id	sid	tid	token	lemma	pos
asir-6084	1	1	applied	apply	VERB
asir-6084	1	2	science	science	NOUN
asir-6084	1	3	and	and	CCONJ
asir-6084	1	4	innovative	innovative	ADJ
asir-6084	1	5	research	research	NOUN
asir-6084	1	6	issn	issn	VERB
asir-6084	1	7	2474	2474	NUM
asir-6084	1	8	-	-	SYM
asir-6084	1	9	4972	4972	NUM
asir-6084	1	10	(	(	PUNCT
asir-6084	1	11	print	print	NOUN
asir-6084	1	12	)	)	PUNCT
asir-6084	1	13	issn	issn	VERB
asir-6084	1	14	2474	2474	NUM
asir-6084	1	15	-	-	SYM
asir-6084	1	16	4980	4980	NUM
asir-6084	1	17	(	(	PUNCT
asir-6084	1	18	online	online	ADJ
asir-6084	1	19	)	)	PUNCT
asir-6084	1	20	vol	vol	NOUN
asir-6084	1	21	.	.	PROPN
asir-6084	2	1	7	7	NUM
asir-6084	2	2	,	,	PUNCT
asir-6084	2	3	no	no	INTJ
asir-6084	2	4	.	.	NOUN
asir-6084	2	5	1	1	NUM
asir-6084	2	6	,	,	PUNCT
asir-6084	2	7	2023	2023	NUM
asir-6084	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	2	9	46	46	NUM
asir-6084	2	10	original	original	ADJ
asir-6084	2	11	paper	paper	NOUN
asir-6084	2	12	how	how	SCONJ
asir-6084	2	13	to	to	PART
asir-6084	2	14	deduce	deduce	VERB
asir-6084	2	15	the	the	DET
asir-6084	2	16	other	other	ADJ
asir-6084	2	17	91	91	NUM
asir-6084	2	18	valid	valid	ADJ
asir-6084	2	19	aristotelian	aristotelian	ADJ
asir-6084	2	20	modal	modal	NOUN
asir-6084	2	21	syllogisms	syllogism	NOUN
asir-6084	2	22	from	from	ADP
asir-6084	2	23	the	the	DET
asir-6084	2	24	syllogism	syllogism	NOUN
asir-6084	3	1	iai-3	iai-3	PROPN
asir-6084	3	2	cheng	cheng	PROPN
asir-6084	3	3	zhang1	zhang1	PROPN
asir-6084	3	4	1	1	NUM
asir-6084	3	5	anhui	anhui	PROPN
asir-6084	3	6	university	university	PROPN
asir-6084	3	7	,	,	PUNCT
asir-6084	3	8	guangzhou	guangzhou	PROPN
asir-6084	3	9	,	,	PUNCT
asir-6084	3	10	china	china	PROPN
asir-6084	3	11	received	receive	VERB
asir-6084	3	12	:	:	PUNCT
asir-6084	3	13	january	january	PROPN
asir-6084	3	14	6	6	NUM
asir-6084	3	15	,	,	PUNCT
asir-6084	3	16	2023	2023	NUM
asir-6084	3	17	accepted	accept	VERB
asir-6084	3	18	:	:	PUNCT
asir-6084	3	19	january	january	PROPN
asir-6084	3	20	24	24	NUM
asir-6084	3	21	,	,	PUNCT
asir-6084	3	22	2023	2023	NUM
asir-6084	3	23	online	online	ADV
asir-6084	3	24	published	publish	VERB
asir-6084	3	25	:	:	PUNCT
asir-6084	3	26	january	january	PROPN
asir-6084	3	27	27	27	NUM
asir-6084	3	28	,	,	PUNCT
asir-6084	3	29	2023	2023	NUM
asir-6084	3	30	doi:10.22158	doi:10.22158	NOUN
asir-6084	3	31	/	/	SYM
asir-6084	3	32	asir.v7n1p46	asir.v7n1p46	NOUN
asir-6084	3	33	url	url	PROPN
asir-6084	3	34	:	:	PUNCT
asir-6084	3	35	http://doi.org/10.22158/asir.v7n1p46	http://doi.org/10.22158/asir.v7n1p46	PROPN
asir-6084	4	1	abstract	abstract	ADV
asir-6084	4	2	this	this	DET
asir-6084	4	3	paper	paper	NOUN
asir-6084	4	4	firstly	firstly	ADV
asir-6084	4	5	formalizes	formalize	VERB
asir-6084	4	6	aristotelian	aristotelian	ADJ
asir-6084	4	7	modal	modal	NOUN
asir-6084	4	8	syllogisms	syllogism	NOUN
asir-6084	4	9	by	by	ADP
asir-6084	4	10	taking	take	VERB
asir-6084	4	11	advantage	advantage	NOUN
asir-6084	4	12	of	of	ADP
asir-6084	4	13	the	the	DET
asir-6084	4	14	trisection	trisection	NOUN
asir-6084	4	15	structure	structure	NOUN
asir-6084	4	16	of	of	ADP
asir-6084	4	17	(	(	PUNCT
asir-6084	4	18	modal	modal	NOUN
asir-6084	4	19	)	)	PUNCT
asir-6084	4	20	categorical	categorical	ADJ
asir-6084	4	21	propositions	proposition	NOUN
asir-6084	4	22	.	.	PUNCT
asir-6084	5	1	and	and	CCONJ
asir-6084	5	2	then	then	ADV
asir-6084	5	3	making	make	VERB
asir-6084	5	4	full	full	ADJ
asir-6084	5	5	use	use	NOUN
asir-6084	5	6	of	of	ADP
asir-6084	5	7	the	the	DET
asir-6084	5	8	truth	truth	NOUN
asir-6084	5	9	value	value	NOUN
asir-6084	5	10	definition	definition	NOUN
asir-6084	5	11	of	of	ADP
asir-6084	5	12	(	(	PUNCT
asir-6084	5	13	modal	modal	NOUN
asir-6084	5	14	)	)	PUNCT
asir-6084	5	15	categorical	categorical	ADJ
asir-6084	5	16	propositions	proposition	NOUN
asir-6084	5	17	,	,	PUNCT
asir-6084	5	18	the	the	DET
asir-6084	5	19	transformable	transformable	ADJ
asir-6084	5	20	relations	relation	NOUN
asir-6084	5	21	between	between	ADP
asir-6084	5	22	an	an	DET
asir-6084	5	23	aristotelian	aristotelian	ADJ
asir-6084	5	24	quantifier	quantifier	NOUN
asir-6084	5	25	and	and	CCONJ
asir-6084	5	26	its	its	PRON
asir-6084	5	27	three	three	NUM
asir-6084	5	28	negative	negative	ADJ
asir-6084	5	29	quantifiers	quantifier	NOUN
asir-6084	5	30	,	,	PUNCT
asir-6084	5	31	the	the	DET
asir-6084	5	32	reasoning	reasoning	NOUN
asir-6084	5	33	rules	rule	NOUN
asir-6084	5	34	of	of	ADP
asir-6084	5	35	classical	classical	ADJ
asir-6084	5	36	propositional	propositional	ADJ
asir-6084	5	37	logic	logic	NOUN
asir-6084	5	38	,	,	PUNCT
asir-6084	5	39	and	and	CCONJ
asir-6084	5	40	the	the	DET
asir-6084	5	41	symmetry	symmetry	NOUN
asir-6084	5	42	of	of	ADP
asir-6084	5	43	the	the	DET
asir-6084	5	44	two	two	NUM
asir-6084	5	45	aristotelian	aristotelian	ADJ
asir-6084	5	46	quantifiers	quantifier	NOUN
asir-6084	5	47	(	(	PUNCT
asir-6084	5	48	i.e.	i.e.	X
asir-6084	5	49	some	some	PRON
asir-6084	5	50	and	and	CCONJ
asir-6084	5	51	no	no	NOUN
asir-6084	5	52	)	)	PUNCT
asir-6084	5	53	,	,	PUNCT
asir-6084	5	54	this	this	DET
asir-6084	5	55	paper	paper	NOUN
asir-6084	5	56	shows	show	VERB
asir-6084	5	57	that	that	SCONJ
asir-6084	5	58	at	at	ADV
asir-6084	5	59	least	least	ADV
asir-6084	5	60	91	91	NUM
asir-6084	5	61	valid	valid	ADJ
asir-6084	5	62	aristotelian	aristotelian	ADJ
asir-6084	5	63	modal	modal	NOUN
asir-6084	5	64	syllogisms	syllogism	NOUN
asir-6084	5	65	can	can	AUX
asir-6084	5	66	be	be	AUX
asir-6084	5	67	deduced	deduce	VERB
asir-6084	5	68	from	from	ADP
asir-6084	5	69	iai-3	iai-3	NOUN
asir-6084	5	70	on	on	ADP
asir-6084	5	71	the	the	DET
asir-6084	5	72	basis	basis	NOUN
asir-6084	5	73	of	of	ADP
asir-6084	5	74	possible	possible	ADJ
asir-6084	5	75	world	world	NOUN
asir-6084	5	76	semantics	semantic	NOUN
asir-6084	5	77	and	and	CCONJ
asir-6084	5	78	set	set	VERB
asir-6084	5	79	theory	theory	NOUN
asir-6084	5	80	.	.	PUNCT
asir-6084	6	1	the	the	DET
asir-6084	6	2	reason	reason	NOUN
asir-6084	6	3	why	why	SCONJ
asir-6084	6	4	these	these	DET
asir-6084	6	5	valid	valid	ADJ
asir-6084	6	6	aristotelian	aristotelian	ADJ
asir-6084	6	7	modal	modal	NOUN
asir-6084	6	8	syllogisms	syllogism	NOUN
asir-6084	6	9	can	can	AUX
asir-6084	6	10	be	be	AUX
asir-6084	6	11	reduced	reduce	VERB
asir-6084	6	12	is	be	AUX
asir-6084	6	13	that	that	SCONJ
asir-6084	6	14	any	any	DET
asir-6084	6	15	aristotelian	aristotelian	ADJ
asir-6084	6	16	quantifier	quantifier	NOUN
asir-6084	6	17	can	can	AUX
asir-6084	6	18	be	be	AUX
asir-6084	6	19	defined	define	VERB
asir-6084	6	20	by	by	ADP
asir-6084	6	21	the	the	DET
asir-6084	6	22	other	other	ADJ
asir-6084	6	23	three	three	NUM
asir-6084	6	24	aristotelian	aristotelian	ADJ
asir-6084	6	25	quantifiers	quantifier	NOUN
asir-6084	6	26	,	,	PUNCT
asir-6084	6	27	and	and	CCONJ
asir-6084	6	28	the	the	DET
asir-6084	6	29	necessary	necessary	ADJ
asir-6084	6	30	modality	modality	NOUN
asir-6084	6	31	(	(	PUNCT
asir-6084	6	32			NUM
asir-6084	6	33	)	)	PUNCT
asir-6084	6	34	and	and	CCONJ
asir-6084	6	35	possible	possible	ADJ
asir-6084	6	36	modality	modality	NOUN
asir-6084	6	37	(	(	PUNCT
asir-6084	6	38			NOUN
asir-6084	6	39	)	)	PUNCT
asir-6084	6	40	can	can	AUX
asir-6084	6	41	also	also	ADV
asir-6084	6	42	be	be	AUX
asir-6084	6	43	defined	define	VERB
asir-6084	6	44	mutually	mutually	ADV
asir-6084	6	45	.	.	PUNCT
asir-6084	7	1	this	this	DET
asir-6084	7	2	research	research	NOUN
asir-6084	7	3	method	method	NOUN
asir-6084	7	4	is	be	AUX
asir-6084	7	5	universal	universal	ADJ
asir-6084	7	6	.	.	PUNCT
asir-6084	8	1	this	this	DET
asir-6084	8	2	innovative	innovative	ADJ
asir-6084	8	3	study	study	NOUN
asir-6084	8	4	not	not	PART
asir-6084	8	5	only	only	ADV
asir-6084	8	6	provides	provide	VERB
asir-6084	8	7	a	a	DET
asir-6084	8	8	unified	unified	ADJ
asir-6084	8	9	mathematical	mathematical	ADJ
asir-6084	8	10	research	research	NOUN
asir-6084	8	11	paradigm	paradigm	NOUN
asir-6084	8	12	for	for	ADP
asir-6084	8	13	the	the	DET
asir-6084	8	14	study	study	NOUN
asir-6084	8	15	of	of	ADP
asir-6084	8	16	generalized	generalized	ADJ
asir-6084	8	17	modal	modal	ADJ
asir-6084	8	18	syllogistic	syllogistic	NOUN
asir-6084	8	19	and	and	CCONJ
asir-6084	8	20	other	other	ADJ
asir-6084	8	21	kinds	kind	NOUN
asir-6084	8	22	of	of	ADP
asir-6084	8	23	syllogistic	syllogistic	NOUN
asir-6084	8	24	,	,	PUNCT
asir-6084	8	25	but	but	CCONJ
asir-6084	8	26	also	also	ADV
asir-6084	8	27	makes	make	VERB
asir-6084	8	28	contributions	contribution	NOUN
asir-6084	8	29	to	to	ADP
asir-6084	8	30	knowledge	knowledge	NOUN
asir-6084	8	31	representation	representation	NOUN
asir-6084	8	32	and	and	CCONJ
asir-6084	8	33	knowledge	knowledge	NOUN
asir-6084	8	34	reasoning	reasoning	NOUN
asir-6084	8	35	in	in	ADP
asir-6084	8	36	computer	computer	NOUN
asir-6084	8	37	science	science	NOUN
asir-6084	8	38	.	.	PUNCT
asir-6084	9	1	keywords	keyword	NOUN
asir-6084	9	2	aristotelian	aristotelian	VERB
asir-6084	9	3	modal	modal	NOUN
asir-6084	9	4	syllogisms	syllogism	NOUN
asir-6084	9	5	,	,	PUNCT
asir-6084	9	6	trisection	trisection	NOUN
asir-6084	9	7	structure	structure	NOUN
asir-6084	9	8	,	,	PUNCT
asir-6084	9	9	reduction	reduction	NOUN
asir-6084	9	10	,	,	PUNCT
asir-6084	9	11	possible	possible	ADJ
asir-6084	9	12	world	world	NOUN
asir-6084	9	13	,	,	PUNCT
asir-6084	9	14	aristotelian	aristotelian	PROPN
asir-6084	9	15	quantifiers	quantifier	VERB
asir-6084	9	16	1	1	NUM
asir-6084	9	17	.	.	PUNCT
asir-6084	10	1	introduction	introduction	NOUN
asir-6084	10	2	syllogistic	syllogistic	ADJ
asir-6084	10	3	reasoning	reasoning	NOUN
asir-6084	10	4	plays	play	VERB
asir-6084	10	5	an	an	DET
asir-6084	10	6	important	important	ADJ
asir-6084	10	7	role	role	NOUN
asir-6084	10	8	in	in	ADP
asir-6084	10	9	the	the	DET
asir-6084	10	10	production	production	NOUN
asir-6084	10	11	and	and	CCONJ
asir-6084	10	12	life	life	NOUN
asir-6084	10	13	of	of	ADP
asir-6084	10	14	human	human	ADJ
asir-6084	10	15	society	society	NOUN
asir-6084	10	16	,	,	PUNCT
asir-6084	10	17	so	so	SCONJ
asir-6084	10	18	it	it	PRON
asir-6084	10	19	has	have	AUX
asir-6084	10	20	become	become	VERB
asir-6084	10	21	one	one	NUM
asir-6084	10	22	of	of	ADP
asir-6084	10	23	the	the	DET
asir-6084	10	24	focuses	focus	NOUN
asir-6084	10	25	in	in	ADP
asir-6084	10	26	logic	logic	NOUN
asir-6084	10	27	.	.	PUNCT
asir-6084	11	1	there	there	PRON
asir-6084	11	2	are	be	VERB
asir-6084	11	3	many	many	ADJ
asir-6084	11	4	kinds	kind	NOUN
asir-6084	11	5	of	of	ADP
asir-6084	11	6	syllogisms	syllogism	NOUN
asir-6084	11	7	,	,	PUNCT
asir-6084	11	8	such	such	ADJ
asir-6084	11	9	as	as	ADP
asir-6084	11	10	aristotelian	aristotelian	ADJ
asir-6084	11	11	syllogisms	syllogism	NOUN
asir-6084	11	12	(	(	PUNCT
asir-6084	11	13	patzig	patzig	NOUN
asir-6084	11	14	,	,	PUNCT
asir-6084	11	15	1969	1969	NUM
asir-6084	11	16	;	;	PUNCT
asir-6084	11	17	moss	moss	NOUN
asir-6084	11	18	,	,	PUNCT
asir-6084	11	19	2008	2008	NUM
asir-6084	11	20	)	)	PUNCT
asir-6084	11	21	,	,	PUNCT
asir-6084	11	22	generalized	generalized	ADJ
asir-6084	11	23	syllogisms	syllogism	NOUN
asir-6084	11	24	(	(	PUNCT
asir-6084	11	25	murinová	murinová	NOUN
asir-6084	11	26	&	&	CCONJ
asir-6084	11	27	novák	novák	NOUN
asir-6084	11	28	,	,	PUNCT
asir-6084	11	29	2012	2012	NUM
asir-6084	11	30	;	;	PUNCT
asir-6084	11	31	endrullis	endrullis	PROPN
asir-6084	11	32	et	et	PROPN
asir-6084	11	33	al	al	PROPN
asir-6084	11	34	.	.	PROPN
asir-6084	11	35	,	,	PUNCT
asir-6084	11	36	2015	2015	NUM
asir-6084	11	37	)	)	PUNCT
asir-6084	11	38	,	,	PUNCT
asir-6084	11	39	relational	relational	ADJ
asir-6084	11	40	syllogisms	syllogism	NOUN
asir-6084	11	41	(	(	PUNCT
asir-6084	11	42	ivanov	ivanov	NOUN
asir-6084	11	43	,	,	PUNCT
asir-6084	11	44	2012	2012	NUM
asir-6084	11	45	;	;	PUNCT
asir-6084	11	46	pratt	pratt	PROPN
asir-6084	11	47	-	-	PUNCT
asir-6084	11	48	hartmann	hartmann	PROPN
asir-6084	11	49	,	,	PUNCT
asir-6084	11	50	2014	2014	NUM
asir-6084	11	51	)	)	PUNCT
asir-6084	11	52	,	,	PUNCT
asir-6084	11	53	syllogisms	syllogism	VERB
asir-6084	11	54	with	with	ADP
asir-6084	11	55	verbs	verbs	PROPN
asir-6084	11	56	(	(	PUNCT
asir-6084	11	57	moss	moss	NOUN
asir-6084	11	58	,	,	PUNCT
asir-6084	11	59	2010	2010	NUM
asir-6084	11	60	)	)	PUNCT
asir-6084	11	61	,	,	PUNCT
asir-6084	11	62	aristotelian	aristotelian	PROPN
asir-6084	11	63	modal	modal	NOUN
asir-6084	11	64	syllogisms	syllogism	NOUN
asir-6084	11	65	(	(	PUNCT
asir-6084	11	66	johnson	johnson	PROPN
asir-6084	11	67	,	,	PUNCT
asir-6084	11	68	2004	2004	NUM
asir-6084	11	69	)	)	PUNCT
asir-6084	11	70	,	,	PUNCT
asir-6084	11	71	and	and	CCONJ
asir-6084	11	72	generalized	generalized	ADJ
asir-6084	11	73	modal	modal	ADJ
asir-6084	11	74	syllogisms	syllogism	NOUN
asir-6084	11	75	,	,	PUNCT
asir-6084	11	76	and	and	CCONJ
asir-6084	11	77	so	so	ADV
asir-6084	11	78	on	on	ADP
asir-6084	11	79	(	(	PUNCT
asir-6084	11	80	zhang	zhang	PROPN
asir-6084	11	81	,	,	PUNCT
asir-6084	11	82	2020a	2020a	NUM
asir-6084	11	83	)	)	PUNCT
asir-6084	11	84	.	.	PUNCT
asir-6084	12	1	up	up	ADP
asir-6084	12	2	to	to	ADP
asir-6084	12	3	now	now	ADV
asir-6084	12	4	,	,	PUNCT
asir-6084	12	5	the	the	DET
asir-6084	12	6	most	most	ADV
asir-6084	12	7	studied	study	VERB
asir-6084	12	8	is	be	AUX
asir-6084	12	9	aristotelian	aristotelian	ADJ
asir-6084	12	10	syllogisms	syllogism	NOUN
asir-6084	12	11	.	.	PUNCT
asir-6084	13	1	so	so	ADV
asir-6084	13	2	far	far	ADV
asir-6084	13	3	,	,	PUNCT
asir-6084	13	4	the	the	DET
asir-6084	13	5	author	author	NOUN
asir-6084	13	6	has	have	AUX
asir-6084	13	7	not	not	PART
asir-6084	13	8	searched	search	VERB
