT
bracis-33646	381	4	49–76	49–76	NUM
bracis-33646	381	5	(	(	PUNCT
bracis-33646	381	6	2002	2002	NUM
bracis-33646	381	7	)	)	PUNCT
bracis-33646	381	8	article	article	NOUN
bracis-33646	381	9	  	  	SPACE
bracis-33646	381	10	mathscinet	mathscinet	NOUN
bracis-33646	381	11	  	  	SPACE
bracis-33646	381	12	math	math	NOUN
bracis-33646	381	13	  	  	SPACE
bracis-33646	381	14	google	google	PROPN
bracis-33646	381	15	scholar	scholar	NOUN
bracis-33646	381	16	  	  	SPACE
bracis-33646	381	17	kelly	kelly	PROPN
bracis-33646	381	18	,	,	PUNCT
bracis-33646	381	19	k.t	k.t	PROPN
bracis-33646	381	20	.	.	PROPN
bracis-33646	381	21	:	:	PUNCT
bracis-33646	382	1	the	the	DET
bracis-33646	382	2	logic	logic	NOUN
bracis-33646	382	3	of	of	ADP
bracis-33646	382	4	reliable	reliable	ADJ
bracis-33646	382	5	inquiry	inquiry	NOUN
bracis-33646	382	6	.	.	PUNCT
bracis-33646	383	1	oup	oup	PROPN
bracis-33646	383	2	usa	usa	PROPN
bracis-33646	383	3	(	(	PUNCT
bracis-33646	383	4	1996	1996	NUM
bracis-33646	383	5	)	)	PUNCT
bracis-33646	383	6	google	google	PROPN
bracis-33646	383	7	scholar	scholar	NOUN
bracis-33646	383	8	  	  	SPACE
bracis-33646	383	9	lewitzka	lewitzka	NOUN
bracis-33646	383	10	,	,	PUNCT
bracis-33646	383	11	s.	s.	PROPN
bracis-33646	383	12	,	,	PUNCT
bracis-33646	383	13	brunner	brunner	PROPN
bracis-33646	383	14	,	,	PUNCT
bracis-33646	383	15	a.b	a.b	PROPN
bracis-33646	383	16	.	.	PROPN
bracis-33646	383	17	:	:	PUNCT
bracis-33646	383	18	minimally	minimally	ADV
bracis-33646	383	19	generated	generate	VERB
bracis-33646	383	20	abstract	abstract	ADJ
bracis-33646	383	21	logics	logic	NOUN
bracis-33646	383	22	.	.	PUNCT
bracis-33646	384	1	log	log	PROPN
bracis-33646	384	2	.	.	PUNCT
bracis-33646	385	1	univ	univ	PROPN
bracis-33646	385	2	.	.	PUNCT
bracis-33646	386	1	3	3	NUM
bracis-33646	386	2	,	,	PUNCT
bracis-33646	386	3	219–241	219–241	NUM
bracis-33646	386	4	(	(	PUNCT
bracis-33646	386	5	2009	2009	NUM
bracis-33646	386	6	)	)	PUNCT
bracis-33646	386	7	google	google	PROPN
bracis-33646	386	8	scholar	scholar	NOUN
bracis-33646	386	9	  	  	SPACE
bracis-33646	386	10	makowsky	makowsky	PROPN
bracis-33646	386	11	,	,	PUNCT
bracis-33646	386	12	j.a	j.a	PROPN
bracis-33646	386	13	.	.	PROPN
bracis-33646	386	14	,	,	PUNCT
bracis-33646	386	15	shelah	shelah	PROPN
bracis-33646	386	16	,	,	PUNCT
bracis-33646	386	17	s.	s.	PROPN
bracis-33646	386	18	:	:	PUNCT
bracis-33646	386	19	positive	positive	ADJ
bracis-33646	386	20	results	result	NOUN
bracis-33646	386	21	in	in	ADP
bracis-33646	386	22	abstract	abstract	ADJ
bracis-33646	386	23	model	model	NOUN
bracis-33646	386	24	theory	theory	NOUN
bracis-33646	386	25	:	:	PUNCT
bracis-33646	386	26	a	a	DET
bracis-33646	386	27	theory	theory	NOUN
bracis-33646	386	28	of	of	ADP
bracis-33646	386	29	compact	compact	ADJ
bracis-33646	386	30	logics	logic	NOUN
bracis-33646	386	31	.	.	PUNCT
bracis-33646	387	1	ann	ann	PROPN
bracis-33646	387	2	.	.	PUNCT
bracis-33646	388	1	pure	pure	ADJ
bracis-33646	388	2	appl	appl	PROPN
bracis-33646	388	3	.	.	PUNCT
bracis-33646	389	1	logic	logic	NOUN
bracis-33646	389	2	25(3	25(3	NUM
bracis-33646	389	3	)	)	PUNCT
bracis-33646	389	4	,	,	PUNCT
bracis-33646	389	5	263–299	263–299	NUM
bracis-33646	389	6	(	(	PUNCT
bracis-33646	389	7	1983	1983	NUM
bracis-33646	389	8	)	)	PUNCT
bracis-33646	389	9	article	article	NOUN
bracis-33646	389	10	  	  	SPACE
bracis-33646	389	11	mathscinet	mathscinet	NOUN
bracis-33646	389	12	  	  	SPACE
bracis-33646	389	13	math	math	NOUN
bracis-33646	389	14	  	  	SPACE
bracis-33646	389	15	google	google	PROPN
bracis-33646	389	16	scholar	scholar	NOUN
bracis-33646	389	17	  	  	SPACE