asir-6084	13	9	the	the	DET
asir-6084	13	10	literature	literature	NOUN
asir-6084	13	11	of	of	ADP
asir-6084	13	12	generalized	generalized	ADJ
asir-6084	13	13	modal	modal	ADJ
asir-6084	13	14	syllogisms	syllogism	NOUN
asir-6084	13	15	.	.	PUNCT
asir-6084	14	1	unless	unless	SCONJ
asir-6084	14	2	otherwise	otherwise	ADV
asir-6084	14	3	specified	specify	VERB
asir-6084	14	4	,	,	PUNCT
asir-6084	14	5	the	the	DET
asir-6084	14	6	following	follow	VERB
asir-6084	14	7	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	14	8	applied	apply	VERB
asir-6084	14	9	science	science	NOUN
asir-6084	14	10	and	and	CCONJ
asir-6084	14	11	innovative	innovative	ADJ
asir-6084	14	12	research	research	NOUN
asir-6084	14	13	vol	vol	NOUN
asir-6084	14	14	.	.	PUNCT
asir-6084	15	1	7	7	NUM
asir-6084	15	2	,	,	PUNCT
asir-6084	15	3	no	no	INTJ
asir-6084	15	4	.	.	NOUN
asir-6084	15	5	1	1	NUM
asir-6084	15	6	,	,	PUNCT
asir-6084	15	7	2023	2023	NUM
asir-6084	15	8	47	47	NUM
asir-6084	15	9	published	publish	VERB
asir-6084	15	10	by	by	ADP
asir-6084	15	11	scholink	scholink	PROPN
asir-6084	15	12	inc	inc	PROPN
asir-6084	15	13	.	.	PROPN
asir-6084	15	14	modal	modal	ADJ
asir-6084	15	15	syllogisms	syllogism	NOUN
asir-6084	15	16	in	in	ADP
asir-6084	15	17	this	this	DET
asir-6084	15	18	paper	paper	NOUN
asir-6084	15	19	refer	refer	NOUN
asir-6084	15	20	to	to	ADP
asir-6084	15	21	aristotelian	aristotelian	ADJ
asir-6084	15	22	modal	modal	ADJ
asir-6084	15	23	syllogisms	syllogism	NOUN
asir-6084	15	24	.	.	PUNCT
asir-6084	16	1	aristotle	aristotle	PROPN
asir-6084	16	2	was	be	AUX
asir-6084	16	3	the	the	DET
asir-6084	16	4	first	first	ADJ
asir-6084	16	5	logician	logician	NOUN
asir-6084	16	6	to	to	PART
asir-6084	16	7	systematically	systematically	ADV
asir-6084	16	8	study	study	VERB
asir-6084	16	9	modal	modal	NOUN
asir-6084	16	10	syllogisms	syllogism	NOUN
asir-6084	16	11	.	.	PUNCT
asir-6084	17	1	in	in	ADP
asir-6084	17	2	organon	organon	PROPN
asir-6084	17	3	,	,	PUNCT
asir-6084	17	4	he	he	PRON
asir-6084	17	5	discussed	discuss	VERB
asir-6084	17	6	modal	modal	NOUN
asir-6084	17	7	syllogisms	syllogism	NOUN
asir-6084	17	8	more	more	ADJ
asir-6084	17	9	than	than	ADP
asir-6084	17	10	non	non	ADJ
asir-6084	17	11	-	-	ADJ
asir-6084	17	12	modal	modal	ADJ
asir-6084	17	13	syllogisms	syllogism	NOUN
asir-6084	17	14	.	.	PUNCT
asir-6084	18	1	after	after	ADP
asir-6084	18	2	that	that	PRON
asir-6084	18	3	,	,	PUNCT
asir-6084	18	4	łukasiewicz	łukasiewicz	NOUN
asir-6084	18	5	(	(	PUNCT
asir-6084	18	6	1957	1957	NUM
asir-6084	18	7	)	)	PUNCT
asir-6084	18	8	,	,	PUNCT
asir-6084	18	9	mccall	mccall	PROPN
asir-6084	18	10	(	(	PUNCT
asir-6084	18	11	1963	1963	NUM
asir-6084	18	12	)	)	PUNCT
asir-6084	18	13	,	,	PUNCT
asir-6084	18	14	geach	geach	NOUN
asir-6084	18	15	(	(	PUNCT
asir-6084	18	16	1964	1964	NUM
asir-6084	18	17	)	)	PUNCT
asir-6084	18	18	,	,	PUNCT
asir-6084	18	19	johnson	johnson	PROPN
asir-6084	18	20	(	(	PUNCT
asir-6084	18	21	1989	1989	NUM
asir-6084	18	22	)	)	PUNCT
asir-6084	18	23	and	and	CCONJ
asir-6084	18	24	others	other	NOUN
asir-6084	18	25	have	have	AUX
asir-6084	18	26	discussed	discuss	VERB
asir-6084	18	27	modal	modal	ADJ
asir-6084	18	28	syllogisms	syllogism	NOUN
asir-6084	18	29	and	and	CCONJ
asir-6084	18	30	made	make	VERB
asir-6084	18	31	some	some	DET
asir-6084	18	32	progress	progress	NOUN
asir-6084	18	33	,	,	PUNCT
asir-6084	18	34	but	but	CCONJ
asir-6084	18	35	a	a	DET
asir-6084	18	36	formal	formal	ADJ
asir-6084	18	37	axiom	axiom	NOUN
asir-6084	18	38	system	system	NOUN
asir-6084	18	39	of	of	ADP
asir-6084	18	40	aristotelian	aristotelian	PROPN
asir-6084	18	41	modal	modal	ADJ
asir-6084	18	42	syllogistic	syllogistic	NOUN
asir-6084	18	43	has	have	AUX
asir-6084	18	44	not	not	PART
asir-6084	18	45	yet	yet	ADV
asir-6084	18	46	been	be	AUX
asir-6084	18	47	established	establish	VERB
asir-6084	18	48	.	.	PUNCT
asir-6084	19	1	thomason	thomason	PROPN
asir-6084	19	2	(	(	PUNCT
asir-6084	19	3	1993	1993	NUM
asir-6084	19	4	,	,	PUNCT
asir-6084	19	5	1997	1997	NUM
asir-6084	19	6	)	)	PUNCT
asir-6084	19	7	,	,	PUNCT
asir-6084	19	8	thom(1996	thom(1996	NOUN
asir-6084	19	9	)	)	PUNCT
asir-6084	19	10	,	,	PUNCT
asir-6084	19	11	johnson	johnson	PROPN
asir-6084	19	12	(	(	PUNCT
asir-6084	19	13	2004	2004	NUM
asir-6084	19	14	)	)	PUNCT
asir-6084	19	15	,	,	PUNCT
asir-6084	19	16	malink	malink	NOUN
asir-6084	19	17	(	(	PUNCT
asir-6084	19	18	2006	2006	NUM
asir-6084	19	19	,	,	PUNCT
asir-6084	19	20	2013	2013	NUM
asir-6084	19	21	)	)	PUNCT
asir-6084	19	22	gave	give	VERB
asir-6084	19	23	adequate	adequate	ADJ
asir-6084	19	24	semantic	semantic	ADJ
asir-6084	19	25	analysis	analysis	NOUN
asir-6084	19	26	or	or	CCONJ
asir-6084	19	27	reconstruction	reconstruction	NOUN
asir-6084	19	28	of	of	ADP
asir-6084	19	29	the	the	DET
asir-6084	19	30	syllogistic	syllogistic	NOUN
asir-6084	19	31	,	,	PUNCT
asir-6084	19	32	but	but	CCONJ
asir-6084	19	33	the	the	DET
asir-6084	19	34	prevailing	prevail	VERB
asir-6084	19	35	view	view	NOUN
asir-6084	19	36	is	be	AUX
asir-6084	19	37	that	that	SCONJ
asir-6084	19	38	there	there	PRON
asir-6084	19	39	are	be	VERB
asir-6084	19	40	many	many	ADJ
asir-6084	19	41	faults	fault	NOUN
asir-6084	19	42	and	and	CCONJ
asir-6084	19	43	inconsistencies	inconsistency	NOUN
asir-6084	19	44	(	(	PUNCT
asir-6084	19	45	malink	malink	NOUN
asir-6084	19	46	,	,	PUNCT
asir-6084	19	47	2006	2006	NUM
asir-6084	19	48	,	,	PUNCT
asir-6084	19	49	p.	p.	NOUN
asir-6084	19	50	95	95	NUM
asir-6084	19	51	)	)	PUNCT
asir-6084	19	52	.	.	PUNCT
asir-6084	20	1	when	when	SCONJ
asir-6084	20	2	studying	study	VERB
asir-6084	20	3	this	this	DET
asir-6084	20	4	syllogistic	syllogistic	NOUN
asir-6084	20	5	,	,	PUNCT
asir-6084	20	6	the	the	DET
asir-6084	20	7	difficulty	difficulty	NOUN
asir-6084	20	8	lies	lie	VERB
asir-6084	20	9	in	in	ADP
asir-6084	20	10	how	how	SCONJ
asir-6084	20	11	to	to	PART
asir-6084	20	12	maintain	maintain	VERB
asir-6084	20	13	its	its	PRON
asir-6084	20	14	consistency	consistency	NOUN
asir-6084	20	15	.	.	PUNCT
asir-6084	21	1	therefore	therefore	ADV
asir-6084	21	2	,	,	PUNCT
asir-6084	21	3	this	this	DET
asir-6084	21	4	paper	paper	NOUN
asir-6084	21	5	attempts	attempt	VERB
asir-6084	21	6	to	to	PART
asir-6084	21	7	deduce	deduce	VERB
asir-6084	21	8	the	the	DET
asir-6084	21	9	validity	validity	NOUN
asir-6084	21	10	of	of	ADP
asir-6084	21	11	other	other	ADJ
asir-6084	21	12	syllogisms	syllogism	NOUN
asir-6084	21	13	by	by	ADP
asir-6084	21	14	means	mean	NOUN
asir-6084	21	15	of	of	ADP
asir-6084	21	16	reduction	reduction	NOUN
asir-6084	21	17	on	on	ADP
asir-6084	21	18	the	the	DET
asir-6084	21	19	basis	basis	NOUN
asir-6084	21	20	of	of	ADP
asir-6084	21	21	proving	prove	VERB
asir-6084	21	22	the	the	DET
asir-6084	21	23	validity	validity	NOUN
asir-6084	21	24	of	of	ADP
asir-6084	21	25	one	one	NUM
asir-6084	21	26	aristotelian	aristotelian	ADJ
asir-6084	21	27	modal	modal	NOUN
asir-6084	21	28	syllogism	syllogism	NOUN
asir-6084	21	29	(	(	PUNCT
asir-6084	21	30	i.e.	i.e.	X
asir-6084	21	31	iai-3	iai-3	NOUN
asir-6084	21	32	)	)	PUNCT
asir-6084	21	33	.	.	PUNCT
asir-6084	22	1	this	this	DET
asir-6084	22	2	research	research	NOUN
asir-6084	22	3	method	method	NOUN
asir-6084	22	4	can	can	AUX
asir-6084	22	5	well	well	ADV
asir-6084	22	6	ensure	ensure	VERB
asir-6084	22	7	the	the	DET
asir-6084	22	8	consistency	consistency	NOUN
asir-6084	22	9	of	of	ADP
asir-6084	22	10	this	this	DET
asir-6084	22	11	logic	logic	NOUN
asir-6084	22	12	.	.	PUNCT
asir-6084	23	1	more	more	ADV
asir-6084	23	2	specifically	specifically	ADV
asir-6084	23	3	,	,	PUNCT
asir-6084	23	4	this	this	DET
asir-6084	23	5	paper	paper	NOUN
asir-6084	23	6	discusses	discuss	VERB
asir-6084	23	7	the	the	DET
asir-6084	23	8	reduction	reduction	NOUN
asir-6084	23	9	between	between	ADP
asir-6084	23	10	the	the	DET
asir-6084	23	11	aristotelian	aristotelian	PROPN
asir-6084	23	12	modal	modal	ADJ
asir-6084	23	13	syllogism	syllogism	NOUN
asir-6084	23	14	iai-3	iai-3	NOUN
asir-6084	23	15	and	and	CCONJ
asir-6084	23	16	other	other	ADJ
asir-6084	23	17	valid	valid	ADJ
asir-6084	23	18	aristotelian	aristotelian	PROPN
asir-6084	23	19	modal	modal	NOUN
asir-6084	23	20	syllogisms	syllogism	NOUN
asir-6084	23	21	.	.	PUNCT
asir-6084	24	1	in	in	ADP
asir-6084	24	2	the	the	DET
asir-6084	24	3	syllogistic	syllogistic	NOUN
asir-6084	24	4	,	,	PUNCT
asir-6084	24	5	the	the	DET
asir-6084	24	6	proposition	proposition	NOUN
asir-6084	24	7	“	"	PUNCT
asir-6084	24	8	all	all	DET
asir-6084	24	9	xs	xs	NOUN
asir-6084	24	10	are	be	AUX
asir-6084	24	11	z	z	NOUN
asir-6084	24	12	”	"	PUNCT
asir-6084	24	13	is	be	AUX
asir-6084	24	14	denoted	denote	VERB
asir-6084	24	15	by	by	ADP
asir-6084	24	16	all(x	all(x	PROPN
asir-6084	24	17	,	,	PUNCT
asir-6084	24	18	z	z	NOUN
asir-6084	24	19	)	)	PUNCT
asir-6084	24	20	,	,	PUNCT
asir-6084	24	21	and	and	CCONJ
asir-6084	24	22	called	call	VERB
asir-6084	24	23	by	by	ADP
asir-6084	24	24	propositions	proposition	NOUN
asir-6084	24	25	a	a	PRON
asir-6084	24	26	;	;	PUNCT
asir-6084	24	27	“	"	PUNCT
asir-6084	24	28	no	no	DET
asir-6084	24	29	xs	xs	NOUN
asir-6084	24	30	are	be	AUX
asir-6084	24	31	z	z	NOUN
asir-6084	24	32	”	"	PUNCT
asir-6084	24	33	is	be	AUX
asir-6084	24	34	denoted	denote	VERB
asir-6084	24	35	by	by	ADP
asir-6084	24	36	no(x	no(x	ADJ
asir-6084	24	37	,	,	PUNCT
asir-6084	24	38	z	z	NOUN
asir-6084	24	39	)	)	PUNCT
asir-6084	24	40	,	,	PUNCT
asir-6084	24	41	and	and	CCONJ
asir-6084	24	42	called	call	VERB
asir-6084	24	43	by	by	ADP
asir-6084	24	44	propositions	proposition	NOUN
asir-6084	24	45	e	e	NOUN
asir-6084	24	46	;	;	PUNCT
asir-6084	24	47	“	"	PUNCT
asir-6084	24	48	some	some	DET
asir-6084	24	49	xs	xs	PROPN
asir-6084	24	50	are	be	AUX
asir-6084	24	51	z	z	NOUN
asir-6084	24	52	”	"	PUNCT
asir-6084	24	53	is	be	AUX
asir-6084	24	54	denoted	denote	VERB
asir-6084	24	55	by	by	ADP
asir-6084	24	56	some(x	some(x	PROPN
asir-6084	24	57	,	,	PUNCT
asir-6084	24	58	z	z	NOUN
asir-6084	24	59	)	)	PUNCT
asir-6084	24	60	,	,	PUNCT
asir-6084	24	61	and	and	CCONJ
asir-6084	24	62	called	call	VERB
asir-6084	24	63	by	by	ADP
asir-6084	24	64	propositions	proposition	NOUN
asir-6084	24	65	i	i	PRON
asir-6084	24	66	;	;	PUNCT
asir-6084	24	67	“	"	PUNCT
asir-6084	24	68	not	not	PART
asir-6084	24	69	all	all	DET
asir-6084	24	70	xs	xs	NOUN
asir-6084	24	71	are	be	AUX
asir-6084	24	72	z	z	NOUN
asir-6084	24	73	”	"	PUNCT
asir-6084	24	74	is	be	AUX
asir-6084	24	75	denoted	denote	VERB
asir-6084	24	76	by	by	ADP
asir-6084	24	77	not	not	PART
asir-6084	24	78	all(x	all(x	PROPN
asir-6084	24	79	,	,	PUNCT
asir-6084	24	80	z	z	NOUN
asir-6084	24	81	)	)	PUNCT
asir-6084	24	82	,	,	PUNCT
asir-6084	24	83	and	and	CCONJ
asir-6084	24	84	called	call	VERB
asir-6084	24	85	by	by	ADP
asir-6084	24	86	propositions	proposition	NOUN
asir-6084	24	87	o	o	NOUN
asir-6084	24	88	,	,	PUNCT
asir-6084	24	89	in	in	ADP
asir-6084	24	90	which	which	PRON
asir-6084	24	91	x	x	SYM
asir-6084	24	92	and	and	CCONJ
asir-6084	24	93	z	z	AUX
asir-6084	24	94	represent	represent	VERB
asir-6084	24	95	(	(	PUNCT
asir-6084	24	96	the	the	DET
asir-6084	24	97	set	set	NOUN
asir-6084	24	98	of	of	ADP
asir-6084	24	99	)	)	PUNCT
asir-6084	24	100	lexical	lexical	ADJ
asir-6084	24	101	variables	variable	NOUN
asir-6084	24	102	.	.	PUNCT
asir-6084	25	1	the	the	DET
asir-6084	25	2	symbols	symbol	NOUN
asir-6084	25	3	used	use	VERB
asir-6084	25	4	in	in	ADP
asir-6084	25	5	this	this	DET
asir-6084	25	6	paper	paper	NOUN
asir-6084	25	7	are	be	AUX
asir-6084	25	8	the	the	DET
asir-6084	25	9	basic	basic	ADJ
asir-6084	25	10	symbols	symbol	NOUN
asir-6084	25	11	in	in	ADP
asir-6084	25	12	modal	modal	ADJ
asir-6084	25	13	logic	logic	NOUN
asir-6084	25	14	(	(	PUNCT
asir-6084	25	15	chagrov	chagrov	ADJ
asir-6084	25	16	,	,	PUNCT
asir-6084	25	17	1997	1997	NUM
asir-6084	25	18	)	)	PUNCT
asir-6084	25	19	and	and	CCONJ
asir-6084	25	20	set	set	VERB
asir-6084	25	21	theory	theory	NOUN
asir-6084	25	22	,	,	PUNCT
asir-6084	25	23	for	for	ADP
asir-6084	25	24	example	example	NOUN
asir-6084	25	25	,	,	PUNCT
asir-6084	25	26			ADJ
asir-6084	25	27	,	,	PUNCT
asir-6084	25	28			PROPN
asir-6084	25	29	,	,	PUNCT
asir-6084	25	30			NOUN
asir-6084	25	31	,	,	PUNCT
asir-6084	25	32			ADJ
asir-6084	25	33	,	,	PUNCT
asir-6084	25	34			NOUN
asir-6084	25	35	,	,	PUNCT
asir-6084	25	36	and	and	CCONJ
asir-6084	25	37			NOUN
asir-6084	25	38	are	be	AUX
asir-6084	25	39	symbols	symbol	NOUN
asir-6084	25	40	of	of	ADP
asir-6084	25	41	negation	negation	NOUN
asir-6084	25	42	,	,	PUNCT
asir-6084	25	43	conjunction	conjunction	NOUN
asir-6084	25	44	,	,	PUNCT
asir-6084	25	45	conditionality	conditionality	NOUN
asir-6084	25	46	,	,	PUNCT
asir-6084	25	47	biconditionality	biconditionality	NOUN
asir-6084	25	48	,	,	PUNCT
asir-6084	25	49	necessity	necessity	NOUN
asir-6084	25	50	,	,	PUNCT
asir-6084	25	51	and	and	CCONJ
asir-6084	25	52	possibility	possibility	NOUN
asir-6084	25	53	,	,	PUNCT
asir-6084	25	54	respectively	respectively	ADV
asir-6084	25	55	.	.	PUNCT
asir-6084	26	1	since	since	SCONJ
asir-6084	26	2	any	any	DET
asir-6084	26	3	premise	premise	NOUN
asir-6084	26	4	and	and	CCONJ
asir-6084	26	5	conclusion	conclusion	NOUN
asir-6084	26	6	of	of	ADP
asir-6084	26	7	aristotelian	aristotelian	ADJ
asir-6084	26	8	modal	modal	NOUN
asir-6084	26	9	syllogisms	syllogism	NOUN
asir-6084	26	10	can	can	AUX
asir-6084	26	11	be	be	AUX
asir-6084	26	12	any	any	PRON
asir-6084	26	13	of	of	ADP
asir-6084	26	14	the	the	DET
asir-6084	26	15	12	12	NUM
asir-6084	26	16	propositions	proposition	NOUN
asir-6084	26	17	a	a	DET
asir-6084	26	18	,	,	PUNCT
asir-6084	26	19	e	e	NOUN
asir-6084	26	20	,	,	PUNCT
asir-6084	26	21	i	i	PRON
asir-6084	26	22	,	,	PUNCT
asir-6084	26	23	o	o	NOUN
asir-6084	26	24	,	,	PUNCT
asir-6084	26	25	a	a	NOUN
asir-6084	26	26	,	,	PUNCT
asir-6084	26	27	e	e	PRON
asir-6084	26	28	,	,	PUNCT
asir-6084	26	29	i	i	NOUN
asir-6084	26	30	,	,	PUNCT
asir-6084	26	31	o	o	NOUN
asir-6084	26	32	,	,	PUNCT
asir-6084	26	33	a	a	INTJ
asir-6084	26	34	,	,	PUNCT
asir-6084	26	35	e	e	NOUN
asir-6084	26	36	,	,	PUNCT
asir-6084	26	37	i	i	NOUN
asir-6084	26	38	and	and	CCONJ
asir-6084	26	39	o	o	NOUN
asir-6084	26	40	,	,	PUNCT
asir-6084	26	41	and	and	CCONJ
asir-6084	26	42	the	the	DET
asir-6084	26	43	middle	middle	ADJ
asir-6084	26	44	term	term	NOUN
asir-6084	26	45	has	have	VERB
asir-6084	26	46	four	four	NUM
asir-6084	26	47	different	different	ADJ
asir-6084	26	48	positions	position	NOUN
asir-6084	26	49	(	(	PUNCT
asir-6084	26	50	that	that	PRON
asir-6084	26	51	is	is	ADV
asir-6084	26	52	,	,	PUNCT
asir-6084	26	53	four	four	NUM
asir-6084	26	54	figures	figure	NOUN
asir-6084	26	55	)	)	PUNCT
asir-6084	26	56	,	,	PUNCT
asir-6084	26	57	there	there	PRON
asir-6084	26	58	are	be	VERB
asir-6084	26	59	(	(	PUNCT
asir-6084	26	60	1212124256=	1212124256=	NOUN
asir-6084	26	61	)	)	PUNCT
asir-6084	26	62	6656	6656	NUM
asir-6084	26	63	aristotelian	aristotelian	PROPN
asir-6084	26	64	modal	modal	NOUN
asir-6084	26	65	syllogisms	syllogism	NOUN
asir-6084	26	66	in	in	ADP
asir-6084	26	67	natural	natural	ADJ
asir-6084	26	68	language	language	NOUN
asir-6084	26	69	,	,	PUNCT
asir-6084	26	70	of	of	ADP
asir-6084	26	71	which	which	PRON
asir-6084	26	72	256	256	NUM
asir-6084	26	73	represents	represent	VERB
asir-6084	26	74	the	the	DET
asir-6084	26	75	number	number	NOUN
asir-6084	26	76	of	of	ADP
asir-6084	26	77	aristotelian	aristotelian	ADJ
asir-6084	26	78	syllogisms	syllogism	NOUN
asir-6084	26	79	.	.	PUNCT
asir-6084	27	1	zhang	zhang	PROPN
asir-6084	27	2	(	(	PUNCT
asir-6084	27	3	2020b	2020b	NUM
asir-6084	27	4	)	)	PUNCT
asir-6084	27	5	screened	screen	VERB
asir-6084	27	6	out	out	ADP
asir-6084	27	7	384	384	NUM
asir-6084	27	8	valid	valid	ADJ
asir-6084	27	9	syllogisms	syllogism	NOUN
asir-6084	27	10	from	from	ADP
asir-6084	27	11	6656	6656	NUM
asir-6084	27	12	aristotelian	aristotelian	ADJ
asir-6084	27	13	modal	modal	NOUN
asir-6084	27	14	syllogisms	syllogism	NOUN
asir-6084	27	15	.	.	PUNCT
asir-6084	28	1	through	through	ADP
asir-6084	28	2	the	the	DET
asir-6084	28	3	way	way	NOUN
asir-6084	28	4	of	of	ADP
asir-6084	28	5	reduction	reduction	NOUN
asir-6084	28	6	,	,	PUNCT
asir-6084	28	7	this	this	DET
asir-6084	28	8	paper	paper	NOUN
asir-6084	28	9	profoundly	profoundly	ADV
asir-6084	28	10	reveals	reveal	VERB
asir-6084	28	11	the	the	DET
asir-6084	28	12	logical	logical	ADJ
asir-6084	28	13	relations	relation	NOUN
asir-6084	28	14	between	between	ADP
asir-6084	28	15	/	/	SYM
asir-6084	28	16	among	among	ADP
asir-6084	28	17	91	91	NUM
asir-6084	28	18	valid	valid	ADJ
asir-6084	28	19	aristotelian	aristotelian	ADJ
asir-6084	28	20	modal	modal	NOUN
asir-6084	28	21	syllogisms	syllogism	NOUN
asir-6084	28	22	.	.	PUNCT
asir-6084	29	1	2	2	X
asir-6084	29	2	.	.	NUM
asir-6084	29	3	preliminaries	preliminary	NOUN
asir-6084	29	4	in	in	ADP
asir-6084	29	5	the	the	DET
asir-6084	29	6	following	follow	VERB
asir-6084	29	7	propositions	proposition	NOUN
asir-6084	29	8	,	,	PUNCT
asir-6084	29	9	x	x	PRON
asir-6084	29	10	,	,	PUNCT
asir-6084	29	11	y	y	PROPN
asir-6084	29	12	and	and	CCONJ
asir-6084	29	13	z	z	PROPN
asir-6084	29	14	represent	represent	VERB
asir-6084	29	15	(	(	PUNCT
asir-6084	29	16	the	the	DET
asir-6084	29	17	set	set	NOUN
asir-6084	29	18	of	of	ADP
asir-6084	29	19	)	)	PUNCT
asir-6084	29	20	lexical	lexical	ADJ
asir-6084	29	21	variables	variable	NOUN
asir-6084	29	22	(	(	PUNCT
asir-6084	29	23	subjects	subject	NOUN
asir-6084	29	24	or	or	CCONJ
asir-6084	29	25	predicates	predicate	NOUN
asir-6084	29	26	)	)	PUNCT
asir-6084	29	27	involved	involve	VERB
asir-6084	29	28	in	in	ADP
asir-6084	29	29	categorical	categorical	ADJ
asir-6084	29	30	propositions	proposition	NOUN
asir-6084	29	31	or	or	CCONJ
asir-6084	29	32	modal	modal	ADJ
asir-6084	29	33	categorical	categorical	ADJ
asir-6084	29	34	propositions	proposition	NOUN
asir-6084	29	35	.	.	PUNCT
asir-6084	30	1	the	the	DET
asir-6084	30	2	definition	definition	NOUN
asir-6084	30	3	of	of	ADP
asir-6084	30	4	figures	figure	NOUN
asir-6084	30	5	of	of	ADP
asir-6084	30	6	aristotelian	aristotelian	ADJ
asir-6084	30	7	modal	modal	NOUN
asir-6084	30	8	syllogisms	syllogism	NOUN
asir-6084	30	9	are	be	AUX
asir-6084	30	10	similar	similar	ADJ
asir-6084	30	11	to	to	ADP
asir-6084	30	12	those	those	PRON
asir-6084	30	13	of	of	ADP
asir-6084	30	14	aristotelian	aristotelian	ADJ
asir-6084	30	15	syllogisms	syllogism	NOUN
asir-6084	30	16	.	.	PUNCT
asir-6084	31	1	aristotelian	aristotelian	PROPN
asir-6084	31	2	modal	modal	NOUN
asir-6084	31	3	syllogisms	syllogism	NOUN
asir-6084	31	4	can	can	AUX
asir-6084	31	5	be	be	AUX
asir-6084	31	6	seen	see	VERB
asir-6084	31	7	as	as	ADP
asir-6084	31	8	extended	extended	ADJ
asir-6084	31	9	syllogisms	syllogism	NOUN
asir-6084	31	10	obtained	obtain	VERB
asir-6084	31	11	by	by	ADP
asir-6084	31	12	adding	add	VERB
asir-6084	31	13	necessary	necessary	ADJ
asir-6084	31	14	modality	modality	NOUN
asir-6084	31	15			NOUN
asir-6084	31	16	or	or	CCONJ
asir-6084	31	17	possible	possible	ADJ
asir-6084	31	18	modality	modality	NOUN
asir-6084	31	19			NOUN
asir-6084	31	20	to	to	ADP
asir-6084	31	21	aristotelian	aristotelian	PROPN
asir-6084	31	22	syllogisms	syllogism	NOUN
asir-6084	31	23	.	.	PUNCT
asir-6084	32	1	aristotelian	aristotelian	PROPN
asir-6084	32	2	syllogisms	syllogism	NOUN
asir-6084	32	3	represent	represent	VERB
asir-6084	32	4	the	the	DET
asir-6084	32	5	semantic	semantic	ADJ
asir-6084	32	6	and	and	CCONJ
asir-6084	32	7	reasoning	reasoning	NOUN
asir-6084	32	8	properties	property	NOUN
asir-6084	32	9	of	of	ADP
asir-6084	32	10	the	the	DET
asir-6084	32	11	four	four	NUM
asir-6084	32	12	aristotelian	aristotelian	ADJ
asir-6084	32	13	quantifiers	quantifier	NOUN
asir-6084	32	14	(	(	PUNCT
asir-6084	32	15	that	that	PRON
asir-6084	32	16	is	is	ADV
asir-6084	32	17	,	,	PUNCT
asir-6084	32	18	all	all	PRON
asir-6084	32	19	,	,	PUNCT
asir-6084	32	20	some	some	PRON
asir-6084	32	21	,	,	PUNCT
asir-6084	32	22	no	no	INTJ
asir-6084	32	23	and	and	CCONJ
asir-6084	32	24	not	not	PART
asir-6084	32	25	all	all	PRON
asir-6084	32	26	)	)	PUNCT
asir-6084	32	27	.	.	PUNCT
asir-6084	33	1	similarly	similarly	ADV
asir-6084	33	2	,	,	PUNCT
asir-6084	33	3	aristotelian	aristotelian	ADJ
asir-6084	33	4	modal	modal	NOUN
asir-6084	33	5	syllogisms	syllogism	NOUN
asir-6084	33	6	are	be	AUX
asir-6084	33	7	syllogisms	syllogism	NOUN
asir-6084	33	8	that	that	PRON
asir-6084	33	9	just	just	ADV
asir-6084	33	10	contain	contain	VERB
asir-6084	33	11	the	the	DET
asir-6084	33	12	four	four	NUM
asir-6084	33	13	aristotelian	aristotelian	ADJ
asir-6084	33	14	quantifiers	quantifier	NOUN
asir-6084	33	15	,	,	PUNCT
asir-6084	33	16	and	and	CCONJ
asir-6084	33	17	at	at	ADP
asir-6084	33	18	least	least	ADJ
asir-6084	33	19	contain	contain	VERB
asir-6084	33	20	one	one	NUM
asir-6084	33	21	necessary	necessary	ADJ
asir-6084	33	22	modality	modality	NOUN
asir-6084	33	23	(	(	PUNCT
asir-6084	33	24			NUM
asir-6084	33	25	)	)	PUNCT
asir-6084	33	26	or	or	CCONJ
asir-6084	33	27	possible	possible	ADJ
asir-6084	33	28	modality	modality	NOUN
asir-6084	33	29	(	(	PUNCT
asir-6084	33	30			NOUN
asir-6084	33	31	)	)	PUNCT
asir-6084	33	32	.	.	PUNCT
asir-6084	34	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-6084	34	2	applied	apply	VERB
asir-6084	34	3	science	science	NOUN
asir-6084	34	4	and	and	CCONJ
asir-6084	34	5	innovative	innovative	ADJ
asir-6084	34	6	research	research	NOUN
asir-6084	34	7	vol	vol	NOUN
asir-6084	34	8	.	.	PUNCT
asir-6084	35	1	7	7	NUM
asir-6084	35	2	,	,	PUNCT
asir-6084	35	3	no	no	INTJ
asir-6084	35	4	.	.	NOUN
asir-6084	35	5	1	1	NUM
asir-6084	35	6	,	,	PUNCT
asir-6084	35	7	2023	2023	NUM
asir-6084	35	8	48	48	NUM
asir-6084	35	9	published	publish	VERB
asir-6084	35	10	by	by	ADP
asir-6084	35	11	scholink	scholink	PROPN
asir-6084	35	12	inc	inc	PROPN
asir-6084	35	13	.	.	PROPN
asir-6084	35	14	example	example	NOUN
asir-6084	35	15	1	1	NUM
asir-6084	35	16	:	:	PUNCT
asir-6084	35	17	major	major	ADJ
asir-6084	35	18	premise	premise	NOUN
asir-6084	35	19	:	:	PUNCT
asir-6084	35	20	some	some	DET
asir-6084	35	21	apples	apple	NOUN
asir-6084	35	22	are	be	AUX
asir-6084	35	23	necessarily	necessarily	ADV
asir-6084	35	24	green	green	ADJ
asir-6084	35	25	apples	apple	NOUN
asir-6084	35	26	.	.	PUNCT
asir-6084	36	1	minor	minor	ADJ
asir-6084	36	2	premise	premise	NOUN
asir-6084	36	3	:	:	PUNCT
asir-6084	36	4	all	all	DET
asir-6084	36	5	apples	apple	NOUN
asir-6084	36	6	are	be	AUX
asir-6084	36	7	necessarily	necessarily	ADV
asir-6084	36	8	fruits	fruit	NOUN
asir-6084	36	9	.	.	PUNCT
asir-6084	37	1	conclusion	conclusion	NOUN
asir-6084	37	2	:	:	PUNCT
asir-6084	37	3	some	some	DET
asir-6084	37	4	green	green	ADJ
asir-6084	37	5	apples	apple	NOUN
asir-6084	37	6	are	be	AUX
asir-6084	37	7	necessarily	necessarily	ADV
asir-6084	37	8	fruits	fruit	NOUN
asir-6084	37	9	.	.	PUNCT
asir-6084	38	1	the	the	DET
asir-6084	38	2	syllogism	syllogism	NOUN
asir-6084	38	3	contains	contain	VERB
asir-6084	38	4	the	the	DET
asir-6084	38	5	aristotelian	aristotelian	PROPN
asir-6084	38	6	quantifiers	quantifier	VERB
asir-6084	38	7	some	some	PRON
asir-6084	38	8	and	and	CCONJ
asir-6084	38	9	all	all	PRON
asir-6084	38	10	,	,	PUNCT
asir-6084	38	11	and	and	CCONJ
asir-6084	38	12	contains	contain	VERB
asir-6084	38	13	three	three	NUM
asir-6084	38	14	necessary	necessary	ADJ
asir-6084	38	15	modalities	modality	NOUN
asir-6084	38	16	(	(	PUNCT
asir-6084	38	17			NUM
asir-6084	38	18	)	)	PUNCT
asir-6084	38	19	,	,	PUNCT
asir-6084	38	20	and	and	CCONJ
asir-6084	38	21	the	the	DET
asir-6084	38	22	middle	middle	ADJ
asir-6084	38	23	term	term	NOUN
asir-6084	38	24	is	be	AUX
asir-6084	38	25	the	the	DET
asir-6084	38	26	subject	subject	NOUN
asir-6084	38	27	of	of	ADP
asir-6084	38	28	the	the	DET
asir-6084	38	29	major	major	ADJ
asir-6084	38	30	and	and	CCONJ
asir-6084	38	31	minor	minor	ADJ
asir-6084	38	32	premise	premise	NOUN
asir-6084	38	33	,	,	PUNCT
asir-6084	38	34	so	so	ADV
asir-6084	38	35	it	it	PRON
asir-6084	38	36	is	be	AUX
asir-6084	38	37	an	an	DET
asir-6084	38	38	aristotelian	aristotelian	ADJ
asir-6084	38	39	modal	modal	ADJ
asir-6084	38	40	syllogism	syllogism	NOUN
asir-6084	38	41	,	,	PUNCT
asir-6084	38	42	and	and	CCONJ
asir-6084	38	43	the	the	DET
asir-6084	38	44	third	third	ADJ
asir-6084	38	45	figure	figure	NOUN
asir-6084	38	46	.	.	PUNCT
asir-6084	39	1	let	let	VERB
asir-6084	39	2	x	x	PRON
asir-6084	39	3	is	be	AUX
asir-6084	39	4	the	the	DET
asir-6084	39	5	set	set	NOUN
asir-6084	39	6	of	of	ADP
asir-6084	39	7	green	green	ADJ
asir-6084	39	8	apples	apple	NOUN
asir-6084	39	9	in	in	ADP
asir-6084	39	10	a	a	DET
asir-6084	39	11	given	give	VERB
asir-6084	39	12	domain	domain	NOUN
asir-6084	39	13	,	,	PUNCT
asir-6084	39	14	y	y	PROPN
asir-6084	39	15	is	be	AUX
asir-6084	39	16	the	the	DET
asir-6084	39	17	set	set	NOUN
asir-6084	39	18	of	of	ADP
asir-6084	39	19	apples	apple	NOUN
asir-6084	39	20	in	in	ADP
asir-6084	39	21	the	the	DET
asir-6084	39	22	domain	domain	NOUN
asir-6084	39	23	,	,	PUNCT
asir-6084	39	24	and	and	CCONJ
asir-6084	39	25	z	z	NOUN
asir-6084	39	26	is	be	AUX
asir-6084	39	27	the	the	DET
asir-6084	39	28	set	set	NOUN
asir-6084	39	29	of	of	ADP
asir-6084	39	30	fruits	fruit	NOUN
asir-6084	39	31	in	in	ADP
asir-6084	39	32	the	the	DET
asir-6084	39	33	domain	domain	NOUN
asir-6084	39	34	.	.	PUNCT
asir-6084	40	1	example	example	NOUN
asir-6084	40	2	1	1	NUM
asir-6084	40	3	of	of	ADP
asir-6084	40	4	the	the	DET
asir-6084	40	5	third	third	ADJ
asir-6084	40	6	figure	figure	NOUN
asir-6084	40	7	syllogism	syllogism	NOUN
asir-6084	40	8	can	can	AUX
asir-6084	40	9	be	be	AUX
asir-6084	40	10	formalized	formalize	VERB
asir-6084	40	11	by	by	ADP
asir-6084	40	12	some(y	some(y	ADJ
asir-6084	40	13	,	,	PUNCT
asir-6084	40	14	z)all(y	z)all(y	PROPN
asir-6084	40	15	,	,	PUNCT
asir-6084	40	16	x)some(x	x)some(x	PROPN
asir-6084	40	17	,	,	PUNCT
asir-6084	40	18	z	z	PROPN
asir-6084	40	19	)	)	PUNCT
asir-6084	40	20	,	,	PUNCT
asir-6084	40	21	abbreviated	abbreviate	VERB
asir-6084	40	22	by	by	ADP
asir-6084	40	23	iai-3	iai-3	PROPN
asir-6084	40	24	.	.	PUNCT
asir-6084	41	1	in	in	ADP
asir-6084	41	2	all	all	PRON
asir-6084	41	3	of	of	ADP
asir-6084	41	4	the	the	DET
asir-6084	41	5	syllogisms	syllogism	NOUN
asir-6084	41	6	in	in	ADP
asir-6084	41	7	this	this	DET
asir-6084	41	8	article	article	NOUN
asir-6084	41	9	,	,	PUNCT
asir-6084	41	10	x	x	PRON
asir-6084	41	11	,	,	PUNCT
asir-6084	41	12	y	y	PROPN
asir-6084	41	13	and	and	CCONJ
asir-6084	41	14	z	z	PROPN
asir-6084	41	15	represent	represent	VERB
asir-6084	41	16	the	the	DET
asir-6084	41	17	minor	minor	ADJ
asir-6084	41	18	,	,	PUNCT
asir-6084	41	19	medium	medium	ADJ
asir-6084	41	20	and	and	CCONJ
asir-6084	41	21	major	major	ADJ
asir-6084	41	22	terms	term	NOUN
asir-6084	41	23	of	of	ADP
asir-6084	41	24	syllogisms	syllogism	NOUN
asir-6084	41	25	respectively	respectively	ADV
asir-6084	41	26	.	.	PUNCT
asir-6084	42	1	the	the	DET
asir-6084	42	2	formalization	formalization	NOUN
asir-6084	42	3	of	of	ADP
asir-6084	42	4	other	other	ADJ
asir-6084	42	5	modal	modal	ADJ
asir-6084	42	6	syllogisms	syllogism	NOUN
asir-6084	42	7	are	be	AUX
asir-6084	42	8	similar	similar	ADJ
asir-6084	42	9	to	to	ADP