bracis-33646	389	18	özgün	özgün	NOUN
bracis-33646	389	19	,	,	PUNCT
bracis-33646	389	20	a.	a.	NOUN
bracis-33646	389	21	:	:	PUNCT
bracis-33646	389	22	topological	topological	ADJ
bracis-33646	389	23	models	model	NOUN
bracis-33646	389	24	for	for	ADP
bracis-33646	389	25	belief	belief	NOUN
bracis-33646	389	26	and	and	CCONJ
bracis-33646	389	27	belief	belief	NOUN
bracis-33646	389	28	revision	revision	NOUN
bracis-33646	389	29	.	.	PUNCT
bracis-33646	390	1	ph.d	ph.d	PROPN
bracis-33646	390	2	.	.	PUNCT
bracis-33646	391	1	thesis	thesis	PROPN
bracis-33646	391	2	,	,	PUNCT
bracis-33646	391	3	universiteit	universiteit	PROPN
bracis-33646	391	4	van	van	PROPN
bracis-33646	391	5	amsterdam	amsterdam	PROPN
bracis-33646	391	6	(	(	PUNCT
bracis-33646	391	7	2013	2013	NUM
bracis-33646	391	8	)	)	PUNCT
bracis-33646	391	9	google	google	PROPN
bracis-33646	391	10	scholar	scholar	NOUN
bracis-33646	391	11	  	  	SPACE
bracis-33646	391	12	peppas	peppa	NOUN
bracis-33646	391	13	,	,	PUNCT
bracis-33646	391	14	p.	p.	NOUN
bracis-33646	391	15	:	:	PUNCT
bracis-33646	391	16	the	the	DET
bracis-33646	391	17	limit	limit	NOUN
bracis-33646	391	18	assumption	assumption	NOUN
bracis-33646	391	19	and	and	CCONJ
bracis-33646	391	20	multiple	multiple	ADJ
bracis-33646	391	21	revision	revision	NOUN
bracis-33646	391	22	.	.	PUNCT
bracis-33646	392	1	j.	j.	PROPN
bracis-33646	392	2	log	log	PROPN
bracis-33646	392	3	.	.	PUNCT
bracis-33646	393	1	comput	comput	NOUN
bracis-33646	393	2	.	.	PUNCT
bracis-33646	394	1	14(3	14(3	NUM
bracis-33646	394	2	)	)	PUNCT
bracis-33646	394	3	,	,	PUNCT
bracis-33646	394	4	355–371	355–371	NUM
bracis-33646	394	5	(	(	PUNCT
bracis-33646	394	6	2004	2004	NUM
bracis-33646	394	7	)	)	PUNCT
bracis-33646	394	8	article	article	NOUN
bracis-33646	394	9	  	  	SPACE
bracis-33646	394	10	mathscinet	mathscinet	NOUN
bracis-33646	394	11	  	  	SPACE
bracis-33646	394	12	math	math	NOUN
bracis-33646	394	13	  	  	SPACE
bracis-33646	394	14	google	google	PROPN
bracis-33646	394	15	scholar	scholar	NOUN
bracis-33646	394	16	  	  	SPACE
bracis-33646	394	17	ribeiro	ribeiro	PROPN
bracis-33646	394	18	,	,	PUNCT
bracis-33646	394	19	j.s	j.s	PROPN
bracis-33646	394	20	.	.	PROPN
bracis-33646	394	21	,	,	PUNCT
bracis-33646	394	22	nayak	nayak	PROPN
bracis-33646	394	23	,	,	PUNCT
bracis-33646	394	24	a.	a.	NOUN
bracis-33646	394	25	,	,	PUNCT
bracis-33646	394	26	wassermann	wassermann	PROPN
bracis-33646	394	27	,	,	PUNCT
bracis-33646	394	28	r.	r.	PROPN
bracis-33646	394	29	:	:	PUNCT
bracis-33646	394	30	towards	towards	ADP
bracis-33646	394	31	belief	belief	NOUN
bracis-33646	394	32	contraction	contraction	NOUN
bracis-33646	394	33	without	without	ADP
bracis-33646	394	34	compactness	compactness	NOUN
bracis-33646	394	35	.	.	PUNCT
bracis-33646	395	1	in	in	ADP
bracis-33646	395	2	:	:	PUNCT
bracis-33646	395	3	16th	16th	ADJ
bracis-33646	395	4	international	international	ADJ
bracis-33646	395	5	conference	conference	NOUN
bracis-33646	395	6	on	on	ADP
bracis-33646	395	7	principles	principle	NOUN
bracis-33646	395	8	of	of	ADP
bracis-33646	395	9	knowledge	knowledge	NOUN
bracis-33646	395	10	representation	representation	NOUN
bracis-33646	395	11	and	and	CCONJ
bracis-33646	395	12	reasoning	reasoning	NOUN
bracis-33646	395	13	,	,	PUNCT
bracis-33646	395	14	pp	pp	ADJ
bracis-33646	395	15	.	.	PUNCT
bracis-33646	396	1	287–296	287–296	NUM
bracis-33646	396	2	.	.	X
bracis-33646	396	3	association	association	NOUN
bracis-33646	396	4	for	for	ADP
bracis-33646	396	5	the	the	DET
bracis-33646	396	6	advancement	advancement	NOUN
bracis-33646	396	7	of	of	ADP
bracis-33646	396	8	artificial	artificial	ADJ