asir-6084	42	10	that	that	PRON
asir-6084	42	11	of	of	ADP
asir-6084	42	12	this	this	DET
asir-6084	42	13	syllogism	syllogism	NOUN
asir-6084	42	14	.	.	PUNCT
asir-6084	43	1	in	in	ADP
asir-6084	43	2	fact	fact	NOUN
asir-6084	43	3	,	,	PUNCT
asir-6084	43	4	all	all	DET
asir-6084	43	5	modal	modal	NOUN
asir-6084	43	6	syllogisms	syllogism	NOUN
asir-6084	43	7	can	can	AUX
asir-6084	43	8	be	be	AUX
asir-6084	43	9	formalized	formalize	VERB
asir-6084	43	10	into	into	ADP
asir-6084	43	11	the	the	DET
asir-6084	43	12	forms	form	NOUN
asir-6084	43	13	similar	similar	ADJ
asir-6084	43	14	to	to	ADP
asir-6084	43	15	q1(x	q1(x	PROPN
asir-6084	43	16	,	,	PUNCT
asir-6084	43	17	y)q2(y	y)q2(y	PROPN
asir-6084	43	18	,	,	PUNCT
asir-6084	43	19	z)q3(x	z)q3(x	PROPN
asir-6084	43	20	,	,	PUNCT
asir-6084	43	21	z	z	NOUN
asir-6084	43	22	)	)	PUNCT
asir-6084	43	23	,	,	PUNCT
asir-6084	43	24	where	where	SCONJ
asir-6084	43	25	q1	q1	PROPN
asir-6084	43	26	,	,	PUNCT
asir-6084	43	27	q2	q2	PROPN
asir-6084	43	28	and	and	CCONJ
asir-6084	43	29	q3	q3	PROPN
asir-6084	43	30	can	can	AUX
asir-6084	43	31	be	be	AUX
asir-6084	43	32	any	any	PRON
asir-6084	43	33	of	of	ADP
asir-6084	43	34	the	the	DET
asir-6084	43	35	following	follow	VERB
asir-6084	43	36	12	12	NUM
asir-6084	43	37	generalized	generalized	ADJ
asir-6084	43	38	quantifiers	quantifier	NOUN
asir-6084	43	39	:	:	PUNCT
asir-6084	43	40	all	all	PRON
asir-6084	43	41	,	,	PUNCT
asir-6084	43	42	some	some	PRON
asir-6084	43	43	,	,	PUNCT
asir-6084	43	44	no	no	INTJ
asir-6084	43	45	,	,	PUNCT
asir-6084	43	46	not	not	PART
asir-6084	43	47	all	all	PRON
asir-6084	43	48	,	,	PUNCT
asir-6084	43	49	all	all	ADV
asir-6084	43	50	,	,	PUNCT
asir-6084	43	51	some	some	PROPN
asir-6084	43	52	,	,	PUNCT
asir-6084	43	53	no	no	PROPN
asir-6084	43	54	,	,	PUNCT
asir-6084	43	55	not	not	ADV
asir-6084	43	56	all	all	PRON
asir-6084	43	57	,	,	PUNCT
asir-6084	43	58	all	all	ADV
asir-6084	43	59	,	,	PUNCT
asir-6084	43	60	some	some	PROPN
asir-6084	43	61	,	,	PUNCT
asir-6084	43	62	no	no	PROPN
asir-6084	43	63	and	and	CCONJ
asir-6084	43	64	not	not	ADV
asir-6084	43	65	all	all	PRON
asir-6084	43	66	.	.	PUNCT
asir-6084	44	1	2.1	2.1	NUM
asir-6084	44	2	relevant	relevant	ADJ
asir-6084	44	3	definitions	definition	NOUN
asir-6084	44	4	according	accord	VERB
asir-6084	44	5	to	to	ADP
asir-6084	44	6	the	the	DET
asir-6084	44	7	generalized	generalize	VERB
asir-6084	44	8	quantifier	quantifier	NOUN
asir-6084	44	9	theory	theory	NOUN
asir-6084	44	10	(	(	PUNCT
asir-6084	44	11	peters	peters	PROPN
asir-6084	44	12	&	&	CCONJ
asir-6084	44	13	westerståhl	westerståhl	PROPN
asir-6084	44	14	,	,	PUNCT
asir-6084	44	15	2006	2006	NUM
asir-6084	44	16	)	)	PUNCT
asir-6084	44	17	,	,	PUNCT
asir-6084	44	18	set	set	VERB
asir-6084	44	19	theory	theory	NOUN
asir-6084	44	20	and	and	CCONJ
asir-6084	44	21	possible	possible	ADJ
asir-6084	44	22	world	world	NOUN
asir-6084	44	23	semantics	semantic	NOUN
asir-6084	44	24	(	(	PUNCT
asir-6084	44	25	chellas	chella	NOUN
asir-6084	44	26	,	,	PUNCT
asir-6084	44	27	1980	1980	NUM
asir-6084	44	28	)	)	PUNCT
asir-6084	44	29	,	,	PUNCT
asir-6084	44	30	one	one	PRON
asir-6084	44	31	can	can	AUX
asir-6084	44	32	give	give	VERB
asir-6084	44	33	the	the	DET
asir-6084	44	34	truth	truth	NOUN
asir-6084	44	35	value	value	NOUN
asir-6084	44	36	definition	definition	NOUN
asir-6084	44	37	of	of	ADP
asir-6084	44	38	the	the	DET
asir-6084	44	39	following	follow	VERB
asir-6084	44	40	propositions	proposition	NOUN
asir-6084	44	41	:	:	PUNCT
asir-6084	44	42	definition	definition	NOUN
asir-6084	44	43	1	1	NUM
asir-6084	44	44	(	(	PUNCT
asir-6084	44	45	truth	truth	NOUN
asir-6084	44	46	value	value	NOUN
asir-6084	44	47	definition	definition	NOUN
asir-6084	44	48	):	):	PUNCT
asir-6084	44	49	(	(	PUNCT
asir-6084	44	50	1	1	X
asir-6084	44	51	)	)	PUNCT
asir-6084	44	52	all(x	all(x	PROPN
asir-6084	44	53	,	,	PUNCT
asir-6084	44	54	z	z	NOUN
asir-6084	44	55	)	)	PUNCT
asir-6084	44	56	is	be	AUX
asir-6084	44	57	true	true	ADJ
asir-6084	44	58	if	if	SCONJ
asir-6084	44	59	and	and	CCONJ
asir-6084	44	60	only	only	ADV
asir-6084	44	61	if	if	SCONJ
asir-6084	44	62	xz	xz	NOUN
asir-6084	44	63	is	be	AUX
asir-6084	44	64	true	true	ADJ
asir-6084	44	65	.	.	PUNCT
asir-6084	45	1	(	(	PUNCT
asir-6084	45	2	2	2	X
asir-6084	45	3	)	)	PUNCT
asir-6084	45	4	some(x	some(x	PROPN
asir-6084	45	5	,	,	PUNCT
asir-6084	45	6	z	z	NOUN
asir-6084	45	7	)	)	PUNCT
asir-6084	45	8	is	be	AUX
asir-6084	45	9	true	true	ADJ
asir-6084	45	10	if	if	SCONJ
asir-6084	46	1	and	and	CCONJ
asir-6084	46	2	only	only	ADV
asir-6084	46	3	if	if	SCONJ
asir-6084	46	4	x∩z	x∩z	PROPN
asir-6084	46	5	is	be	AUX
asir-6084	46	6	true	true	ADJ
asir-6084	46	7	.	.	PUNCT
asir-6084	47	1	(	(	PUNCT
asir-6084	47	2	3	3	NUM
asir-6084	47	3	)	)	PUNCT
asir-6084	47	4	no(x	no(x	ADJ
asir-6084	47	5	,	,	PUNCT
asir-6084	47	6	z	z	NOUN
asir-6084	47	7	)	)	PUNCT
asir-6084	47	8	is	be	AUX
asir-6084	47	9	true	true	ADJ
asir-6084	47	10	if	if	SCONJ
asir-6084	47	11	and	and	CCONJ
asir-6084	47	12	only	only	ADV
asir-6084	47	13	if	if	SCONJ
asir-6084	47	14	x∩z=	x∩z=	PROPN
asir-6084	47	15	is	be	AUX
asir-6084	47	16	true	true	ADJ
asir-6084	47	17	.	.	PUNCT
asir-6084	48	1	(	(	PUNCT
asir-6084	48	2	4	4	X
asir-6084	48	3	)	)	PUNCT
asir-6084	48	4	not	not	PART
asir-6084	48	5	all(x	all(x	PROPN
asir-6084	48	6	,	,	PUNCT
asir-6084	48	7	z	z	NOUN
asir-6084	48	8	)	)	PUNCT
asir-6084	48	9	is	be	AUX
asir-6084	48	10	true	true	ADJ
asir-6084	48	11	if	if	SCONJ
asir-6084	48	12	and	and	CCONJ
asir-6084	48	13	only	only	ADV
asir-6084	48	14	if	if	SCONJ
asir-6084	48	15	x⊈z	x⊈z	PROPN
asir-6084	48	16	is	be	AUX
asir-6084	48	17	true	true	ADJ
asir-6084	48	18	.	.	PUNCT
asir-6084	49	1	(	(	PUNCT
asir-6084	49	2	5	5	X
asir-6084	49	3	)	)	PUNCT
asir-6084	49	4	all(x	all(x	PROPN
asir-6084	49	5	,	,	PUNCT
asir-6084	49	6	z	z	NOUN
asir-6084	49	7	)	)	PUNCT
asir-6084	49	8	is	be	AUX
asir-6084	49	9	true	true	ADJ
asir-6084	49	10	if	if	SCONJ
asir-6084	49	11	and	and	CCONJ
asir-6084	49	12	only	only	ADV
asir-6084	49	13	if	if	SCONJ
asir-6084	49	14	xz	xz	NOUN
asir-6084	49	15	is	be	AUX
asir-6084	49	16	true	true	ADJ
asir-6084	49	17	in	in	ADP
asir-6084	49	18	any	any	DET
asir-6084	49	19	possible	possible	ADJ
asir-6084	49	20	world	world	NOUN
asir-6084	49	21	.	.	PUNCT
asir-6084	50	1	(	(	PUNCT
asir-6084	50	2	6	6	NUM
asir-6084	50	3	)	)	PUNCT
asir-6084	50	4	all(x	all(x	PROPN
asir-6084	50	5	,	,	PUNCT
asir-6084	50	6	z	z	NOUN
asir-6084	50	7	)	)	PUNCT
asir-6084	50	8	is	be	AUX
asir-6084	50	9	true	true	ADJ
asir-6084	50	10	if	if	SCONJ
asir-6084	51	1	and	and	CCONJ
asir-6084	51	2	only	only	ADV
asir-6084	51	3	if	if	SCONJ
asir-6084	51	4	xz	xz	NOUN
asir-6084	51	5	is	be	AUX
asir-6084	51	6	true	true	ADJ
asir-6084	51	7	in	in	ADP
asir-6084	51	8	at	at	ADV
asir-6084	51	9	least	least	ADV
asir-6084	51	10	one	one	NUM
asir-6084	51	11	possible	possible	ADJ
asir-6084	51	12	world	world	NOUN
asir-6084	51	13	.	.	PUNCT
asir-6084	52	1	(	(	PUNCT
asir-6084	52	2	7	7	X
asir-6084	52	3	)	)	PUNCT
asir-6084	52	4	some(x	some(x	NOUN
asir-6084	52	5	,	,	PUNCT
asir-6084	52	6	z	z	NOUN
asir-6084	52	7	)	)	PUNCT
asir-6084	52	8	is	be	AUX
asir-6084	52	9	true	true	ADJ
asir-6084	52	10	if	if	SCONJ
asir-6084	52	11	and	and	CCONJ
asir-6084	52	12	only	only	ADV
asir-6084	52	13	if	if	SCONJ
asir-6084	52	14	x∩z	x∩z	PROPN
asir-6084	52	15	is	be	AUX
asir-6084	52	16	true	true	ADJ
asir-6084	52	17	in	in	ADP
asir-6084	52	18	any	any	DET
asir-6084	52	19	possible	possible	ADJ
asir-6084	52	20	world	world	NOUN
asir-6084	52	21	.	.	PUNCT
asir-6084	53	1	(	(	PUNCT
asir-6084	53	2	8)	8)	NUM
asir-6084	53	3	some(x	some(x	NOUN
asir-6084	53	4	,	,	PUNCT
asir-6084	53	5	z	z	NOUN
asir-6084	53	6	)	)	PUNCT
asir-6084	53	7	is	be	AUX
asir-6084	53	8	true	true	ADJ
asir-6084	53	9	if	if	SCONJ
asir-6084	53	10	and	and	CCONJ
asir-6084	53	11	only	only	ADV
asir-6084	53	12	if	if	SCONJ
asir-6084	53	13	x∩z	x∩z	PROPN
asir-6084	53	14	is	be	AUX
asir-6084	53	15	true	true	ADJ
asir-6084	53	16	in	in	ADP
asir-6084	53	17	at	at	ADV
asir-6084	53	18	least	least	ADV
asir-6084	53	19	one	one	NUM
asir-6084	53	20	possible	possible	ADJ
asir-6084	53	21	world	world	NOUN
asir-6084	53	22	.	.	PUNCT
asir-6084	54	1	(	(	PUNCT
asir-6084	54	2	9	9	X
asir-6084	54	3	)	)	PUNCT
asir-6084	54	4	no(x	no(x	PROPN
asir-6084	54	5	,	,	PUNCT
asir-6084	54	6	z	z	NOUN
asir-6084	54	7	)	)	PUNCT
asir-6084	54	8	is	be	AUX
asir-6084	54	9	true	true	ADJ
asir-6084	54	10	if	if	SCONJ
asir-6084	54	11	and	and	CCONJ
asir-6084	54	12	only	only	ADV
asir-6084	54	13	if	if	SCONJ
asir-6084	54	14	x∩z=	x∩z=	PROPN
asir-6084	54	15	is	be	AUX
asir-6084	54	16	true	true	ADJ
asir-6084	54	17	in	in	ADP
asir-6084	54	18	any	any	DET
asir-6084	54	19	possible	possible	ADJ
asir-6084	54	20	world	world	NOUN
asir-6084	54	21	.	.	PUNCT
asir-6084	55	1	(	(	PUNCT
asir-6084	55	2	10	10	NUM
asir-6084	55	3	)	)	PUNCT
asir-6084	55	4	no(x	no(x	NUM
asir-6084	55	5	,	,	PUNCT
asir-6084	55	6	z	z	NOUN
asir-6084	55	7	)	)	PUNCT
asir-6084	55	8	is	be	AUX
asir-6084	55	9	true	true	ADJ
asir-6084	55	10	if	if	SCONJ
asir-6084	55	11	and	and	CCONJ
asir-6084	55	12	only	only	ADV
asir-6084	55	13	if	if	SCONJ
asir-6084	55	14	x∩z=	x∩z=	PROPN
asir-6084	55	15	is	be	AUX
asir-6084	55	16	true	true	ADJ
asir-6084	55	17	in	in	ADP
asir-6084	55	18	at	at	ADV
asir-6084	55	19	least	least	ADV
asir-6084	55	20	one	one	NUM
asir-6084	55	21	possible	possible	ADJ
asir-6084	55	22	world	world	NOUN
asir-6084	55	23	.	.	PUNCT
asir-6084	56	1	(	(	PUNCT
asir-6084	56	2	11	11	NUM
asir-6084	56	3	)	)	PUNCT
asir-6084	56	4	not	not	ADV
asir-6084	56	5	all(x	all(x	PROPN
asir-6084	56	6	,	,	PUNCT
asir-6084	56	7	z	z	NOUN
asir-6084	56	8	)	)	PUNCT
asir-6084	56	9	is	be	AUX
asir-6084	56	10	true	true	ADJ
asir-6084	56	11	if	if	SCONJ
asir-6084	56	12	and	and	CCONJ
asir-6084	56	13	only	only	ADV
asir-6084	56	14	if	if	SCONJ
asir-6084	56	15	x⊈z	x⊈z	PROPN
asir-6084	56	16	is	be	AUX
asir-6084	56	17	true	true	ADJ
asir-6084	56	18	in	in	ADP
asir-6084	56	19	any	any	DET
asir-6084	56	20	possible	possible	ADJ
asir-6084	56	21	world	world	NOUN
asir-6084	56	22	.	.	PUNCT
asir-6084	57	1	(	(	PUNCT
asir-6084	57	2	12	12	NUM
asir-6084	57	3	)	)	PUNCT
asir-6084	57	4	not	not	ADV
asir-6084	57	5	all(x	all(x	PROPN
asir-6084	57	6	,	,	PUNCT
asir-6084	57	7	z	z	NOUN
asir-6084	57	8	)	)	PUNCT
asir-6084	57	9	is	be	AUX
asir-6084	57	10	true	true	ADJ
asir-6084	57	11	if	if	SCONJ
asir-6084	57	12	and	and	CCONJ
asir-6084	57	13	only	only	ADV
asir-6084	57	14	if	if	SCONJ
asir-6084	57	15	x⊈z	x⊈z	PROPN
asir-6084	57	16	is	be	AUX
asir-6084	57	17	true	true	ADJ
asir-6084	57	18	in	in	ADP
asir-6084	57	19	at	at	ADV
asir-6084	57	20	least	least	ADV
asir-6084	57	21	one	one	NUM
asir-6084	57	22	possible	possible	ADJ
asir-6084	57	23	world	world	NOUN
asir-6084	57	24	.	.	PUNCT
asir-6084	58	1	in	in	ADP
asir-6084	58	2	the	the	DET
asir-6084	58	3	following	following	NOUN
asir-6084	58	4	,	,	PUNCT
asir-6084	58	5	d	d	PROPN
asir-6084	58	6	stands	stand	VERB
asir-6084	58	7	for	for	ADP
asir-6084	58	8	the	the	DET
asir-6084	58	9	domain	domain	NOUN
asir-6084	58	10	of	of	ADP
asir-6084	58	11	lexical	lexical	ADJ
asir-6084	58	12	variables	variable	NOUN
asir-6084	58	13	,	,	PUNCT
asir-6084	58	14	q	q	NOUN
asir-6084	58	15	for	for	ADP
asir-6084	58	16	any	any	PRON
asir-6084	58	17	of	of	ADP
asir-6084	58	18	the	the	DET
asir-6084	58	19	four	four	NUM
asir-6084	58	20	aristotelian	aristotelian	ADJ
asir-6084	58	21	quantifiers	quantifier	NOUN
asir-6084	58	22	(	(	PUNCT
asir-6084	58	23	that	that	PRON
asir-6084	58	24	is	is	ADV
asir-6084	58	25	,	,	PUNCT
asir-6084	58	26	all	all	PRON
asir-6084	58	27	,	,	PUNCT
asir-6084	58	28	some	some	PRON
asir-6084	58	29	,	,	PUNCT
asir-6084	58	30	no	no	INTJ
asir-6084	58	31	and	and	CCONJ
asir-6084	58	32	not	not	PART
asir-6084	58	33	all	all	PRON
asir-6084	58	34	)	)	PUNCT
asir-6084	58	35	,	,	PUNCT
asir-6084	58	36	q	q	PUNCT
asir-6084	58	37	and	and	CCONJ
asir-6084	58	38	q	q	PROPN
asir-6084	58	39	for	for	ADP
asir-6084	58	40	the	the	DET
asir-6084	58	41	outer	outer	ADJ
asir-6084	58	42	and	and	CCONJ
asir-6084	58	43	inner	inner	ADJ
asir-6084	58	44	negative	negative	ADJ
asir-6084	58	45	quantifier	quantifier	NOUN
asir-6084	58	46	of	of	ADP
asir-6084	58	47	q	q	NOUN
asir-6084	58	48	,	,	PUNCT
asir-6084	58	49	respectively	respectively	ADV
asir-6084	58	50	.	.	PUNCT
asir-6084	59	1	and	and	CCONJ
asir-6084	59	2	the	the	DET
asir-6084	59	3	symbol	symbol	NOUN
asir-6084	59	4	=	=	NOUN
asir-6084	59	5	def	def	ADJ
asir-6084	59	6	indicates	indicate	VERB
asir-6084	59	7	that	that	SCONJ
asir-6084	59	8	the	the	DET
asir-6084	59	9	left	left	NOUN
asir-6084	59	10	can	can	AUX
asir-6084	59	11	be	be	AUX
asir-6084	59	12	defined	define	VERB
asir-6084	59	13	by	by	ADP
asir-6084	59	14	the	the	DET
asir-6084	59	15	right	right	NOUN
asir-6084	59	16	.	.	PUNCT
asir-6084	60	1	definition	definition	NOUN
asir-6084	60	2	2	2	NUM
asir-6084	60	3	(	(	PUNCT
asir-6084	60	4	inner	inner	ADJ
asir-6084	60	5	negation	negation	NOUN
asir-6084	60	6	):	):	PUNCT
asir-6084	60	7	q(x	q(x	ADJ
asir-6084	60	8	,	,	PUNCT
asir-6084	60	9	z	z	NOUN
asir-6084	60	10	)	)	PUNCT
asir-6084	60	11	=	=	NOUN
asir-6084	60	12	def	def	ADJ
asir-6084	60	13	q(x	q(x	PROPN
asir-6084	60	14	,	,	PUNCT
asir-6084	60	15	dz	dz	PROPN
asir-6084	60	16	)	)	PUNCT
asir-6084	60	17	.	.	PUNCT
asir-6084	61	1	definition	definition	NOUN
asir-6084	61	2	3	3	NUM
asir-6084	61	3	(	(	PUNCT
asir-6084	61	4	outer	outer	ADJ
asir-6084	61	5	negation	negation	NOUN
asir-6084	61	6	):	):	PUNCT
asir-6084	61	7	q(x	q(x	NOUN
asir-6084	61	8	,	,	PUNCT
asir-6084	61	9	z	z	NOUN
asir-6084	61	10	)	)	PUNCT