bracis-33646	396	9	intelligence	intelligence	NOUN
bracis-33646	396	10	(	(	PUNCT
bracis-33646	396	11	2018	2018	NUM
bracis-33646	396	12	)	)	PUNCT
bracis-33646	396	13	google	google	PROPN
bracis-33646	396	14	scholar	scholar	NOUN
bracis-33646	396	15	  	  	SPACE
bracis-33646	396	16	ribeiro	ribeiro	PROPN
bracis-33646	396	17	,	,	PUNCT
bracis-33646	396	18	m.m	m.m	PROPN
bracis-33646	396	19	.	.	PROPN
bracis-33646	396	20	,	,	PUNCT
bracis-33646	396	21	wassermann	wassermann	PROPN
bracis-33646	396	22	,	,	PUNCT
bracis-33646	396	23	r.	r.	PROPN
bracis-33646	396	24	:	:	PUNCT
bracis-33646	396	25	base	base	NOUN
bracis-33646	396	26	revision	revision	NOUN
bracis-33646	396	27	for	for	ADP
bracis-33646	396	28	ontology	ontology	NOUN
bracis-33646	396	29	debugging	debugging	NOUN
bracis-33646	396	30	.	.	PUNCT
bracis-33646	397	1	j.	j.	PROPN
bracis-33646	397	2	log	log	PROPN
bracis-33646	397	3	.	.	PUNCT
bracis-33646	398	1	comput	comput	NOUN
bracis-33646	398	2	.	.	PUNCT
bracis-33646	399	1	19(5	19(5	NUM
bracis-33646	399	2	)	)	PUNCT
bracis-33646	399	3	,	,	PUNCT
bracis-33646	399	4	721–743	721–743	NUM
bracis-33646	399	5	(	(	PUNCT
bracis-33646	399	6	2009	2009	NUM
bracis-33646	399	7	)	)	PUNCT
bracis-33646	399	8	.	.	PUNCT
bracis-33646	400	1	https://doi.org/10.1093/logcom/exn048	https://doi.org/10.1093/logcom/exn048	NOUN
bracis-33646	400	2	article	article	NOUN
bracis-33646	400	3	  	  	SPACE
bracis-33646	400	4	mathscinet	mathscinet	NOUN
bracis-33646	400	5	  	  	SPACE
bracis-33646	400	6	math	math	NOUN
bracis-33646	400	7	  	  	SPACE
bracis-33646	400	8	google	google	PROPN
bracis-33646	400	9	scholar	scholar	NOUN
bracis-33646	400	10	  	  	SPACE
bracis-33646	400	11	ribeiro	ribeiro	PROPN
bracis-33646	400	12	,	,	PUNCT
bracis-33646	400	13	m.m	m.m	PROPN
bracis-33646	400	14	.	.	PROPN
bracis-33646	400	15	:	:	PUNCT
bracis-33646	400	16	belief	belief	NOUN
bracis-33646	400	17	revision	revision	NOUN
bracis-33646	400	18	in	in	ADP
bracis-33646	400	19	non	non	ADJ
bracis-33646	400	20	-	-	ADJ
bracis-33646	400	21	classical	classical	ADJ
bracis-33646	400	22	logics	logic	NOUN
bracis-33646	400	23	.	.	PUNCT
bracis-33646	401	1	springer	springer	NOUN
bracis-33646	401	2	(	(	PUNCT
bracis-33646	401	3	2013	2013	NUM
bracis-33646	401	4	)	)	PUNCT
bracis-33646	401	5	google	google	PROPN
bracis-33646	401	6	scholar	scholar	NOUN
bracis-33646	401	7	  	  	SPACE
bracis-33646	401	8	souza	souza	PROPN
bracis-33646	401	9	,	,	PUNCT
bracis-33646	401	10	m.	m.	NOUN
bracis-33646	401	11	,	,	PUNCT
bracis-33646	401	12	wassermann	wassermann	PROPN
bracis-33646	401	13	,	,	PUNCT
bracis-33646	401	14	r.	r.	PROPN
bracis-33646	401	15	:	:	PUNCT
bracis-33646	401	16	hyperintensional	hyperintensional	ADJ
bracis-33646	401	17	models	model	NOUN
bracis-33646	401	18	and	and	CCONJ
bracis-33646	401	19	belief	belief	NOUN
bracis-33646	401	20	change	change	NOUN
bracis-33646	401	21	.	.	PUNCT
bracis-33646	402	1	in	in	ADP
bracis-33646	402	2	:	:	PUNCT
bracis-33646	402	3	brazilian	brazilian	ADJ
bracis-33646	402	4	conference	conference	NOUN
bracis-33646	402	5	on	on	ADP
bracis-33646	402	6	intelligent	intelligent	ADJ
bracis-33646	402	7	systems	system	NOUN
bracis-33646	402	8	,	,	PUNCT
bracis-33646	402	9	pp	pp	ADP
bracis-33646	402	10	.	.	PUNCT
bracis-33646	403	1	429–443	429–443	NUM
bracis-33646	403	2	.	.	PUNCT
bracis-33646	404	1	springer	springer	NOUN
bracis-33646	404	2	(	(	PUNCT
bracis-33646	404	3	2022	2022	NUM
bracis-33646	404	4	)	)	PUNCT
bracis-33646	404	5	google	google	PROPN
bracis-33646	404	6	scholar	scholar	NOUN
bracis-33646	404	7	  	  	SPACE
bracis-33646	404	8	souza	souza	PROPN
bracis-33646	404	9	,	,	PUNCT
bracis-33646	404	10	m.	m.	NOUN
bracis-33646	404	11	,	,	PUNCT
bracis-33646	404	12	wassermann	wassermann	PROPN
bracis-33646	404	13	,	,	PUNCT
bracis-33646	404	14	r.	r.	PROPN
bracis-33646	404	15	:	:	PUNCT
bracis-33646	404	16	hyperintensional	hyperintensional	ADJ
bracis-33646	404	17	partial	partial	ADJ
bracis-33646	404	18	meet	meet	NOUN
bracis-33646	404	19	contractions	contraction	NOUN
bracis-33646	404	20	.	.	PUNCT
bracis-33646	405	1	in	in	ADP
bracis-33646	405	2	:	:	PUNCT
bracis-33646	405	3	proceedings	proceeding	NOUN
bracis-33646	405	4	of	of	ADP
bracis-33646	405	5	the	the	DET
bracis-33646	405	6	international	international	ADJ
bracis-33646	405	7	conference	conference	NOUN
bracis-33646	405	8	on	on	ADP
bracis-33646	405	9	principles	principle	NOUN
bracis-33646	405	10	of	of	ADP
bracis-33646	405	11	knowledge	knowledge	NOUN
bracis-33646	405	12	representation	representation	NOUN
bracis-33646	405	13	and	and	CCONJ
bracis-33646	405	14	reasoning	reasoning	NOUN
bracis-33646	405	15	(	(	PUNCT
bracis-33646	405	16	2022	2022	NUM
bracis-33646	405	17	)	)	PUNCT
bracis-33646	405	18	google	google	NOUN
bracis-33646	405	19	scholar	scholar	NOUN
bracis-33646	405	20	  	  	SPACE
bracis-33646	405	21	stone	stone	NOUN
bracis-33646	405	22	,	,	PUNCT
bracis-33646	405	23	m.h	m.h	PROPN
bracis-33646	405	24	.	.	PROPN
bracis-33646	405	25	:	:	PUNCT
bracis-33646	406	1	the	the	DET
bracis-33646	406	2	theory	theory	NOUN
bracis-33646	406	3	of	of	ADP
bracis-33646	406	4	representation	representation	NOUN
bracis-33646	406	5	for	for	ADP
bracis-33646	406	6	boolean	boolean	ADJ
bracis-33646	406	7	algebras	algebra	NOUN
bracis-33646	406	8	.	.	PUNCT
bracis-33646	407	1	trans	trans	AUX
bracis-33646	407	2	.	.	PROPN
bracis-33646	407	3	am	be	AUX
bracis-33646	407	4	.	.	PUNCT
bracis-33646	408	1	math	math	NOUN
bracis-33646	408	2	.	.	PUNCT
bracis-33646	409	1	soc	soc	PROPN
bracis-33646	409	2	.	.	PUNCT
bracis-33646	410	1	40(1	40(1	NUM
bracis-33646	410	2	)	)	PUNCT
bracis-33646	410	3	,	,	PUNCT
bracis-33646	410	4	37–111	37–111	NUM
bracis-33646	410	5	(	(	PUNCT
bracis-33646	410	6	1936	1936	NUM
bracis-33646	410	7	)	)	PUNCT
bracis-33646	410	8	mathscinet	mathscinet	NOUN
bracis-33646	410	9	  	  	SPACE
bracis-33646	410	10	math	math	NOUN
bracis-33646	410	11	  	  	SPACE
bracis-33646	410	12	google	google	PROPN
bracis-33646	410	13	scholar	scholar	NOUN
bracis-33646	410	14	  	  	SPACE
bracis-33646	410	15	van	van	PROPN
bracis-33646	410	16	 	 	SPACE
bracis-33646	410	17	fraassen	fraassen	PROPN
bracis-33646	410	18	,	,	PUNCT
bracis-33646	410	19	b.c	b.c	PROPN
bracis-33646	410	20	.	.	PROPN
bracis-33646	410	21	,	,	PUNCT
bracis-33646	410	22	fraassen	fraassen	PROPN
bracis-33646	410	23	,	,	PUNCT
bracis-33646	410	24	v.	v.	ADP
bracis-33646	410	25	:	:	PUNCT
bracis-33646	410	26	formal	formal	ADJ
bracis-33646	410	27	semantics	semantic	NOUN
bracis-33646	410	28	and	and	CCONJ
bracis-33646	410	29	logic	logic	NOUN
bracis-33646	410	30	,	,	PUNCT
bracis-33646	410	31	vol	vol	NOUN
bracis-33646	410	32	.	.	PUNCT
bracis-33646	410	33	 	 	SPACE
bracis-33646	410	34	214	214	NUM
bracis-33646	410	35	.	.	PUNCT
bracis-33646	411	1	macmillan	macmillan	PROPN
bracis-33646	411	2	,	,	PUNCT
bracis-33646	411	3	new	new	PROPN
bracis-33646	411	4	york	york	PROPN
bracis-33646	411	5	(	(	PUNCT
bracis-33646	411	6	1971	1971	NUM
bracis-33646	411	7	)	)	PUNCT
bracis-33646	411	8	google	google	PROPN
bracis-33646	411	9	scholar	scholar	NOUN
bracis-33646	411	10	  	  	SPACE
bracis-33646	411	11	download	download	NOUN
bracis-33646	411	12	references	reference	NOUN
bracis-33646	411	13	author	author	NOUN