asir-6084	62	1	=	=	PRON
asir-6084	62	2	def	def	ADJ
asir-6084	62	3	it	it	PRON
asir-6084	62	4	is	be	AUX
asir-6084	62	5	not	not	PART
asir-6084	62	6	that	that	SCONJ
asir-6084	62	7	q(x	q(x	NOUN
asir-6084	62	8	,	,	PUNCT
asir-6084	62	9	z	z	NOUN
asir-6084	62	10	)	)	PUNCT
asir-6084	62	11	.	.	PUNCT
asir-6084	63	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-6084	63	2	applied	apply	VERB
asir-6084	63	3	science	science	NOUN
asir-6084	63	4	and	and	CCONJ
asir-6084	63	5	innovative	innovative	ADJ
asir-6084	63	6	research	research	NOUN
asir-6084	63	7	vol	vol	NOUN
asir-6084	63	8	.	.	PUNCT
asir-6084	64	1	7	7	NUM
asir-6084	64	2	,	,	PUNCT
asir-6084	64	3	no	no	INTJ
asir-6084	64	4	.	.	NOUN
asir-6084	64	5	1	1	NUM
asir-6084	64	6	,	,	PUNCT
asir-6084	64	7	2023	2023	NUM
asir-6084	64	8	49	49	NUM
asir-6084	64	9	published	publish	VERB
asir-6084	64	10	by	by	ADP
asir-6084	64	11	scholink	scholink	PROPN
asir-6084	64	12	inc	inc	PROPN
asir-6084	64	13	.	.	PROPN
asir-6084	64	14	2.2	2.2	NUM
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asir-6084	64	16	facts	fact	NOUN
asir-6084	64	17	fact	fact	NOUN
asir-6084	64	18	1	1	NUM
asir-6084	64	19	(	(	PUNCT
asir-6084	64	20	inner	inner	ADJ
asir-6084	64	21	negation	negation	NOUN
asir-6084	64	22	for	for	ADP
asir-6084	64	23	aristotelian	aristotelian	PROPN
asir-6084	64	24	quantifiers	quantifier	NOUN
asir-6084	64	25	)	)	PUNCT
asir-6084	64	26	(	(	PUNCT
asir-6084	64	27	1	1	X
asir-6084	64	28	)	)	PUNCT
asir-6084	64	29	all(x	all(x	PROPN
asir-6084	64	30	,	,	PUNCT
asir-6084	64	31	z)=no(x	z)=no(x	PROPN
asir-6084	64	32	,	,	PUNCT
asir-6084	64	33	z	z	NOUN
asir-6084	64	34	)	)	PUNCT
asir-6084	64	35	;	;	PUNCT
asir-6084	64	36	(	(	PUNCT
asir-6084	64	37	2	2	X
asir-6084	64	38	)	)	PUNCT
asir-6084	64	39	no(x	no(x	ADJ
asir-6084	64	40	,	,	PUNCT
asir-6084	64	41	z)=all(x	z)=all(x	PROPN
asir-6084	64	42	,	,	PUNCT
asir-6084	64	43	z	z	NOUN
asir-6084	64	44	)	)	PUNCT
asir-6084	64	45	;	;	PUNCT
asir-6084	64	46	(	(	PUNCT
asir-6084	64	47	3	3	X
asir-6084	64	48	)	)	PUNCT
asir-6084	64	49	some(x	some(x	PROPN
asir-6084	64	50	,	,	PUNCT
asir-6084	64	51	z)=not	z)=not	ADV
asir-6084	64	52	all(x	all(x	ADV
asir-6084	64	53	,	,	PUNCT
asir-6084	64	54	z	z	NOUN
asir-6084	64	55	)	)	PUNCT
asir-6084	64	56	;	;	PUNCT
asir-6084	64	57	(	(	PUNCT
asir-6084	64	58	4	4	X
asir-6084	64	59	)	)	PUNCT
asir-6084	64	60	not	not	PART
asir-6084	64	61	all(x	all(x	PROPN
asir-6084	64	62	,	,	PUNCT
asir-6084	64	63	z)=some(x	z)=some(x	PROPN
asir-6084	64	64	,	,	PUNCT
asir-6084	64	65	z	z	NOUN
asir-6084	64	66	)	)	PUNCT
asir-6084	64	67	.	.	PUNCT
asir-6084	65	1	fact	fact	NOUN
asir-6084	65	2	1	1	NUM
asir-6084	65	3	can	can	AUX
asir-6084	65	4	be	be	AUX
asir-6084	65	5	easily	easily	ADV
asir-6084	65	6	proved	prove	VERB
asir-6084	65	7	by	by	ADP
asir-6084	65	8	definition	definition	NOUN
asir-6084	65	9	2	2	NUM
asir-6084	65	10	.	.	PUNCT
asir-6084	66	1	fact	fact	NOUN
asir-6084	66	2	2	2	NUM
asir-6084	66	3	(	(	PUNCT
asir-6084	66	4	outer	outer	ADJ
asir-6084	66	5	negation	negation	NOUN
asir-6084	66	6	for	for	ADP
asir-6084	66	7	aristotelian	aristotelian	ADJ
asir-6084	66	8	quantifiers	quantifier	NOUN
asir-6084	66	9	):	):	PUNCT
asir-6084	66	10	(	(	PUNCT
asir-6084	66	11	1	1	X
asir-6084	66	12	)	)	PUNCT
asir-6084	66	13	not	not	ADV
asir-6084	66	14	all(x	all(x	PROPN
asir-6084	66	15	,	,	PUNCT
asir-6084	66	16	z)=all(x	z)=all(x	PROPN
asir-6084	66	17	,	,	PUNCT
asir-6084	66	18	z	z	NOUN
asir-6084	66	19	)	)	PUNCT
asir-6084	66	20	;	;	PUNCT
asir-6084	66	21	(	(	PUNCT
asir-6084	66	22	2	2	X
asir-6084	66	23	)	)	PUNCT
asir-6084	66	24	all(x	all(x	PROPN
asir-6084	66	25	,	,	PUNCT
asir-6084	66	26	z)=not	z)=not	PROPN
asir-6084	66	27	all(x	all(x	PROPN
asir-6084	66	28	,	,	PUNCT
asir-6084	66	29	z	z	NOUN
asir-6084	66	30	)	)	PUNCT
asir-6084	66	31	;	;	PUNCT
asir-6084	66	32	(	(	PUNCT
asir-6084	66	33	3	3	X
asir-6084	66	34	)	)	PUNCT
asir-6084	66	35	no(x	no(x	PROPN
asir-6084	66	36	,	,	PUNCT
asir-6084	66	37	z)=some(x	z)=some(x	PROPN
asir-6084	66	38	,	,	PUNCT
asir-6084	66	39	z	z	NOUN
asir-6084	66	40	)	)	PUNCT
asir-6084	66	41	;	;	PUNCT
asir-6084	66	42	(	(	PUNCT
asir-6084	66	43	4	4	X
asir-6084	66	44	)	)	PUNCT
asir-6084	66	45	some(x	some(x	NOUN
asir-6084	66	46	,	,	PUNCT
asir-6084	66	47	z)=no(x	z)=no(x	PROPN
asir-6084	66	48	,	,	PUNCT
asir-6084	66	49	z	z	NOUN
asir-6084	66	50	)	)	PUNCT
asir-6084	66	51	.	.	PUNCT
asir-6084	67	1	fact	fact	NOUN
asir-6084	67	2	2	2	NUM
asir-6084	67	3	can	can	AUX
asir-6084	67	4	be	be	AUX
asir-6084	67	5	easily	easily	ADV
asir-6084	67	6	proved	prove	VERB
asir-6084	67	7	by	by	ADP
asir-6084	67	8	definition	definition	NOUN
asir-6084	67	9	3	3	NUM
asir-6084	67	10	.	.	PUNCT
asir-6084	68	1	the	the	DET
asir-6084	68	2	necessary	necessary	ADJ
asir-6084	68	3	modality	modality	NOUN
asir-6084	68	4			NOUN
asir-6084	68	5	and	and	CCONJ
asir-6084	68	6	possible	possible	ADJ
asir-6084	68	7	modality	modality	NOUN
asir-6084	68	8			NOUN
asir-6084	68	9	are	be	AUX
asir-6084	68	10	mutually	mutually	ADV
asir-6084	68	11	dual	dual	ADJ
asir-6084	68	12	.	.	PUNCT
asir-6084	69	1	then	then	ADV
asir-6084	69	2	let	let	VERB
asir-6084	69	3	q(x	q(x	NOUN
asir-6084	69	4	,	,	PUNCT
asir-6084	69	5	z	z	NOUN
asir-6084	69	6	)	)	PUNCT
asir-6084	69	7	is	be	AUX
asir-6084	69	8	a	a	DET
asir-6084	69	9	categorical	categorical	ADJ
asir-6084	69	10	proposition	proposition	NOUN
asir-6084	69	11	,	,	PUNCT
asir-6084	69	12	then	then	ADV
asir-6084	69	13	q(x	q(x	NOUN
asir-6084	69	14	,	,	PUNCT
asir-6084	69	15	z)=def	z)=def	PROPN
asir-6084	69	16	q(x	q(x	NOUN
asir-6084	69	17	,	,	PUNCT
asir-6084	69	18	z	z	NOUN
asir-6084	69	19	)	)	PUNCT
asir-6084	69	20	and	and	CCONJ
asir-6084	69	21	q(x	q(x	ADP
asir-6084	69	22	,	,	PUNCT
asir-6084	69	23	z)=def	z)=def	ADJ
asir-6084	69	24	q(x	q(x	NUM
asir-6084	69	25	,	,	PUNCT
asir-6084	69	26	z	z	NOUN
asir-6084	69	27	)	)	PUNCT
asir-6084	69	28	,	,	PUNCT
asir-6084	69	29	hence	hence	ADV
asir-6084	69	30	,	,	PUNCT
asir-6084	69	31	one	one	PRON
asir-6084	69	32	can	can	AUX
asir-6084	69	33	obtain	obtain	VERB
asir-6084	69	34	the	the	DET
asir-6084	69	35	following	following	ADJ
asir-6084	69	36	fact	fact	NOUN
asir-6084	69	37	3	3	X
asir-6084	69	38	.	.	PUNCT
asir-6084	69	39	fact	fact	NOUN
asir-6084	69	40	3	3	NUM
asir-6084	69	41	:	:	PUNCT
asir-6084	69	42	(	(	PUNCT
asir-6084	69	43	1	1	X
asir-6084	69	44	)	)	PUNCT
asir-6084	69	45	q(x	q(x	NOUN
asir-6084	69	46	,	,	PUNCT
asir-6084	69	47	z)=q(x	z)=q(x	NOUN
asir-6084	69	48	,	,	PUNCT
asir-6084	69	49	z	z	NOUN
asir-6084	69	50	)	)	PUNCT
asir-6084	69	51	;	;	PUNCT
asir-6084	69	52	(	(	PUNCT
asir-6084	69	53	2	2	X
asir-6084	69	54	)	)	PUNCT
asir-6084	69	55	q(x	q(x	PROPN
asir-6084	69	56	,	,	PUNCT
asir-6084	69	57	z	z	NOUN
asir-6084	69	58	)	)	PUNCT
asir-6084	69	59	=	=	SYM
asir-6084	69	60	q(x	q(x	PROPN
asir-6084	69	61	,	,	PUNCT
asir-6084	69	62	z	z	NOUN
asir-6084	69	63	)	)	PUNCT
asir-6084	69	64	.	.	PUNCT
asir-6084	70	1	fact	fact	NOUN
asir-6084	70	2	4	4	NUM
asir-6084	70	3	(	(	PUNCT
asir-6084	70	4	a	a	DET
asir-6084	70	5	necessary	necessary	ADJ
asir-6084	70	6	proposition	proposition	NOUN
asir-6084	70	7	implies	imply	VERB
asir-6084	70	8	an	an	DET
asir-6084	70	9	assertoric	assertoric	ADJ
asir-6084	70	10	proposition	proposition	NOUN
asir-6084	70	11	):	):	PUNCT
asir-6084	70	12	⊢q(x	⊢q(x	NUM
asir-6084	70	13	,	,	PUNCT
asir-6084	70	14	z)q(x	z)q(x	PROPN
asir-6084	70	15	,	,	PUNCT
asir-6084	70	16	z	z	NOUN
asir-6084	70	17	)	)	PUNCT
asir-6084	70	18	.	.	PUNCT
asir-6084	71	1	fact	fact	NOUN
asir-6084	71	2	5	5	NUM
asir-6084	71	3	(	(	PUNCT
asir-6084	71	4	a	a	DET
asir-6084	71	5	necessary	necessary	ADJ
asir-6084	71	6	proposition	proposition	NOUN
asir-6084	71	7	implies	imply	VERB
asir-6084	71	8	a	a	DET
asir-6084	71	9	possible	possible	ADJ
asir-6084	71	10	proposition	proposition	NOUN
asir-6084	71	11	):	):	PUNCT
asir-6084	71	12	⊢q(x	⊢q(x	NUM
asir-6084	71	13	,	,	PUNCT
asir-6084	71	14	z)q(x	z)q(x	NUM
asir-6084	71	15	,	,	PUNCT
asir-6084	71	16	z	z	NOUN
asir-6084	71	17	)	)	PUNCT
asir-6084	71	18	.	.	PUNCT
asir-6084	72	1	fact	fact	NOUN
asir-6084	72	2	6	6	NUM
asir-6084	72	3	(	(	PUNCT
asir-6084	72	4	a	a	DET
asir-6084	72	5	universal	universal	ADJ
asir-6084	72	6	proposition	proposition	NOUN
asir-6084	72	7	implies	imply	VERB
asir-6084	72	8	a	a	DET
asir-6084	72	9	particular	particular	ADJ
asir-6084	72	10	proposition	proposition	NOUN
asir-6084	72	11	):	):	PUNCT
asir-6084	72	12	(	(	PUNCT
asir-6084	72	13	1	1	X
asir-6084	72	14	)	)	PUNCT
asir-6084	72	15	⊢all(x	⊢all(x	PROPN
asir-6084	72	16	,	,	PUNCT
asir-6084	72	17	z)some(x	z)some(x	PROPN
asir-6084	72	18	,	,	PUNCT
asir-6084	72	19	z	z	NOUN
asir-6084	72	20	)	)	PUNCT
asir-6084	72	21	;	;	PUNCT
asir-6084	72	22	(	(	PUNCT
asir-6084	72	23	2)⊢no(x	2)⊢no(x	NUM
asir-6084	72	24	,	,	PUNCT
asir-6084	72	25	z)not	z)not	PROPN
asir-6084	72	26	all(x	all(x	PROPN
asir-6084	72	27	,	,	PUNCT
asir-6084	72	28	z	z	NOUN
asir-6084	72	29	)	)	PUNCT
asir-6084	72	30	.	.	PUNCT
asir-6084	73	1	fact	fact	NOUN
asir-6084	73	2	7	7	NUM
asir-6084	73	3	(	(	PUNCT
asir-6084	73	4	symmetry	symmetry	NOUN
asir-6084	73	5	of	of	ADP
asir-6084	73	6	some	some	PRON
asir-6084	73	7	and	and	CCONJ
asir-6084	73	8	no	no	NOUN
asir-6084	73	9	):	):	PUNCT
asir-6084	73	10	(	(	PUNCT
asir-6084	73	11	1	1	X
asir-6084	73	12	)	)	PUNCT
asir-6084	73	13	some(x	some(x	PROPN
asir-6084	73	14	,	,	PUNCT
asir-6084	73	15	z)some(z	z)some(z	PROPN
asir-6084	73	16	,	,	PUNCT
asir-6084	73	17	x	x	NOUN
asir-6084	73	18	)	)	PUNCT
asir-6084	73	19	;	;	PUNCT
asir-6084	73	20	(	(	PUNCT
asir-6084	73	21	2	2	X
asir-6084	73	22	)	)	PUNCT
asir-6084	73	23	no(x	no(x	ADJ
asir-6084	73	24	,	,	PUNCT
asir-6084	73	25	z)no(z	z)no(z	NOUN
asir-6084	73	26	,	,	PUNCT
asir-6084	73	27	x	x	NOUN
asir-6084	73	28	)	)	PUNCT
asir-6084	73	29	.	.	PUNCT
asir-6084	74	1	all	all	PRON
asir-6084	74	2	of	of	ADP
asir-6084	74	3	the	the	DET
asir-6084	74	4	above	above	ADJ
asir-6084	74	5	facts	fact	NOUN
asir-6084	74	6	are	be	AUX
asir-6084	74	7	the	the	DET
asir-6084	74	8	general	general	ADJ
asir-6084	74	9	knowledge	knowledge	NOUN
asir-6084	74	10	of	of	ADP
asir-6084	74	11	generalized	generalized	ADJ
asir-6084	74	12	quantifier	quantifier	NOUN
asir-6084	74	13	theory	theory	NOUN
asir-6084	74	14	(	(	PUNCT
asir-6084	74	15	zhang	zhang	PROPN
asir-6084	74	16	,	,	PUNCT
asir-6084	74	17	2018	2018	NUM
asir-6084	74	18	)	)	PUNCT
asir-6084	74	19	or	or	CCONJ
asir-6084	74	20	modal	modal	ADJ
asir-6084	74	21	logic	logic	NOUN
asir-6084	74	22	(	(	PUNCT
asir-6084	74	23	zhang	zhang	PROPN
asir-6084	74	24	,	,	PUNCT
asir-6084	74	25	2020b	2020b	NUM
asir-6084	74	26	)	)	PUNCT
asir-6084	74	27	,	,	PUNCT
asir-6084	74	28	thus	thus	ADV
asir-6084	74	29	their	their	PRON
asir-6084	74	30	proofs	proof	NOUN
asir-6084	74	31	are	be	AUX
asir-6084	74	32	omitted	omit	VERB
asir-6084	74	33	here	here	ADV
asir-6084	74	34	.	.	PUNCT
asir-6084	75	1	2.3	2.3	NUM
asir-6084	75	2	relevant	relevant	ADJ
asir-6084	75	3	inference	inference	NOUN
asir-6084	75	4	rules	rule	NOUN
asir-6084	75	5	aristotelian	aristotelian	PROPN
asir-6084	75	6	modal	modal	ADJ
asir-6084	75	7	syllogistic	syllogistic	NOUN
asir-6084	75	8	is	be	AUX
asir-6084	75	9	an	an	DET
asir-6084	75	10	extension	extension	NOUN
asir-6084	75	11	of	of	ADP
asir-6084	75	12	classical	classical	ADJ
asir-6084	75	13	propositional	propositional	ADJ
asir-6084	75	14	logic	logic	NOUN
asir-6084	75	15	(	(	PUNCT
asir-6084	75	16	hamilton	hamilton	PROPN
asir-6084	75	17	,	,	PUNCT
asir-6084	75	18	1978	1978	NUM
asir-6084	75	19	)	)	PUNCT
asir-6084	75	20	,	,	PUNCT
asir-6084	75	21	and	and	CCONJ
asir-6084	75	22	the	the	DET
asir-6084	75	23	reasoning	reasoning	NOUN
asir-6084	75	24	rules	rule	NOUN
asir-6084	75	25	of	of	ADP
asir-6084	75	26	the	the	DET
asir-6084	75	27	latter	latter	ADJ
asir-6084	75	28	are	be	AUX
asir-6084	75	29	also	also	ADV
asir-6084	75	30	applicable	applicable	ADJ
asir-6084	75	31	to	to	ADP
asir-6084	75	32	the	the	DET
asir-6084	75	33	former	former	NOUN
asir-6084	75	34	.	.	PUNCT
asir-6084	76	1	the	the	DET
asir-6084	76	2	following	follow	VERB
asir-6084	76	3	rules	rule	NOUN
asir-6084	76	4	are	be	AUX
asir-6084	76	5	the	the	DET
asir-6084	76	6	basic	basic	ADJ
asir-6084	76	7	rules	rule	NOUN
asir-6084	76	8	of	of	ADP
asir-6084	76	9	propositional	propositional	ADJ
asir-6084	76	10	logic	logic	NOUN
asir-6084	76	11	,	,	PUNCT
asir-6084	76	12	in	in	ADP
asir-6084	76	13	which	which	PRON
asir-6084	76	14	p	p	X
asir-6084	76	15	,	,	PUNCT
asir-6084	76	16	q	q	ADJ
asir-6084	76	17	,	,	PUNCT
asir-6084	76	18	r	r	NOUN
asir-6084	76	19	and	and	CCONJ
asir-6084	76	20	s	s	NOUN
asir-6084	76	21	are	be	AUX
asir-6084	76	22	propositions	proposition	NOUN
asir-6084	76	23	.	.	PUNCT
asir-6084	77	1	(	(	PUNCT
asir-6084	77	2	1	1	X
asir-6084	77	3	)	)	PUNCT
asir-6084	77	4	rule	rule	NOUN
asir-6084	77	5	1	1	NUM
asir-6084	77	6	(	(	PUNCT
asir-6084	77	7	subsequent	subsequent	ADJ
asir-6084	77	8	weakening	weakening	NOUN
asir-6084	77	9	):	):	PUNCT
asir-6084	77	10	if	if	SCONJ
asir-6084	77	11	⊢(pqr	⊢(pqr	NOUN
asir-6084	77	12	)	)	PUNCT
asir-6084	77	13	and	and	CCONJ
asir-6084	77	14	⊢(rs	⊢(r	NOUN
asir-6084	77	15	)	)	PUNCT
asir-6084	77	16	,	,	PUNCT
asir-6084	77	17	then	then	ADV
asir-6084	77	18	⊢(pqs	⊢(pqs	PROPN
asir-6084	77	19	)	)	PUNCT
asir-6084	77	20	.	.	PUNCT
asir-6084	78	1	(	(	PUNCT
asir-6084	78	2	2	2	X
asir-6084	78	3	)	)	PUNCT
asir-6084	78	4	rule	rule	NOUN
asir-6084	78	5	2	2	NUM
asir-6084	78	6	(	(	PUNCT
asir-6084	78	7	anti	anti	ADJ
asir-6084	78	8	-	-	NOUN
asir-6084	78	9	syllogism	syllogism	NOUN
asir-6084	78	10	):	):	PUNCT
asir-6084	78	11	if	if	SCONJ