bracis-33646	411	14	information	information	NOUN
bracis-33646	411	15	authors	author	NOUN
bracis-33646	411	16	and	and	CCONJ
bracis-33646	411	17	affiliations	affiliation	NOUN
bracis-33646	411	18	federal	federal	PROPN
bracis-33646	411	19	university	university	PROPN
bracis-33646	411	20	of	of	ADP
bracis-33646	411	21	bahia	bahia	PROPN
bracis-33646	411	22	,	,	PUNCT
bracis-33646	411	23	salvador	salvador	PROPN
bracis-33646	411	24	,	,	PUNCT
bracis-33646	411	25	brazil	brazil	PROPN
bracis-33646	411	26	marlo	marlo	PROPN
bracis-33646	411	27	souza	souza	PROPN
bracis-33646	411	28	authors	authors	PROPN
bracis-33646	411	29	marlo	marlo	PROPN
bracis-33646	411	30	souzaview	souzaview	PROPN
bracis-33646	411	31	author	author	NOUN
bracis-33646	411	32	publications	publication	VERB
bracis-33646	411	33	search	search	NOUN
bracis-33646	411	34	author	author	NOUN
bracis-33646	411	35	on	on	ADP
bracis-33646	411	36	:	:	PUNCT
bracis-33646	411	37	pubmed	pubmed	PROPN
bracis-33646	411	38	 	 	SPACE
bracis-33646	411	39	google	google	PROPN
bracis-33646	411	40	scholar	scholar	NOUN
bracis-33646	411	41	corresponding	correspond	VERB
bracis-33646	411	42	author	author	NOUN
bracis-33646	411	43	correspondence	correspondence	NOUN
bracis-33646	411	44	to	to	ADP
bracis-33646	411	45	marlo	marlo	PROPN
bracis-33646	411	46	souza	souza	PROPN
bracis-33646	411	47	.	.	PUNCT
bracis-33646	412	1	editor	editor	NOUN
bracis-33646	412	2	information	information	NOUN
bracis-33646	412	3	editors	editor	NOUN
bracis-33646	412	4	and	and	CCONJ
bracis-33646	412	5	affiliations	affiliation	NOUN
bracis-33646	412	6	universidade	universidade	VERB
bracis-33646	412	7	federal	federal	PROPN
bracis-33646	412	8	fluminense	fluminense	PROPN
bracis-33646	412	9	,	,	PUNCT
bracis-33646	412	10	niterói	niterói	PROPN
bracis-33646	412	11	,	,	PUNCT
bracis-33646	412	12	brazil	brazil	PROPN
bracis-33646	412	13	aline	aline	PROPN
bracis-33646	412	14	paes	paes	PROPN
bracis-33646	412	15	instituto	instituto	PROPN
bracis-33646	412	16	tecnológico	tecnológico	PROPN
bracis-33646	412	17	de	de	PROPN
bracis-33646	412	18	aeronáutica	aeronáutica	PROPN
bracis-33646	412	19	,	,	PUNCT
bracis-33646	412	20	são	são	PROPN
bracis-33646	412	21	josé	josé	PROPN
bracis-33646	412	22	dos	dos	PROPN
bracis-33646	412	23	campos	campos	PROPN
bracis-33646	412	24	,	,	PUNCT
bracis-33646	412	25	brazil	brazil	PROPN
bracis-33646	412	26	filipe	filipe	PROPN
bracis-33646	412	27	a.	a.	PROPN
bracis-33646	412	28	n.	n.	PROPN
bracis-33646	412	29	verri	verri	PROPN
bracis-33646	412	30	rights	right	NOUN
bracis-33646	412	31	and	and	CCONJ
bracis-33646	412	32	permissions	permission	NOUN
bracis-33646	412	33	reprints	reprint	NOUN
bracis-33646	412	34	and	and	CCONJ
bracis-33646	412	35	permissions	permission	VERB
bracis-33646	412	36	copyright	copyright	NOUN
bracis-33646	412	37	information	information	NOUN
bracis-33646	412	38	©	©	ADP
bracis-33646	412	39	2025	2025	NUM
bracis-33646	412	40	the	the	DET
bracis-33646	412	41	author(s	author(s	NOUN
bracis-33646	412	42	)	)	PUNCT
bracis-33646	412	43	,	,	PUNCT
bracis-33646	412	44	under	under	ADP
bracis-33646	412	45	exclusive	exclusive	ADJ
bracis-33646	412	46	license	license	NOUN
bracis-33646	412	47	to	to	ADP
bracis-33646	412	48	springer	springer	NOUN
bracis-33646	412	49	nature	nature	PROPN
bracis-33646	412	50	switzerland	switzerland	PROPN
bracis-33646	412	51	ag	ag	PROPN
bracis-33646	412	52	about	about	ADP
bracis-33646	412	53	this	this	DET
bracis-33646	412	54	paper	paper	NOUN
bracis-33646	412	55	cite	cite	VERB
bracis-33646	412	56	this	this	DET
bracis-33646	412	57	paper	paper	NOUN
bracis-33646	412	58	souza	souza	NOUN
bracis-33646	412	59	,	,	PUNCT
bracis-33646	412	60	m.	m.	NOUN
bracis-33646	412	61	(	(	PUNCT
bracis-33646	412	62	2025	2025	NUM
bracis-33646	412	63	)	)	PUNCT
bracis-33646	412	64	.	.	PUNCT
bracis-33646	413	1	a	a	DET
bracis-33646	413	2	topology	topology	NOUN
bracis-33646	413	3	-	-	PUNCT
bracis-33646	413	4	inspired	inspire	VERB
bracis-33646	413	5	approach	approach	NOUN
bracis-33646	413	6	to	to	ADP
bracis-33646	413	7	 	 	SPACE
bracis-33646	413	8	agm	agm	PROPN
bracis-33646	413	9	belief	belief	NOUN
bracis-33646	413	10	change	change	NOUN
bracis-33646	413	11	.	.	PUNCT
bracis-33646	414	1	in	in	ADP
bracis-33646	414	2	:	:	PUNCT
bracis-33646	414	3	paes	paes	PROPN
bracis-33646	414	4	,	,	PUNCT
bracis-33646	414	5	a.	a.	PROPN
bracis-33646	414	6	,	,	PUNCT
bracis-33646	414	7	verri	verri	NOUN
bracis-33646	414	8	,	,	PUNCT
bracis-33646	414	9	f.a.n	f.a.n	ADJ
bracis-33646	414	10	.	.	PUNCT
bracis-33646	414	11	(	(	PUNCT
bracis-33646	414	12	eds	ed	NOUN
bracis-33646	414	13	)	)	PUNCT
bracis-33646	414	14	intelligent	intelligent	ADJ
bracis-33646	414	15	systems	system	NOUN
bracis-33646	414	16	.	.	PUNCT
bracis-33646	414	17	bracis	bracis	PROPN
bracis-33646	414	18	2024	2024	NUM
bracis-33646	414	19	.	.	PUNCT
bracis-33646	415	1	lecture	lecture	NOUN
bracis-33646	415	2	notes	note	NOUN
bracis-33646	415	3	in	in	ADP
bracis-33646	415	4	computer	computer	NOUN
bracis-33646	415	5	science	science	NOUN
bracis-33646	415	6	(	(	PUNCT
bracis-33646	415	7	)	)	PUNCT
bracis-33646	415	8	,	,	PUNCT
bracis-33646	415	9	vol	vol	NOUN
bracis-33646	415	10	15415	15415	NUM
bracis-33646	415	11	.	.	PUNCT
bracis-33646	416	1	springer	springer	NOUN
bracis-33646	416	2	,	,	PUNCT
bracis-33646	416	3	cham	cham	PROPN
bracis-33646	416	4	.	.	PUNCT
bracis-33646	417	1	https://doi.org/10.1007/978-3-031-79038-6_1	https://doi.org/10.1007/978-3-031-79038-6_1	PROPN
bracis-33646	417	2	download	download	PROPN
bracis-33646	417	3	citation	citation	NOUN
bracis-33646	417	4	.ris	.ris	PUNCT
bracis-33646	417	5	.enw	.enw	PROPN
bracis-33646	417	6	.bib	.bib	PUNCT
bracis-33646	418	1	doi	doi	PROPN
bracis-33646	418	2	:	:	PUNCT
bracis-33646	418	3	https://doi.org/10.1007/978-3-031-79038-6_1	https://doi.org/10.1007/978-3-031-79038-6_1	NUM
bracis-33646	418	4	published	publish	VERB
bracis-33646	418	5	:	:	PUNCT
bracis-33646	418	6	31	31	NUM
bracis-33646	418	7	january	january	PROPN
bracis-33646	418	8	2025	2025	NUM
bracis-33646	418	9	publisher	publisher	NOUN
bracis-33646	418	10	name	name	NOUN
bracis-33646	418	11	:	:	PUNCT
bracis-33646	418	12	springer	springer	NOUN
bracis-33646	418	13	,	,	PUNCT
bracis-33646	418	14	cham	cham	PROPN
bracis-33646	418	15	print	print	PROPN
bracis-33646	418	16	isbn	isbn	PROPN
bracis-33646	418	17	:	:	PUNCT
bracis-33646	418	18	978	978	NUM
bracis-33646	418	19	-	-	SYM
bracis-33646	418	20	3	3	NUM
bracis-33646	418	21	-	-	PUNCT
bracis-33646	418	22	031	031	NUM
bracis-33646	418	23	-	-	PUNCT
bracis-33646	418	24	79037	79037	NUM
bracis-33646	418	25	-	-	SYM
bracis-33646	418	26	9	9	NUM
bracis-33646	418	27	online	online	ADJ
bracis-33646	418	28	isbn	isbn	NOUN
bracis-33646	418	29	:	:	PUNCT
bracis-33646	418	30	978	978	NUM
bracis-33646	418	31	-	-	SYM
bracis-33646	418	32	3	3	NUM
bracis-33646	418	33	-	-	PUNCT
bracis-33646	418	34	031	031	NUM
bracis-33646	418	35	-	-	PUNCT
bracis-33646	418	36	79038	79038	NUM
bracis-33646	418	37	-	-	SYM
bracis-33646	418	38	6	6	NUM
bracis-33646	418	39	ebook	ebook	NOUN
bracis-33646	418	40	packages	package	NOUN
bracis-33646	418	41	:	:	PUNCT
bracis-33646	418	42	computer	computer	NOUN
bracis-33646	418	43	sciencecomputer	sciencecomputer	NOUN