asir-6084	78	12	⊢(pqr	⊢(pqr	PROPN
asir-6084	78	13	)	)	PUNCT
asir-6084	78	14	,	,	PUNCT
asir-6084	78	15	then	then	ADV
asir-6084	78	16	⊢(rpq	⊢(rpq	PROPN
asir-6084	78	17	)	)	PUNCT
asir-6084	78	18	or	or	CCONJ
asir-6084	78	19	⊢(rqp	⊢(rqp	NOUN
asir-6084	78	20	)	)	PUNCT
asir-6084	78	21	.	.	PUNCT
asir-6084	79	1	3	3	X
asir-6084	79	2	.	.	X
asir-6084	79	3	reduction	reduction	NOUN
asir-6084	79	4	between	between	ADP
asir-6084	79	5	the	the	DET
asir-6084	79	6	modal	modal	ADJ
asir-6084	79	7	syllogism	syllogism	NOUN
asir-6084	79	8	iai-3	iai-3	NOUN
asir-6084	79	9	and	and	CCONJ
asir-6084	79	10	other	other	ADJ
asir-6084	79	11	valid	valid	ADJ
asir-6084	79	12	modal	modal	ADJ
asir-6084	79	13	syllogisms	syllogism	NOUN
asir-6084	79	14	there	there	PRON
asir-6084	79	15	is	be	VERB
asir-6084	79	16	reducibility	reducibility	NOUN
asir-6084	79	17	between	between	ADP
asir-6084	79	18	valid	valid	ADJ
asir-6084	79	19	aristotelian	aristotelian	ADJ
asir-6084	79	20	syllogisms	syllogism	NOUN
asir-6084	79	21	of	of	ADP
asir-6084	79	22	different	different	ADJ
asir-6084	79	23	figures	figure	NOUN
asir-6084	79	24	and	and	CCONJ
asir-6084	79	25	forms	form	NOUN
asir-6084	79	26	,	,	PUNCT
asir-6084	79	27	similarly	similarly	ADV
asir-6084	79	28	,	,	PUNCT
asir-6084	79	29	there	there	PRON
asir-6084	79	30	is	be	VERB
asir-6084	79	31	also	also	ADV
asir-6084	79	32	reducibility	reducibility	NOUN
asir-6084	79	33	between	between	ADP
asir-6084	79	34	valid	valid	ADJ
asir-6084	79	35	aristotelian	aristotelian	ADJ
asir-6084	79	36	modal	modal	NOUN
asir-6084	79	37	syllogisms	syllogism	NOUN
asir-6084	79	38	of	of	ADP
asir-6084	79	39	different	different	ADJ
asir-6084	79	40	figures	figure	NOUN
asir-6084	79	41	and	and	CCONJ
asir-6084	79	42	forms	form	NOUN
asir-6084	79	43	.	.	PUNCT
asir-6084	80	1	according	accord	VERB
asir-6084	80	2	to	to	ADP
asir-6084	80	3	the	the	DET
asir-6084	80	4	following	follow	VERB
asir-6084	80	5	theorem	theorem	NOUN
asir-6084	80	6	1	1	NUM
asir-6084	80	7	,	,	PUNCT
asir-6084	80	8	the	the	DET
asir-6084	80	9	modal	modal	ADJ
asir-6084	80	10	syllogism	syllogism	NOUN
asir-6084	80	11	iai-3	iai-3	ADJ
asir-6084	80	12	is	be	AUX
asir-6084	80	13	valid	valid	ADJ
asir-6084	80	14	,	,	PUNCT
asir-6084	80	15	therefore	therefore	ADV
asir-6084	80	16	,	,	PUNCT
asir-6084	80	17	all	all	DET
asir-6084	80	18	the	the	DET
asir-6084	80	19	following	follow	VERB
asir-6084	80	20	syllogisms	syllogism	NOUN
asir-6084	80	21	derived	derive	VERB
asir-6084	80	22	from	from	ADP
asir-6084	80	23	this	this	DET
asir-6084	80	24	syllogism	syllogism	NOUN
asir-6084	80	25	are	be	AUX
asir-6084	80	26	valid	valid	ADJ
asir-6084	80	27	.	.	PUNCT
asir-6084	81	1	in	in	ADP
asir-6084	81	2	the	the	DET
asir-6084	81	3	following	follow	VERB
asir-6084	81	4	theorem	theorem	ADJ
asir-6084	81	5	2	2	NUM
asir-6084	81	6	,	,	PUNCT
asir-6084	81	7	iai-3iai-4	iai-3iai-4	PROPN
asir-6084	81	8	means	mean	VERB
asir-6084	81	9	that	that	SCONJ
asir-6084	81	10	the	the	DET
asir-6084	81	11	validity	validity	NOUN
asir-6084	81	12	of	of	ADP
asir-6084	81	13	syllogism	syllogism	NOUN
asir-6084	81	14	iai-4	iai-4	NOUN
asir-6084	81	15	can	can	AUX
asir-6084	81	16	be	be	AUX
asir-6084	81	17	deduced	deduce	VERB
asir-6084	81	18	from	from	ADP
asir-6084	81	19	the	the	DET
asir-6084	81	20	validity	validity	NOUN
asir-6084	81	21	of	of	ADP
asir-6084	81	22	syllogism	syllogism	NOUN
asir-6084	81	23	iai-3	iai-3	ADJ
asir-6084	81	24	,	,	PUNCT
asir-6084	81	25	hence	hence	ADV
asir-6084	81	26	one	one	PRON
asir-6084	81	27	can	can	AUX
asir-6084	81	28	say	say	VERB
asir-6084	81	29	that	that	SCONJ
asir-6084	81	30	there	there	PRON
asir-6084	81	31	is	be	VERB
asir-6084	81	32	reducibility	reducibility	NOUN
asir-6084	81	33	between	between	ADP
asir-6084	81	34	the	the	DET
asir-6084	81	35	two	two	NUM
asir-6084	81	36	syllogisms	syllogism	NOUN
asir-6084	81	37	.	.	PUNCT
asir-6084	82	1	other	other	ADJ
asir-6084	82	2	cases	case	NOUN
asir-6084	82	3	are	be	AUX
asir-6084	82	4	similar	similar	ADJ
asir-6084	82	5	.	.	PUNCT
asir-6084	83	1	theorem	theorem	ADJ
asir-6084	83	2	1	1	NUM
asir-6084	83	3	(	(	PUNCT
asir-6084	83	4	iai-3	iai-3	ADJ
asir-6084	83	5	):	):	PUNCT
asir-6084	83	6	some(y	some(y	ADJ
asir-6084	83	7	,	,	PUNCT
asir-6084	83	8	z)all(y	z)all(y	PROPN
asir-6084	83	9	,	,	PUNCT
asir-6084	83	10	x)some(x	x)some(x	PROPN
asir-6084	83	11	,	,	PUNCT
asir-6084	83	12	z	z	NOUN
asir-6084	83	13	)	)	PUNCT
asir-6084	83	14	is	be	AUX
asir-6084	83	15	valid	valid	ADJ
asir-6084	83	16	.	.	PUNCT
asir-6084	84	1	proof	proof	NOUN
asir-6084	84	2	:	:	PUNCT
asir-6084	84	3	according	accord	VERB
asir-6084	84	4	to	to	ADP
asir-6084	84	5	example	example	NOUN
asir-6084	84	6	1	1	NUM
asir-6084	84	7	,	,	PUNCT
asir-6084	84	8	iai-3	iai-3	NOUN
asir-6084	84	9	is	be	AUX
asir-6084	84	10	the	the	DET
asir-6084	84	11	abbreviation	abbreviation	NOUN
asir-6084	84	12	of	of	ADP
asir-6084	84	13	the	the	DET
asir-6084	84	14	third	third	ADJ
asir-6084	84	15	figure	figure	NOUN
asir-6084	84	16	syllogism	syllogism	NOUN
asir-6084	84	17	some(y	some(y	ADJ
asir-6084	84	18	,	,	PUNCT
asir-6084	84	19	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-6084	84	20	applied	apply	VERB
asir-6084	84	21	science	science	NOUN
asir-6084	84	22	and	and	CCONJ
asir-6084	84	23	innovative	innovative	ADJ
asir-6084	84	24	research	research	NOUN
asir-6084	84	25	vol	vol	NOUN
asir-6084	84	26	.	.	PUNCT
asir-6084	85	1	7	7	NUM
asir-6084	85	2	,	,	PUNCT
asir-6084	85	3	no	no	INTJ
asir-6084	85	4	.	.	NOUN
asir-6084	85	5	1	1	NUM
asir-6084	85	6	,	,	PUNCT
asir-6084	85	7	2023	2023	NUM
asir-6084	85	8	50	50	NUM
asir-6084	85	9	published	publish	VERB
asir-6084	85	10	by	by	ADP
asir-6084	85	11	scholink	scholink	PROPN
asir-6084	85	12	inc	inc	PROPN
asir-6084	85	13	.	.	PROPN
asir-6084	85	14	z)all(y	z)all(y	PROPN
asir-6084	85	15	,	,	PUNCT
asir-6084	85	16	x)	x)	PROPN
asir-6084	85	17	some(x	some(x	PROPN
asir-6084	85	18	,	,	PUNCT
asir-6084	85	19	z	z	NOUN
asir-6084	85	20	)	)	PUNCT
asir-6084	85	21	.	.	PUNCT
asir-6084	86	1	suppose	suppose	VERB
asir-6084	86	2	that	that	SCONJ
asir-6084	86	3	some(y	some(y	ADJ
asir-6084	86	4	,	,	PUNCT
asir-6084	86	5	z	z	NOUN
asir-6084	86	6	)	)	PUNCT
asir-6084	86	7	and	and	CCONJ
asir-6084	86	8	all(y	all(y	PROPN
asir-6084	86	9	,	,	PUNCT
asir-6084	86	10	x	x	X
asir-6084	86	11	)	)	PUNCT
asir-6084	86	12	are	be	AUX
asir-6084	86	13	true	true	ADJ
asir-6084	86	14	,	,	PUNCT
asir-6084	86	15	then	then	ADV
asir-6084	86	16	y∩z	y∩z	PROPN
asir-6084	86	17	and	and	CCONJ
asir-6084	86	18	yx	yx	NOUN
asir-6084	86	19	is	be	AUX
asir-6084	86	20	true	true	ADJ
asir-6084	86	21	at	at	ADP
asir-6084	86	22	any	any	DET
asir-6084	86	23	possible	possible	ADJ
asir-6084	86	24	world	world	NOUN
asir-6084	86	25	in	in	ADP
asir-6084	86	26	terms	term	NOUN
asir-6084	86	27	of	of	ADP
asir-6084	86	28	the	the	DET
asir-6084	86	29	clause	clause	NOUN
asir-6084	86	30	(	(	PUNCT
asir-6084	86	31	7	7	NUM
asir-6084	86	32	)	)	PUNCT
asir-6084	86	33	and	and	CCONJ
asir-6084	86	34	(	(	PUNCT
asir-6084	86	35	5	5	NUM
asir-6084	86	36	)	)	PUNCT
asir-6084	86	37	in	in	ADP
asir-6084	86	38	definition	definition	NOUN
asir-6084	86	39	1	1	NUM
asir-6084	86	40	.	.	PUNCT
asir-6084	87	1	now	now	ADV
asir-6084	87	2	it	it	PRON
asir-6084	87	3	follows	follow	VERB
asir-6084	87	4	that	that	SCONJ
asir-6084	87	5	x∩z	x∩z	PROPN
asir-6084	87	6	is	be	AUX
asir-6084	87	7	true	true	ADJ
asir-6084	87	8	at	at	ADP
asir-6084	87	9	every	every	DET
asir-6084	87	10	possible	possible	ADJ
asir-6084	87	11	world	world	NOUN
asir-6084	87	12	.	.	PUNCT
asir-6084	88	1	hence	hence	ADV
asir-6084	88	2	some(x	some(x	ADV
asir-6084	88	3	,	,	PUNCT
asir-6084	88	4	z	z	NOUN
asir-6084	88	5	)	)	PUNCT
asir-6084	88	6	is	be	AUX
asir-6084	88	7	true	true	ADJ
asir-6084	88	8	according	accord	VERB
asir-6084	88	9	to	to	ADP
asir-6084	88	10	the	the	DET
asir-6084	88	11	clause	clause	NOUN
asir-6084	88	12	(	(	PUNCT
asir-6084	88	13	7	7	NUM
asir-6084	88	14	)	)	PUNCT
asir-6084	88	15	in	in	ADP
asir-6084	88	16	definition	definition	NOUN
asir-6084	88	17	1	1	NUM
asir-6084	88	18	again	again	ADV
asir-6084	88	19	.	.	PUNCT
asir-6084	89	1	this	this	PRON
asir-6084	89	2	proves	prove	VERB
asir-6084	89	3	the	the	DET
asir-6084	89	4	claim	claim	NOUN
asir-6084	89	5	that	that	SCONJ
asir-6084	89	6	the	the	DET
asir-6084	89	7	third	third	ADJ
asir-6084	89	8	figure	figure	NOUN
asir-6084	89	9	syllogism	syllogism	NOUN
asir-6084	89	10	some(y	some(y	ADJ
asir-6084	89	11	,	,	PUNCT
asir-6084	89	12	z)all(y	z)all(y	PROPN
asir-6084	89	13	,	,	PUNCT
asir-6084	89	14	x)some(x	x)some(x	PROPN
asir-6084	89	15	,	,	PUNCT
asir-6084	89	16	z	z	NOUN
asir-6084	89	17	)	)	PUNCT
asir-6084	89	18	is	be	AUX
asir-6084	89	19	valid	valid	ADJ
asir-6084	89	20	,	,	PUNCT
asir-6084	89	21	just	just	ADV
asir-6084	89	22	as	as	SCONJ
asir-6084	89	23	desired	desire	VERB
asir-6084	89	24	.	.	PUNCT
asir-6084	90	1	theorem	theorem	VERB
asir-6084	90	2	2	2	NUM
asir-6084	90	3	:	:	PUNCT
asir-6084	90	4	the	the	DET
asir-6084	90	5	following	follow	VERB
asir-6084	90	6	valid	valid	ADJ
asir-6084	90	7	modal	modal	ADJ
asir-6084	90	8	syllogisms	syllogism	NOUN
asir-6084	90	9	can	can	AUX
asir-6084	90	10	be	be	AUX
asir-6084	90	11	deduced	deduce	VERB
asir-6084	90	12	from	from	ADP
asir-6084	90	13	iai-3	iai-3	NOUN
asir-6084	90	14	:	:	PUNCT
asir-6084	90	15	(	(	PUNCT
asir-6084	90	16	2.1	2.1	NUM
asir-6084	90	17	)	)	PUNCT
asir-6084	90	18	iai-3iai-3	iai-3iai-3	NOUN
asir-6084	90	19	(	(	PUNCT
asir-6084	90	20	2.2	2.2	NUM
asir-6084	90	21	)	)	PUNCT
asir-6084	90	22	iai-3iai-3	iai-3iai-3	PROPN
asir-6084	90	23	proof	proof	NOUN
asir-6084	90	24	:	:	PUNCT
asir-6084	90	25	for	for	ADP
asir-6084	90	26	(	(	PUNCT
asir-6084	90	27	2.1	2.1	NUM
asir-6084	90	28	)	)	PUNCT
asir-6084	90	29	.	.	PUNCT
asir-6084	91	1	as	as	SCONJ
asir-6084	91	2	pointed	point	VERB
asir-6084	91	3	out	out	ADP
asir-6084	91	4	earlier	early	ADV
asir-6084	91	5	,	,	PUNCT
asir-6084	91	6	iai-3	iai-3	NOUN
asir-6084	91	7	is	be	AUX
asir-6084	91	8	valid	valid	ADJ
asir-6084	91	9	,	,	PUNCT
asir-6084	91	10	which	which	PRON
asir-6084	91	11	is	be	AUX
asir-6084	91	12	the	the	DET
asir-6084	91	13	abbreviation	abbreviation	NOUN
asir-6084	91	14	of	of	ADP
asir-6084	91	15	the	the	DET
asir-6084	91	16	modal	modal	ADJ
asir-6084	91	17	syllogism	syllogism	NOUN
asir-6084	91	18	some(y	some(y	ADJ
asir-6084	91	19	,	,	PUNCT
asir-6084	91	20	z)all(y	z)all(y	PROPN
asir-6084	91	21	,	,	PUNCT
asir-6084	91	22	x)some(x	x)some(x	PROPN
asir-6084	91	23	,	,	PUNCT
asir-6084	91	24	z	z	NOUN
asir-6084	91	25	)	)	PUNCT
asir-6084	91	26	.	.	PUNCT
asir-6084	92	1	according	accord	VERB
asir-6084	92	2	to	to	ADP
asir-6084	92	3	fact	fact	NOUN
asir-6084	92	4	4	4	NUM
asir-6084	92	5	:	:	PUNCT
asir-6084	92	6	some(x	some(x	ADJ
asir-6084	92	7	,	,	PUNCT
asir-6084	92	8	z)some(x	z)some(x	PROPN
asir-6084	92	9	,	,	PUNCT
asir-6084	92	10	z	z	NOUN
asir-6084	92	11	)	)	PUNCT
asir-6084	92	12	.	.	PUNCT
asir-6084	93	1	then	then	ADV
asir-6084	93	2	on	on	ADP
asir-6084	93	3	the	the	DET
asir-6084	93	4	basis	basis	NOUN
asir-6084	93	5	of	of	ADP
asir-6084	93	6	rule	rule	NOUN
asir-6084	93	7	1	1	NUM
asir-6084	93	8	,	,	PUNCT
asir-6084	93	9	it	it	PRON
asir-6084	93	10	follows	follow	VERB
asir-6084	93	11	that	that	SCONJ
asir-6084	93	12	some(y	some(y	ADJ
asir-6084	93	13	,	,	PUNCT
asir-6084	93	14	z)all(y	z)all(y	PROPN
asir-6084	93	15	,	,	PUNCT
asir-6084	93	16	x)some(x	x)some(x	PROPN
asir-6084	93	17	,	,	PUNCT
asir-6084	93	18	z	z	NOUN
asir-6084	93	19	)	)	PUNCT
asir-6084	93	20	from	from	ADP
asir-6084	93	21	iai-3	iai-3	NOUN
asir-6084	93	22	.	.	PUNCT
asir-6084	94	1	in	in	ADP
asir-6084	94	2	other	other	ADJ
asir-6084	94	3	words	word	NOUN
asir-6084	94	4	,	,	PUNCT
asir-6084	94	5	the	the	DET
asir-6084	94	6	modal	modal	ADJ
asir-6084	94	7	syllogism	syllogism	NOUN
asir-6084	94	8	iai-3	iai-3	PROPN
asir-6084	94	9	is	be	AUX
asir-6084	94	10	valid	valid	ADJ
asir-6084	94	11	,	,	PUNCT
asir-6084	94	12	as	as	SCONJ
asir-6084	94	13	required	require	VERB
asir-6084	94	14	.	.	PUNCT
asir-6084	95	1	the	the	DET
asir-6084	95	2	proof	proof	NOUN
asir-6084	95	3	of	of	ADP
asir-6084	95	4	(	(	PUNCT
asir-6084	95	5	2.2	2.2	NUM
asir-6084	95	6	)	)	PUNCT
asir-6084	95	7	is	be	AUX
asir-6084	95	8	similar	similar	ADJ
asir-6084	95	9	to	to	ADP
asir-6084	95	10	that	that	PRON
asir-6084	95	11	of	of	ADP
asir-6084	95	12	(	(	PUNCT
asir-6084	95	13	2.1	2.1	NUM
asir-6084	95	14	)	)	PUNCT
asir-6084	95	15	,	,	PUNCT
asir-6084	95	16	except	except	SCONJ
asir-6084	95	17	that	that	SCONJ
asir-6084	95	18	it	it	PRON
asir-6084	95	19	needs	need	VERB
asir-6084	95	20	to	to	PART
asir-6084	95	21	be	be	AUX
asir-6084	95	22	based	base	VERB
asir-6084	95	23	on	on	ADP
asir-6084	95	24	fact	fact	NOUN
asir-6084	95	25	5	5	NUM
asir-6084	95	26	instead	instead	ADV
asir-6084	95	27	of	of	ADP
asir-6084	95	28	fact	fact	NOUN
asir-6084	95	29	4	4	NUM
asir-6084	95	30	.	.	PUNCT
asir-6084	95	31	theorem	theorem	NOUN
asir-6084	95	32	3	3	NUM
asir-6084	95	33	:	:	PUNCT
asir-6084	95	34	the	the	DET
asir-6084	95	35	following	follow	VERB
asir-6084	95	36	valid	valid	ADJ
asir-6084	95	37	modal	modal	ADJ
asir-6084	95	38	syllogisms	syllogism	NOUN
asir-6084	95	39	can	can	AUX
asir-6084	95	40	be	be	AUX
asir-6084	95	41	deduced	deduce	VERB
asir-6084	95	42	from	from	ADP
asir-6084	95	43	iai-3	iai-3	NOUN
asir-6084	95	44	:	:	PUNCT
asir-6084	95	45	(	(	PUNCT
asir-6084	95	46	3.1	3.1	NUM
asir-6084	95	47	)	)	PUNCT
asir-6084	95	48	iai-3oao-3oao-3oao-3	iai-3oao-3oao-3oao-3	NUM
asir-6084	95	49	(	(	PUNCT
asir-6084	95	50	3.2	3.2	NUM
asir-6084	95	51	)	)	PUNCT