bracis-33646	418	44	science	science	NOUN
bracis-33646	418	45	(	(	PUNCT
bracis-33646	418	46	r0	r0	NOUN
bracis-33646	418	47	)	)	PUNCT
bracis-33646	418	48	share	share	VERB
bracis-33646	418	49	this	this	DET
bracis-33646	418	50	paper	paper	NOUN
bracis-33646	418	51	anyone	anyone	PRON
bracis-33646	418	52	you	you	PRON
bracis-33646	418	53	share	share	VERB
bracis-33646	418	54	the	the	DET
bracis-33646	418	55	following	follow	VERB
bracis-33646	418	56	link	link	NOUN
bracis-33646	418	57	with	with	ADP
bracis-33646	418	58	will	will	AUX
bracis-33646	418	59	be	be	AUX
bracis-33646	418	60	able	able	ADJ
bracis-33646	418	61	to	to	PART
bracis-33646	418	62	read	read	VERB
bracis-33646	418	63	this	this	DET
bracis-33646	418	64	content	content	NOUN
bracis-33646	418	65	:	:	PUNCT
bracis-33646	418	66	get	get	VERB
bracis-33646	418	67	shareable	shareable	ADJ
bracis-33646	418	68	linksorry	linksorry	NOUN
bracis-33646	418	69	,	,	PUNCT
bracis-33646	418	70	a	a	DET
bracis-33646	418	71	shareable	shareable	ADJ
bracis-33646	418	72	link	link	NOUN
bracis-33646	418	73	is	be	AUX
bracis-33646	418	74	not	not	PART
bracis-33646	418	75	currently	currently	ADV
bracis-33646	418	76	available	available	ADJ
bracis-33646	418	77	for	for	ADP
bracis-33646	418	78	this	this	DET
bracis-33646	418	79	article	article	NOUN
bracis-33646	418	80	.	.	PUNCT
bracis-33646	419	1	copy	copy	VERB
bracis-33646	419	2	shareable	shareable	ADJ
bracis-33646	419	3	link	link	NOUN
bracis-33646	419	4	to	to	PART
bracis-33646	419	5	clipboard	clipboard	NOUN
bracis-33646	419	6	provided	provide	VERB
bracis-33646	419	7	by	by	ADP
bracis-33646	419	8	the	the	DET
bracis-33646	419	9	springer	springer	NOUN
bracis-33646	419	10	nature	nature	PROPN
bracis-33646	419	11	sharedit	sharedit	PROPN
bracis-33646	419	12	content	content	NOUN
bracis-33646	419	13	-	-	PUNCT
bracis-33646	419	14	sharing	share	VERB
bracis-33646	419	15	initiative	initiative	NOUN
bracis-33646	419	16	keywords	keyword	NOUN
bracis-33646	419	17	belief	belief	NOUN
bracis-33646	419	18	change	change	NOUN
bracis-33646	419	19	model	model	NOUN
bracis-33646	419	20	theory	theory	PROPN
bracis-33646	419	21	non	non	ADJ
bracis-33646	419	22	-	-	ADJ
bracis-33646	419	23	classical	classical	ADJ
bracis-33646	419	24	logics	logic	NOUN
bracis-33646	419	25	publish	publish	VERB
bracis-33646	419	26	with	with	ADP
bracis-33646	419	27	us	us	PROPN
bracis-33646	419	28	policies	policy	NOUN
bracis-33646	419	29	and	and	CCONJ
bracis-33646	419	30	ethics	ethic	NOUN
bracis-33646	419	31	search	search	NOUN
bracis-33646	419	32	search	search	NOUN
bracis-33646	419	33	by	by	ADP
bracis-33646	419	34	keyword	keyword	NOUN
bracis-33646	419	35	or	or	CCONJ
bracis-33646	419	36	author	author	NOUN
bracis-33646	419	37	search	search	NOUN
bracis-33646	419	38	navigation	navigation	NOUN
bracis-33646	419	39	find	find	VERB
bracis-33646	419	40	a	a	DET
bracis-33646	419	41	journal	journal	NOUN
bracis-33646	419	42	publish	publish	VERB
bracis-33646	419	43	with	with	ADP
bracis-33646	419	44	us	we	PRON
bracis-33646	419	45	track	track	VERB
bracis-33646	419	46	your	your	PRON
bracis-33646	419	47	research	research	NOUN
bracis-33646	419	48	discover	discover	VERB
bracis-33646	419	49	content	content	NOUN
bracis-33646	419	50	journals	journal	NOUN
bracis-33646	419	51	a	a	DET
bracis-33646	419	52	-	-	PUNCT
bracis-33646	419	53	z	z	NOUN
bracis-33646	419	54	books	book	NOUN
bracis-33646	419	55	a	a	DET
bracis-33646	419	56	-	-	PUNCT
bracis-33646	419	57	z	z	NOUN
bracis-33646	419	58	publish	publish	NOUN
bracis-33646	419	59	with	with	ADP
bracis-33646	419	60	us	us	PROPN