asir-6084	95	52	iai-3aii-3eio-3	iai-3aii-3eio-3	PUNCT
asir-6084	96	1	proof	proof	NOUN
asir-6084	96	2	:	:	PUNCT
asir-6084	96	3	for	for	ADP
asir-6084	96	4	(	(	PUNCT
asir-6084	96	5	3.1	3.1	NUM
asir-6084	96	6	)	)	PUNCT
asir-6084	96	7	.	.	PUNCT
asir-6084	97	1	according	accord	VERB
asir-6084	97	2	to	to	ADP
asir-6084	97	3	the	the	DET
asir-6084	97	4	clause	clause	NOUN
asir-6084	97	5	(	(	PUNCT
asir-6084	97	6	3	3	NUM
asir-6084	97	7	)	)	PUNCT
asir-6084	97	8	in	in	ADP
asir-6084	97	9	fact	fact	NOUN
asir-6084	97	10	1	1	NUM
asir-6084	97	11	,	,	PUNCT
asir-6084	97	12	some(y	some(y	VERB
asir-6084	97	13	,	,	PUNCT
asir-6084	97	14	z)=not	z)=not	NOUN
asir-6084	97	15	all(y	all(y	ADP
asir-6084	97	16	,	,	PUNCT
asir-6084	97	17	z	z	NOUN
asir-6084	97	18	)	)	PUNCT
asir-6084	97	19	,	,	PUNCT
asir-6084	97	20	and	and	CCONJ
asir-6084	97	21	some(x	some(x	VERB
asir-6084	97	22	,	,	PUNCT
asir-6084	97	23	z)=not	z)=not	ADV
asir-6084	97	24	all(x	all(x	ADV
asir-6084	97	25	,	,	PUNCT
asir-6084	97	26	z	z	NOUN
asir-6084	97	27	)	)	PUNCT
asir-6084	97	28	,	,	PUNCT
asir-6084	97	29	it	it	PRON
asir-6084	97	30	follows	follow	VERB
asir-6084	97	31	that	that	SCONJ
asir-6084	97	32	not	not	ADV
asir-6084	97	33	all(y	all(y	NOUN
asir-6084	97	34	,	,	PUNCT
asir-6084	97	35	z)all(y	z)all(y	PROPN
asir-6084	97	36	,	,	PUNCT
asir-6084	97	37	x)not	x)not	ADV
asir-6084	97	38	all(x	all(x	ADV
asir-6084	97	39	,	,	PUNCT
asir-6084	97	40	z	z	NOUN
asir-6084	97	41	)	)	PUNCT
asir-6084	97	42	from	from	ADP
asir-6084	97	43	iai-3	iai-3	NOUN
asir-6084	97	44	.	.	PUNCT
asir-6084	98	1	according	accord	VERB
asir-6084	98	2	to	to	ADP
asir-6084	98	3	definition	definition	NOUN
asir-6084	98	4	2	2	NUM
asir-6084	98	5	,	,	PUNCT
asir-6084	98	6	not	not	PART
asir-6084	98	7	all(y	all(y	ADV
asir-6084	98	8	,	,	PUNCT
asir-6084	98	9	z)=not	z)=not	PROPN
asir-6084	98	10	all(y	all(y	PROPN
asir-6084	98	11	,	,	PUNCT
asir-6084	98	12	dz	dz	NOUN
asir-6084	98	13	)	)	PUNCT
asir-6084	98	14	,	,	PUNCT
asir-6084	98	15	not	not	PART
asir-6084	98	16	all(x	all(x	ADV
asir-6084	98	17	,	,	PUNCT
asir-6084	98	18	z)=not	z)=not	PROPN
asir-6084	98	19	all(x	all(x	PROPN
asir-6084	98	20	,	,	PUNCT
asir-6084	98	21	dz	dz	NOUN
asir-6084	98	22	)	)	PUNCT
asir-6084	98	23	.	.	PUNCT
asir-6084	99	1	therefore	therefore	ADV
asir-6084	99	2	,	,	PUNCT
asir-6084	99	3	one	one	PRON
asir-6084	99	4	can	can	AUX
asir-6084	99	5	derive	derive	VERB
asir-6084	99	6	that	that	SCONJ
asir-6084	99	7	not	not	CCONJ
asir-6084	99	8	all(y	all(y	PROPN
asir-6084	99	9	,	,	PUNCT
asir-6084	99	10	dz)all(y	dz)all(y	PROPN
asir-6084	99	11	,	,	PUNCT
asir-6084	99	12	x)not	x)not	PRON
asir-6084	99	13	all(x	all(x	PROPN
asir-6084	99	14	,	,	PUNCT
asir-6084	99	15	dz	dz	NOUN
asir-6084	99	16	)	)	PUNCT
asir-6084	99	17	.	.	PUNCT
asir-6084	100	1	in	in	ADP
asir-6084	100	2	other	other	ADJ
asir-6084	100	3	words	word	NOUN
asir-6084	100	4	,	,	PUNCT
asir-6084	100	5	the	the	DET
asir-6084	100	6	syllogism	syllogism	NOUN
asir-6084	100	7	oao-3	oao-3	PROPN
asir-6084	100	8	can	can	AUX
asir-6084	100	9	be	be	AUX
asir-6084	100	10	deduced	deduce	VERB
asir-6084	100	11	from	from	ADP
asir-6084	100	12	iai-3	iai-3	NOUN
asir-6084	100	13	,	,	PUNCT
asir-6084	100	14	just	just	ADV
asir-6084	100	15	as	as	SCONJ
asir-6084	100	16	desired	desire	VERB
asir-6084	100	17	.	.	PUNCT
asir-6084	101	1	with	with	ADP
asir-6084	101	2	the	the	DET
asir-6084	101	3	help	help	NOUN
asir-6084	101	4	of	of	ADP
asir-6084	101	5	fact	fact	NOUN
asir-6084	101	6	4	4	NUM
asir-6084	101	7	and	and	CCONJ
asir-6084	101	8	fact	fact	NOUN
asir-6084	101	9	5	5	NUM
asir-6084	101	10	,	,	PUNCT
asir-6084	101	11	it	it	PRON
asir-6084	101	12	is	be	AUX
asir-6084	101	13	easily	easily	ADV
asir-6084	101	14	seen	see	VERB
asir-6084	101	15	that	that	SCONJ
asir-6084	101	16	oo	oo	PROPN
asir-6084	101	17	and	and	CCONJ
asir-6084	101	18	oo	oo	NOUN
asir-6084	101	19	,	,	PUNCT
asir-6084	101	20	hence	hence	ADV
asir-6084	101	21	(	(	PUNCT
asir-6084	101	22	3.1	3.1	NUM
asir-6084	101	23	)	)	PUNCT
asir-6084	101	24	can	can	AUX
asir-6084	101	25	be	be	AUX
asir-6084	101	26	proved	prove	VERB
asir-6084	101	27	according	accord	VERB
asir-6084	101	28	to	to	PART
asir-6084	101	29	rule	rule	VERB
asir-6084	101	30	1	1	NUM
asir-6084	101	31	.	.	PUNCT
asir-6084	102	1	the	the	DET
asir-6084	102	2	proof	proof	NOUN
asir-6084	102	3	of	of	ADP
asir-6084	102	4	(	(	PUNCT
asir-6084	102	5	3.2	3.2	NUM
asir-6084	102	6	)	)	PUNCT
asir-6084	102	7	is	be	AUX
asir-6084	102	8	similar	similar	ADJ
asir-6084	102	9	to	to	ADP
asir-6084	102	10	that	that	PRON
asir-6084	102	11	of	of	ADP
asir-6084	102	12	(	(	PUNCT
asir-6084	102	13	3.1	3.1	NUM
asir-6084	102	14	)	)	PUNCT
asir-6084	102	15	.	.	PUNCT
asir-6084	103	1	in	in	ADP
asir-6084	103	2	other	other	ADJ
asir-6084	103	3	words	word	NOUN
asir-6084	103	4	,	,	PUNCT
asir-6084	103	5	3.2	3.2	NUM
asir-6084	103	6	can	can	AUX
asir-6084	103	7	be	be	AUX
asir-6084	103	8	proved	prove	VERB
asir-6084	103	9	with	with	ADP
asir-6084	103	10	the	the	DET
asir-6084	103	11	help	help	NOUN
asir-6084	103	12	of	of	ADP
asir-6084	103	13	the	the	DET
asir-6084	103	14	above	above	ADJ
asir-6084	103	15	facts	fact	NOUN
asir-6084	103	16	and	and	CCONJ
asir-6084	103	17	rules	rule	NOUN
asir-6084	103	18	.	.	PUNCT
asir-6084	104	1	theorem	theorem	VERB
asir-6084	104	2	4	4	NUM
asir-6084	104	3	:	:	PUNCT
asir-6084	104	4	the	the	DET
asir-6084	104	5	following	follow	VERB
asir-6084	104	6	valid	valid	ADJ
asir-6084	104	7	modal	modal	ADJ
asir-6084	104	8	syllogisms	syllogism	NOUN
asir-6084	104	9	can	can	AUX
asir-6084	104	10	be	be	AUX
asir-6084	104	11	derived	derive	VERB
asir-6084	104	12	from	from	ADP
asir-6084	104	13	iai-3	iai-3	NOUN
asir-6084	104	14	:	:	PUNCT
asir-6084	104	15	(	(	PUNCT
asir-6084	104	16	4.1	4.1	NUM
asir-6084	104	17	)	)	PUNCT
asir-6084	104	18	iai-3eio-2	iai-3eio-2	PROPN
asir-6084	104	19	(	(	PUNCT
asir-6084	104	20	4.2	4.2	NUM
asir-6084	104	21	)	)	PUNCT
asir-6084	104	22	iai-3iai-3eio-2	iai-3iai-3eio-2	PROPN
asir-6084	104	23	(	(	PUNCT
asir-6084	104	24	4.3	4.3	NUM
asir-6084	104	25	)	)	PUNCT
asir-6084	104	26	iai-3iai-3eio-2	iai-3iai-3eio-2	NOUN
asir-6084	104	27	(	(	PUNCT
asir-6084	104	28	4.4	4.4	NUM
asir-6084	104	29	)	)	PUNCT
asir-6084	104	30	iai-3oao-3aoo-2	iai-3oao-3aoo-2	PROPN
asir-6084	104	31	proof	proof	NOUN
asir-6084	104	32	:	:	PUNCT
asir-6084	104	33	for	for	ADP
asir-6084	104	34	(	(	PUNCT
asir-6084	104	35	4.1	4.1	NUM
asir-6084	104	36	)	)	PUNCT
asir-6084	104	37	.	.	PUNCT
asir-6084	105	1	iai-3	iai-3	NOUN
asir-6084	105	2	is	be	AUX
asir-6084	105	3	valid	valid	ADJ
asir-6084	105	4	,	,	PUNCT
asir-6084	105	5	and	and	CCONJ
asir-6084	105	6	its	its	PRON
asir-6084	105	7	expansion	expansion	NOUN
asir-6084	105	8	is	be	AUX
asir-6084	105	9	that	that	SCONJ
asir-6084	105	10	some(y	some(y	ADJ
asir-6084	105	11	,	,	PUNCT
asir-6084	105	12	z)all(y	z)all(y	PROPN
asir-6084	105	13	,	,	PUNCT
asir-6084	105	14	x)some(x	x)some(x	PROPN
asir-6084	105	15	,	,	PUNCT
asir-6084	105	16	z	z	NOUN
asir-6084	105	17	)	)	PUNCT
asir-6084	105	18	.	.	PUNCT
asir-6084	106	1	according	accord	VERB
asir-6084	106	2	to	to	ADP
asir-6084	106	3	rule	rule	NOUN
asir-6084	106	4	2	2	NUM
asir-6084	106	5	,	,	PUNCT
asir-6084	106	6	it	it	PRON
asir-6084	106	7	can	can	AUX
asir-6084	106	8	be	be	AUX
asir-6084	106	9	seen	see	VERB
asir-6084	106	10	that	that	SCONJ
asir-6084	106	11	some(x	some(x	PROPN
asir-6084	106	12	,	,	PUNCT
asir-6084	106	13	z)some(y	z)some(y	NOUN
asir-6084	106	14	,	,	PUNCT
asir-6084	106	15	z)all(y	z)all(y	NOUN
asir-6084	106	16	,	,	PUNCT
asir-6084	106	17	x	x	NOUN
asir-6084	106	18	)	)	PUNCT
asir-6084	106	19	.	.	PUNCT
asir-6084	107	1	in	in	ADP
asir-6084	107	2	line	line	NOUN
asir-6084	107	3	with	with	ADP
asir-6084	107	4	the	the	DET
asir-6084	107	5	clause	clause	NOUN
asir-6084	107	6	(	(	PUNCT
asir-6084	107	7	1	1	X
asir-6084	107	8	)	)	PUNCT
asir-6084	107	9	in	in	ADP
asir-6084	107	10	fact	fact	NOUN
asir-6084	107	11	3	3	NUM
asir-6084	107	12	,	,	PUNCT
asir-6084	107	13	it	it	PRON
asir-6084	107	14	follows	follow	VERB
asir-6084	107	15	that	that	SCONJ
asir-6084	107	16	some(x	some(x	NOUN
asir-6084	107	17	,	,	PUNCT
asir-6084	107	18	z)some(y	z)some(y	NOUN
asir-6084	107	19	,	,	PUNCT
asir-6084	107	20	z)all(y	z)all(y	NOUN
asir-6084	107	21	,	,	PUNCT
asir-6084	107	22	x	x	NOUN
asir-6084	107	23	)	)	PUNCT
asir-6084	107	24	.	.	PUNCT
asir-6084	108	1	with	with	ADP
asir-6084	108	2	the	the	DET
asir-6084	108	3	help	help	NOUN
asir-6084	108	4	of	of	ADP
asir-6084	108	5	the	the	DET
asir-6084	108	6	clause	clause	NOUN
asir-6084	108	7	(	(	PUNCT
asir-6084	108	8	2	2	NUM
asir-6084	108	9	)	)	PUNCT
asir-6084	108	10	and	and	CCONJ
asir-6084	108	11	(	(	PUNCT
asir-6084	108	12	4	4	X
asir-6084	108	13	)	)	PUNCT
asir-6084	108	14	in	in	ADP
asir-6084	108	15	fact	fact	NOUN
asir-6084	108	16	2	2	NUM
asir-6084	108	17	,	,	PUNCT
asir-6084	108	18	i.e.	i.e.	X
asir-6084	108	19	,	,	PUNCT
asir-6084	108	20	some(x	some(x	NOUN
asir-6084	108	21	,	,	PUNCT
asir-6084	108	22	z)=no(x	z)=no(x	PROPN
asir-6084	108	23	,	,	PUNCT
asir-6084	108	24	z	z	NOUN
asir-6084	108	25	)	)	PUNCT
asir-6084	108	26	and	and	CCONJ
asir-6084	108	27	all(y	all(y	NUM
asir-6084	108	28	,	,	PUNCT
asir-6084	108	29	x)=not	x)=not	ADV
asir-6084	108	30	all(y	all(y	PROPN
asir-6084	108	31	,	,	PUNCT
asir-6084	108	32	x	x	NOUN
asir-6084	108	33	)	)	PUNCT
asir-6084	108	34	,	,	PUNCT
asir-6084	108	35	one	one	PRON
asir-6084	108	36	can	can	AUX
asir-6084	108	37	deduce	deduce	VERB
asir-6084	108	38	that	that	DET
asir-6084	108	39	no(x	no(x	ADJ
asir-6084	108	40	,	,	PUNCT
asir-6084	108	41	z)some(y	z)some(y	X
asir-6084	108	42	,	,	PUNCT
asir-6084	108	43	z)not	z)not	PROPN
asir-6084	108	44	all(y	all(y	PROPN
asir-6084	108	45	,	,	PUNCT
asir-6084	108	46	x	x	NOUN
asir-6084	108	47	)	)	PUNCT
asir-6084	108	48	.	.	PUNCT
asir-6084	109	1	therefore	therefore	ADV
asir-6084	109	2	,	,	PUNCT
asir-6084	109	3	eio-2	eio-2	PROPN
asir-6084	109	4	can	can	AUX
asir-6084	109	5	be	be	AUX
asir-6084	109	6	derived	derive	VERB
asir-6084	109	7	from	from	ADP
asir-6084	109	8	iai-3	iai-3	NOUN
asir-6084	109	9	,	,	PUNCT
asir-6084	109	10	just	just	ADV
asir-6084	109	11	as	as	SCONJ
asir-6084	109	12	required	require	VERB
asir-6084	109	13	.	.	PUNCT
asir-6084	110	1	others	other	NOUN
asir-6084	110	2	can	can	AUX
asir-6084	110	3	be	be	AUX
asir-6084	110	4	similarly	similarly	ADV
asir-6084	110	5	proved	prove	VERB
asir-6084	110	6	on	on	ADP
asir-6084	110	7	the	the	DET
asir-6084	110	8	basis	basis	NOUN
asir-6084	110	9	of	of	ADP
asir-6084	110	10	the	the	DET
asir-6084	110	11	above	above	ADJ
asir-6084	110	12	facts	fact	NOUN
asir-6084	110	13	and	and	CCONJ
asir-6084	110	14	rules	rule	NOUN
asir-6084	110	15	.	.	PUNCT
asir-6084	111	1	theorem	theorem	NOUN
asir-6084	111	2	5	5	NUM
asir-6084	111	3	:	:	PUNCT
asir-6084	111	4	the	the	DET
asir-6084	111	5	following	follow	VERB
asir-6084	111	6	valid	valid	ADJ
asir-6084	111	7	modal	modal	ADJ
asir-6084	111	8	syllogisms	syllogism	NOUN
asir-6084	111	9	can	can	AUX
asir-6084	111	10	be	be	AUX
asir-6084	111	11	followed	follow	VERB
asir-6084	111	12	from	from	ADP
asir-6084	111	13	iai-3	iai-3	NOUN
asir-6084	111	14	:	:	PUNCT
asir-6084	111	15	(	(	PUNCT
asir-6084	111	16	5.1	5.1	NUM
asir-6084	111	17	)	)	PUNCT
asir-6084	111	18	iai-3eae-1	iai-3eae-1	PROPN
asir-6084	111	19	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-6084	111	20	applied	apply	VERB
asir-6084	111	21	science	science	NOUN
asir-6084	111	22	and	and	CCONJ
asir-6084	111	23	innovative	innovative	ADJ
asir-6084	111	24	research	research	NOUN
asir-6084	111	25	vol	vol	NOUN
asir-6084	111	26	.	.	PUNCT
asir-6084	112	1	7	7	NUM
asir-6084	112	2	,	,	PUNCT
asir-6084	112	3	no	no	INTJ
asir-6084	112	4	.	.	NOUN
asir-6084	112	5	1	1	NUM
asir-6084	112	6	,	,	PUNCT
asir-6084	112	7	2023	2023	NUM
asir-6084	112	8	51	51	NUM
asir-6084	112	9	published	publish	VERB
asir-6084	112	10	by	by	ADP
asir-6084	112	11	scholink	scholink	PROPN
asir-6084	112	12	inc	inc	PROPN
asir-6084	112	13	.	.	PROPN
asir-6084	113	1	(	(	PUNCT
asir-6084	113	2	5.2	5.2	NUM
asir-6084	113	3	)	)	PUNCT
asir-6084	113	4	iai-3iai-3eae-1	iai-3iai-3eae-1	NOUN
asir-6084	113	5	(	(	PUNCT
asir-6084	113	6	5.3	5.3	NUM
asir-6084	113	7	)	)	PUNCT
asir-6084	113	8	iai-3iai-3eae-1	iai-3iai-3eae-1	NOUN
asir-6084	113	9	(	(	PUNCT
asir-6084	113	10	5.4	5.4	NUM
asir-6084	113	11	)	)	PUNCT
asir-6084	113	12	iai-3oao-3aaa-1	iai-3oao-3aaa-1	NUM
asir-6084	113	13	proof	proof	NOUN
asir-6084	113	14	:	:	PUNCT
asir-6084	113	15	for	for	ADP
asir-6084	113	16	(	(	PUNCT
asir-6084	113	17	5.1	5.1	NUM
asir-6084	113	18	)	)	PUNCT
asir-6084	113	19	.	.	PUNCT
asir-6084	114	1	the	the	DET
asir-6084	114	2	expansion	expansion	NOUN
asir-6084	114	3	of	of	ADP
asir-6084	114	4	iai-3	iai-3	NOUN
asir-6084	114	5	is	be	AUX
asir-6084	114	6	that	that	SCONJ
asir-6084	114	7	some(y	some(y	ADJ
asir-6084	114	8	,	,	PUNCT
asir-6084	114	9	z)all(y	z)all(y	PROPN
asir-6084	114	10	,	,	PUNCT
asir-6084	114	11	x)some(x	x)some(x	PROPN
asir-6084	114	12	,	,	PUNCT
asir-6084	114	13	z	z	NOUN
asir-6084	114	14	)	)	PUNCT
asir-6084	114	15	.	.	PUNCT
asir-6084	115	1	according	accord	VERB
asir-6084	115	2	to	to	ADP
asir-6084	115	3	rule	rule	NOUN
asir-6084	115	4	2	2	NUM
asir-6084	115	5	,	,	PUNCT
asir-6084	115	6	it	it	PRON
asir-6084	115	7	follows	follow	VERB
asir-6084	115	8	that	that	SCONJ
asir-6084	115	9	some(x	some(x	PROPN
asir-6084	115	10	,	,	PUNCT
asir-6084	115	11	z)all(y	z)all(y	PROPN
asir-6084	115	12	,	,	PUNCT
asir-6084	115	13	x)some(y	x)some(y	PROPN
asir-6084	115	14	,	,	PUNCT
asir-6084	115	15	z	z	NOUN
asir-6084	115	16	)	)	PUNCT
asir-6084	115	17	.	.	PUNCT