bracis-33646	419	61	journal	journal	PROPN
bracis-33646	419	62	finder	finder	PROPN
bracis-33646	419	63	publish	publish	VERB
bracis-33646	419	64	your	your	PRON
bracis-33646	419	65	research	research	NOUN
bracis-33646	419	66	language	language	NOUN
bracis-33646	419	67	editing	edit	VERB
bracis-33646	419	68	open	open	ADJ
bracis-33646	419	69	access	access	NOUN
bracis-33646	419	70	publishing	publishing	NOUN
bracis-33646	419	71	products	product	NOUN
bracis-33646	419	72	and	and	CCONJ
bracis-33646	419	73	services	service	NOUN
bracis-33646	419	74	our	our	PRON
bracis-33646	419	75	products	product	NOUN
bracis-33646	419	76	librarians	librarian	VERB
bracis-33646	419	77	societies	society	NOUN
bracis-33646	419	78	partners	partner	NOUN
bracis-33646	419	79	and	and	CCONJ
bracis-33646	419	80	advertisers	advertiser	NOUN
bracis-33646	419	81	our	our	PRON
bracis-33646	419	82	brands	brand	NOUN
bracis-33646	419	83	springer	springer	NOUN
bracis-33646	419	84	nature	nature	PROPN
bracis-33646	419	85	portfolio	portfolio	PROPN
bracis-33646	419	86	bmc	bmc	PROPN
bracis-33646	419	87	palgrave	palgrave	PROPN
bracis-33646	419	88	macmillan	macmillan	PROPN
bracis-33646	419	89	apress	apress	PROPN
bracis-33646	419	90	discover	discover	VERB
bracis-33646	419	91	your	your	PRON
bracis-33646	419	92	privacy	privacy	NOUN
bracis-33646	419	93	choices	choice	NOUN
bracis-33646	419	94	/	/	SYM
bracis-33646	419	95	manage	manage	NOUN
bracis-33646	419	96	cookies	cookie	NOUN
bracis-33646	419	97	your	your	PRON
bracis-33646	419	98	us	us	PROPN
bracis-33646	420	1	state	state	NOUN
bracis-33646	420	2	privacy	privacy	NOUN
bracis-33646	420	3	rights	right	NOUN
bracis-33646	420	4	accessibility	accessibility	NOUN
bracis-33646	420	5	statement	statement	NOUN
bracis-33646	420	6	terms	term	NOUN
bracis-33646	420	7	and	and	CCONJ
bracis-33646	420	8	conditions	condition	NOUN
bracis-33646	420	9	privacy	privacy	NOUN
bracis-33646	420	10	policy	policy	NOUN
bracis-33646	420	11	help	help	NOUN
bracis-33646	420	12	and	and	CCONJ
bracis-33646	420	13	support	support	VERB
bracis-33646	420	14	legal	legal	ADJ
bracis-33646	420	15	notice	notice	NOUN
bracis-33646	420	16	cancel	cancel	VERB
bracis-33646	420	17	contracts	contract	NOUN
bracis-33646	420	18	here	here	ADV
bracis-33646	420	19	129.74.145.123	129.74.145.123	NUM
bracis-33646	420	20	hesburgh	hesburgh	PROPN
bracis-33646	420	21	library	library	PROPN
bracis-33646	420	22	er	er	INTJ
bracis-33646	420	23	unit	unit	NOUN
bracis-33646	420	24	(	(	PUNCT
bracis-33646	420	25	3005732405	3005732405	NUM
bracis-33646	420	26	)	)	PUNCT
bracis-33646	420	27	northeast	northeast	ADJ
bracis-33646	420	28	research	research	NOUN
bracis-33646	420	29	libraries	library	NOUN
bracis-33646	420	30	(	(	PUNCT
bracis-33646	420	31	nerl	nerl	PROPN
bracis-33646	420	32	)	)	PUNCT
bracis-33646	420	33	(	(	PUNCT
bracis-33646	420	34	8200828607	8200828607	NUM
bracis-33646	420	35	)	)	PUNCT
bracis-33646	420	36	nerl	nerl	VERB
bracis-33646	420	37	ta	ta	X
bracis-33646	420	38	account	account	NOUN
bracis-33646	420	39	(	(	PUNCT
bracis-33646	420	40	3006206169	3006206169	NUM
bracis-33646	420	41	)	)	PUNCT
bracis-33646	420	42	university	university	NOUN
bracis-33646	420	43	of	of	ADP
bracis-33646	420	44	notre	notre	PROPN
bracis-33646	420	45	dame	dame	PROPN
bracis-33646	420	46	hesburgh	hesburgh	PROPN
bracis-33646	420	47	library	library	NOUN
bracis-33646	420	48	(	(	PUNCT
bracis-33646	420	49	3000184373	3000184373	NUM
bracis-33646	420	50	)	)	PUNCT
bracis-33646	421	1	©	©	ADP
bracis-33646	421	2	2025	2025	NUM
bracis-33646	421	3	springer	springer	NOUN
bracis-33646	421	4	nature	nature	NOUN