asir-6084	116	1	in	in	ADP
asir-6084	116	2	terms	term	NOUN
asir-6084	116	3	of	of	ADP
asir-6084	116	4	the	the	DET
asir-6084	116	5	clause	clause	NOUN
asir-6084	116	6	(	(	PUNCT
asir-6084	116	7	1	1	X
asir-6084	116	8	)	)	PUNCT
asir-6084	116	9	in	in	ADP
asir-6084	116	10	fact	fact	NOUN
asir-6084	116	11	3	3	NUM
asir-6084	116	12	,	,	PUNCT
asir-6084	116	13	it	it	PRON
asir-6084	116	14	can	can	AUX
asir-6084	116	15	be	be	AUX
asir-6084	116	16	seen	see	VERB
asir-6084	116	17	that	that	SCONJ
asir-6084	116	18	some(x	some(x	NOUN
asir-6084	116	19	,	,	PUNCT
asir-6084	116	20	z)all(y	z)all(y	PROPN
asir-6084	116	21	,	,	PUNCT
asir-6084	116	22	x)some(y	x)some(y	NOUN
asir-6084	116	23	,	,	PUNCT
asir-6084	116	24	z	z	NOUN
asir-6084	116	25	)	)	PUNCT
asir-6084	116	26	.	.	PUNCT
asir-6084	117	1	according	accord	VERB
asir-6084	117	2	to	to	ADP
asir-6084	117	3	the	the	DET
asir-6084	117	4	clause	clause	NOUN
asir-6084	117	5	(	(	PUNCT
asir-6084	117	6	4	4	NUM
asir-6084	117	7	)	)	PUNCT
asir-6084	117	8	in	in	ADP
asir-6084	117	9	fact	fact	NOUN
asir-6084	117	10	2	2	NUM
asir-6084	117	11	,	,	PUNCT
asir-6084	117	12	some(x	some(x	NOUN
asir-6084	117	13	,	,	PUNCT
asir-6084	117	14	z)=no(x	z)=no(x	PROPN
asir-6084	117	15	,	,	PUNCT
asir-6084	117	16	z	z	NOUN
asir-6084	117	17	)	)	PUNCT
asir-6084	117	18	and	and	CCONJ
asir-6084	117	19	some(y	some(y	NOUN
asir-6084	117	20	,	,	PUNCT
asir-6084	117	21	z)=no(y	z)=no(y	PROPN
asir-6084	117	22	,	,	PUNCT
asir-6084	117	23	z	z	NOUN
asir-6084	117	24	)	)	PUNCT
asir-6084	117	25	.	.	PUNCT
asir-6084	118	1	therefore	therefore	ADV
asir-6084	118	2	,	,	PUNCT
asir-6084	118	3	the	the	DET
asir-6084	118	4	syllogism	syllogism	NOUN
asir-6084	118	5	no(x	no(x	NUM
asir-6084	118	6	,	,	PUNCT
asir-6084	118	7	z)all(y	z)all(y	PROPN
asir-6084	118	8	,	,	PUNCT
asir-6084	118	9	x)no(y	x)no(y	NUM
asir-6084	118	10	,	,	PUNCT
asir-6084	118	11	z	z	NOUN
asir-6084	118	12	)	)	PUNCT
asir-6084	118	13	is	be	AUX
asir-6084	118	14	valid	valid	ADJ
asir-6084	118	15	.	.	PUNCT
asir-6084	119	1	in	in	ADP
asir-6084	119	2	other	other	ADJ
asir-6084	119	3	words	word	NOUN
asir-6084	119	4	,	,	PUNCT
asir-6084	119	5	eae-1	eae-1	PROPN
asir-6084	119	6	can	can	AUX
asir-6084	119	7	be	be	AUX
asir-6084	119	8	derived	derive	VERB
asir-6084	119	9	from	from	ADP
asir-6084	119	10	iai-3	iai-3	NOUN
asir-6084	119	11	.	.	PUNCT
asir-6084	120	1	so	so	ADV
asir-6084	120	2	far	far	ADV
asir-6084	120	3	,	,	PUNCT
asir-6084	120	4	the	the	DET
asir-6084	120	5	proof	proof	NOUN
asir-6084	120	6	of	of	ADP
asir-6084	120	7	(	(	PUNCT
asir-6084	120	8	5.1	5.1	NUM
asir-6084	120	9	)	)	PUNCT
asir-6084	120	10	has	have	AUX
asir-6084	120	11	been	be	AUX
asir-6084	120	12	completed	complete	VERB
asir-6084	120	13	.	.	PUNCT
asir-6084	121	1	others	other	NOUN
asir-6084	121	2	can	can	AUX
asir-6084	121	3	be	be	AUX
asir-6084	121	4	similarly	similarly	ADV
asir-6084	121	5	proved	prove	VERB
asir-6084	121	6	.	.	PUNCT
asir-6084	122	1	theorem	theorem	VERB
asir-6084	122	2	6	6	NUM
asir-6084	122	3	:	:	PUNCT
asir-6084	122	4	the	the	DET
asir-6084	122	5	following	follow	VERB
asir-6084	122	6	valid	valid	ADJ
asir-6084	122	7	modal	modal	ADJ
asir-6084	122	8	syllogisms	syllogism	NOUN
asir-6084	122	9	can	can	AUX
asir-6084	122	10	be	be	AUX
asir-6084	122	11	derived	derive	VERB
asir-6084	122	12	from	from	ADP
asir-6084	122	13	iai-3	iai-3	NOUN
asir-6084	122	14	:	:	PUNCT
asir-6084	122	15	(	(	PUNCT
asir-6084	122	16	6.1	6.1	NUM
asir-6084	122	17	)	)	PUNCT
asir-6084	122	18	iai-3oao-3oao-3aoo-2	iai-3oao-3oao-3aoo-2	NOUN
asir-6084	122	19	(	(	PUNCT
asir-6084	122	20	6.2	6.2	NUM
asir-6084	122	21	)	)	PUNCT
asir-6084	122	22	iai-3oao-3oao-3aoo-2	iai-3oao-3oao-3aoo-2	PROPN
asir-6084	122	23	(	(	PUNCT
asir-6084	122	24	6.3	6.3	NUM
asir-6084	122	25	)	)	PUNCT
asir-6084	122	26	iai-3aii-3eio-3aee-2	iai-3aii-3eio-3aee-2	NOUN
asir-6084	123	1	proof	proof	NOUN
asir-6084	123	2	:	:	PUNCT
asir-6084	123	3	for	for	ADP
asir-6084	123	4	(	(	PUNCT
asir-6084	123	5	6.1	6.1	NUM
asir-6084	123	6	)	)	PUNCT
asir-6084	123	7	.	.	PUNCT
asir-6084	124	1	according	accord	VERB
asir-6084	124	2	to	to	ADP
asir-6084	124	3	(	(	PUNCT
asir-6084	124	4	3.1	3.1	NUM
asir-6084	124	5	)	)	PUNCT
asir-6084	124	6	iai-3oao-3oao-3oao-3	iai-3oao-3oao-3oao-3	NUM
asir-6084	124	7	,	,	PUNCT
asir-6084	124	8	it	it	PRON
asir-6084	124	9	follows	follow	VERB
asir-6084	124	10	that	that	SCONJ
asir-6084	124	11	oao-3	oao-3	PROPN
asir-6084	124	12	is	be	AUX
asir-6084	124	13	valid	valid	ADJ
asir-6084	124	14	,	,	PUNCT
asir-6084	124	15	and	and	CCONJ
asir-6084	124	16	its	its	PRON
asir-6084	124	17	expansion	expansion	NOUN
asir-6084	124	18	is	be	AUX
asir-6084	124	19	that	that	SCONJ
asir-6084	124	20	not	not	CCONJ
asir-6084	124	21	all(y	all(y	PROPN
asir-6084	124	22	,	,	PUNCT
asir-6084	124	23	z)all(y	z)all(y	PROPN
asir-6084	124	24	,	,	PUNCT
asir-6084	124	25	x)not	x)not	PROPN
asir-6084	124	26	all(x	all(x	PROPN
asir-6084	124	27	,	,	PUNCT
asir-6084	124	28	z	z	NOUN
asir-6084	124	29	)	)	PUNCT
asir-6084	124	30	.	.	PUNCT
asir-6084	125	1	according	accord	VERB
asir-6084	125	2	to	to	ADP
asir-6084	125	3	rule	rule	NOUN
asir-6084	125	4	2	2	NUM
asir-6084	125	5	,	,	PUNCT
asir-6084	125	6	it	it	PRON
asir-6084	125	7	can	can	AUX
asir-6084	125	8	be	be	AUX
asir-6084	125	9	seen	see	VERB
asir-6084	125	10	that	that	DET
asir-6084	125	11	not	not	VERB
asir-6084	125	12	all(x	all(x	PROPN
asir-6084	125	13	,	,	PUNCT
asir-6084	125	14	z)not	z)not	ADV
asir-6084	125	15	all(y	all(y	PROPN
asir-6084	125	16	,	,	PUNCT
asir-6084	125	17	z)all(y	z)all(y	NOUN
asir-6084	125	18	,	,	PUNCT
asir-6084	125	19	x	x	NOUN
asir-6084	125	20	)	)	PUNCT
asir-6084	125	21	.	.	PUNCT
asir-6084	126	1	in	in	ADP
asir-6084	126	2	the	the	DET
asir-6084	126	3	light	light	NOUN
asir-6084	126	4	of	of	ADP
asir-6084	126	5	the	the	DET
asir-6084	126	6	clause	clause	NOUN
asir-6084	126	7	(	(	PUNCT
asir-6084	126	8	1	1	X
asir-6084	126	9	)	)	PUNCT
asir-6084	126	10	in	in	ADP
asir-6084	126	11	fact	fact	NOUN
asir-6084	126	12	3	3	NUM
asir-6084	126	13	,	,	PUNCT
asir-6084	126	14	one	one	PRON
asir-6084	126	15	can	can	AUX
asir-6084	126	16	deduce	deduce	VERB
asir-6084	126	17	that	that	DET
asir-6084	126	18	not	not	VERB
asir-6084	126	19	all(x	all(x	PROPN
asir-6084	126	20	,	,	PUNCT
asir-6084	126	21	z)not	z)not	ADV
asir-6084	126	22	all(y	all(y	PROPN
asir-6084	126	23	,	,	PUNCT
asir-6084	126	24	z)all(y	z)all(y	NOUN
asir-6084	126	25	,	,	PUNCT
asir-6084	126	26	x	x	NOUN
asir-6084	126	27	)	)	PUNCT
asir-6084	126	28	.	.	PUNCT
asir-6084	127	1	in	in	ADP
asir-6084	127	2	terms	term	NOUN
asir-6084	127	3	of	of	ADP
asir-6084	127	4	the	the	DET
asir-6084	127	5	clause	clause	NOUN
asir-6084	127	6	(	(	PUNCT
asir-6084	127	7	1	1	X
asir-6084	127	8	)	)	PUNCT
asir-6084	127	9	in	in	ADP
asir-6084	127	10	fact	fact	NOUN
asir-6084	127	11	2	2	NUM
asir-6084	127	12	,	,	PUNCT
asir-6084	127	13	it	it	PRON
asir-6084	127	14	follows	follow	VERB
asir-6084	127	15	that	that	PRON
asir-6084	127	16	not	not	ADV
asir-6084	127	17	all(x	all(x	PROPN
asir-6084	127	18	,	,	PUNCT
asir-6084	127	19	z)=all(x	z)=all(x	PROPN
asir-6084	127	20	,	,	PUNCT
asir-6084	127	21	z	z	NOUN
asir-6084	127	22	)	)	PUNCT
asir-6084	127	23	and	and	CCONJ
asir-6084	127	24	all(y	all(y	NUM
asir-6084	127	25	,	,	PUNCT
asir-6084	127	26	x)=not	x)=not	ADV
asir-6084	127	27	all(y	all(y	PROPN
asir-6084	127	28	,	,	PUNCT
asir-6084	127	29	x	x	NOUN
asir-6084	127	30	)	)	PUNCT
asir-6084	127	31	.	.	PUNCT
asir-6084	128	1	hence	hence	ADV
asir-6084	128	2	,	,	PUNCT
asir-6084	128	3	the	the	DET
asir-6084	128	4	syllogism	syllogism	NOUN
asir-6084	128	5	all(x	all(x	PROPN
asir-6084	128	6	,	,	PUNCT
asir-6084	128	7	z)not	z)not	ADV
asir-6084	128	8	all(y	all(y	PROPN
asir-6084	128	9	,	,	PUNCT
asir-6084	128	10	z)not	z)not	PROPN
asir-6084	128	11	all(y	all(y	PROPN
asir-6084	128	12	,	,	PUNCT
asir-6084	128	13	x	x	PRON
asir-6084	128	14	)	)	PUNCT
asir-6084	128	15	is	be	AUX
asir-6084	128	16	valid	valid	ADJ
asir-6084	128	17	.	.	PUNCT
asir-6084	129	1	that	that	PRON
asir-6084	129	2	is	be	AUX
asir-6084	129	3	to	to	PART
asir-6084	129	4	say	say	VERB
asir-6084	129	5	that	that	SCONJ
asir-6084	129	6	aoo-2	aoo-2	PROPN
asir-6084	129	7	can	can	AUX
asir-6084	129	8	be	be	AUX
asir-6084	129	9	derived	derive	VERB
asir-6084	129	10	from	from	ADP
asir-6084	129	11	iai-3	iai-3	NOUN
asir-6084	129	12	,	,	PUNCT
asir-6084	129	13	the	the	DET
asir-6084	129	14	proof	proof	NOUN
asir-6084	129	15	of	of	ADP
asir-6084	129	16	(	(	PUNCT
asir-6084	129	17	6.1	6.1	NUM
asir-6084	129	18	)	)	PUNCT
asir-6084	129	19	has	have	AUX
asir-6084	129	20	been	be	AUX
asir-6084	129	21	completed	complete	VERB
asir-6084	129	22	.	.	PUNCT
asir-6084	130	1	the	the	DET
asir-6084	130	2	proofs	proof	NOUN
asir-6084	130	3	of	of	ADP
asir-6084	130	4	(	(	PUNCT
asir-6084	130	5	6.2	6.2	NUM
asir-6084	130	6	)	)	PUNCT
asir-6084	130	7	and	and	CCONJ
asir-6084	130	8	(	(	PUNCT
asir-6084	130	9	6.3	6.3	NUM
asir-6084	130	10	)	)	PUNCT
asir-6084	130	11	are	be	AUX
asir-6084	130	12	similar	similar	ADJ
asir-6084	130	13	to	to	ADP
asir-6084	130	14	that	that	PRON
asir-6084	130	15	of	of	ADP
asir-6084	130	16	(	(	PUNCT
asir-6084	130	17	6.1	6.1	NUM
asir-6084	130	18	)	)	PUNCT
asir-6084	130	19	.	.	PUNCT
asir-6084	131	1	theorem	theorem	VERB
asir-6084	131	2	7	7	NUM
asir-6084	131	3	:	:	PUNCT
asir-6084	131	4	the	the	DET
asir-6084	131	5	following	follow	VERB
asir-6084	131	6	valid	valid	ADJ
asir-6084	131	7	modal	modal	ADJ
asir-6084	131	8	syllogisms	syllogism	NOUN
asir-6084	131	9	can	can	AUX
asir-6084	131	10	be	be	AUX
asir-6084	131	11	obtained	obtain	VERB
asir-6084	131	12	from	from	ADP
asir-6084	131	13	iai-3	iai-3	NOUN
asir-6084	131	14	:	:	PUNCT
asir-6084	131	15	(	(	PUNCT
asir-6084	131	16	7.1	7.1	NUM
asir-6084	131	17	)	)	PUNCT
asir-6084	131	18	iai-3oao-3oao-3aaa-1	iai-3oao-3oao-3aaa-1	PROPN
asir-6084	131	19	(	(	PUNCT
asir-6084	131	20	7.2	7.2	NUM
asir-6084	131	21	)	)	PUNCT
asir-6084	131	22	iai-3oao-3oao-3aaa-1	iai-3oao-3oao-3aaa-1	NUM
asir-6084	131	23	(	(	PUNCT
asir-6084	131	24	7.3	7.3	NUM
asir-6084	131	25	)	)	PUNCT
asir-6084	131	26	iai-3aii-3eio-3aii-1	iai-3aii-3eio-3aii-1	NOUN
asir-6084	131	27	proof	proof	NOUN
asir-6084	131	28	:	:	PUNCT
asir-6084	131	29	for	for	ADP
asir-6084	131	30	(	(	PUNCT
asir-6084	131	31	7.1	7.1	NUM
asir-6084	131	32	)	)	PUNCT
asir-6084	131	33	.	.	PUNCT
asir-6084	132	1	according	accord	VERB
asir-6084	132	2	to	to	ADP
asir-6084	132	3	(	(	PUNCT
asir-6084	132	4	3.1	3.1	NUM
asir-6084	132	5	)	)	PUNCT
asir-6084	132	6	,	,	PUNCT
asir-6084	132	7	oao-3	oao-3	PROPN
asir-6084	132	8	is	be	AUX
asir-6084	132	9	valid	valid	ADJ
asir-6084	132	10	,	,	PUNCT
asir-6084	132	11	and	and	CCONJ
asir-6084	132	12	its	its	PRON
asir-6084	132	13	expansion	expansion	NOUN
asir-6084	132	14	is	be	AUX
asir-6084	132	15	that	that	SCONJ
asir-6084	132	16	not	not	CCONJ
asir-6084	132	17	all(y	all(y	PROPN
asir-6084	132	18	,	,	PUNCT
asir-6084	132	19	z)all(y	z)all(y	PROPN
asir-6084	132	20	,	,	PUNCT
asir-6084	132	21	x)not	x)not	PROPN
asir-6084	132	22	all(x	all(x	PROPN
asir-6084	132	23	,	,	PUNCT
asir-6084	132	24	z	z	NOUN
asir-6084	132	25	)	)	PUNCT
asir-6084	132	26	.	.	PUNCT
asir-6084	133	1	according	accord	VERB
asir-6084	133	2	to	to	ADP
asir-6084	133	3	rule	rule	NOUN
asir-6084	133	4	2	2	NUM
asir-6084	133	5	,	,	PUNCT
asir-6084	133	6	one	one	PRON
asir-6084	133	7	can	can	AUX
asir-6084	133	8	derive	derive	VERB
asir-6084	133	9	that	that	DET
asir-6084	133	10	not	not	PROPN
asir-6084	133	11	all(x	all(x	PROPN
asir-6084	133	12	,	,	PUNCT
asir-6084	133	13	z)all(y	z)all(y	PROPN
asir-6084	133	14	,	,	PUNCT
asir-6084	133	15	x)not	x)not	PROPN
asir-6084	133	16	all(y	all(y	PROPN
asir-6084	133	17	,	,	PUNCT
asir-6084	133	18	z	z	NOUN
asir-6084	133	19	)	)	PUNCT
asir-6084	133	20	.	.	PUNCT
asir-6084	134	1	in	in	ADP
asir-6084	134	2	the	the	DET
asir-6084	134	3	light	light	NOUN
asir-6084	134	4	of	of	ADP
asir-6084	134	5	the	the	DET
asir-6084	134	6	clause	clause	NOUN
asir-6084	134	7	(	(	PUNCT
asir-6084	134	8	1	1	X
asir-6084	134	9	)	)	PUNCT
asir-6084	134	10	in	in	ADP
asir-6084	134	11	fact	fact	NOUN
asir-6084	134	12	3	3	NUM
asir-6084	134	13	,	,	PUNCT
asir-6084	134	14	it	it	PRON
asir-6084	134	15	follows	follow	VERB
asir-6084	134	16	that	that	DET
asir-6084	134	17	not	not	VERB
asir-6084	134	18	all(x	all(x	PROPN
asir-6084	134	19	,	,	PUNCT
asir-6084	134	20	z)all(y	z)all(y	PROPN
asir-6084	134	21	,	,	PUNCT
asir-6084	134	22	x)not	x)not	PROPN
asir-6084	134	23	all(y	all(y	PROPN
asir-6084	134	24	,	,	PUNCT
asir-6084	134	25	z	z	NOUN
asir-6084	134	26	)	)	PUNCT
asir-6084	134	27	.	.	PUNCT
asir-6084	135	1	in	in	ADP
asir-6084	135	2	terms	term	NOUN
asir-6084	135	3	of	of	ADP
asir-6084	135	4	fact	fact	NOUN
asir-6084	135	5	2	2	NUM
asir-6084	135	6	,	,	PUNCT
asir-6084	135	7	it	it	PRON
asir-6084	135	8	can	can	AUX
asir-6084	135	9	be	be	AUX
asir-6084	135	10	seen	see	VERB
asir-6084	135	11	that	that	PRON
asir-6084	135	12	not	not	VERB
asir-6084	135	13	all(x	all(x	PROPN
asir-6084	135	14	,	,	PUNCT
asir-6084	135	15	z)=all(x	z)=all(x	PROPN
asir-6084	135	16	,	,	PUNCT
asir-6084	135	17	z	z	NOUN
asir-6084	135	18	)	)	PUNCT
asir-6084	135	19	and	and	CCONJ
asir-6084	135	20	not	not	ADV
asir-6084	135	21	all(y	all(y	PROPN
asir-6084	135	22	,	,	PUNCT
asir-6084	135	23	z)=all(y	z)=all(y	PROPN
asir-6084	135	24	,	,	PUNCT
asir-6084	135	25	z	z	NOUN
asir-6084	135	26	)	)	PUNCT
asir-6084	135	27	.	.	PUNCT
asir-6084	136	1	therefore	therefore	ADV
asir-6084	136	2	,	,	PUNCT
asir-6084	136	3	the	the	DET
asir-6084	136	4	syllogism	syllogism	NOUN
asir-6084	136	5	all(x	all(x	PROPN
asir-6084	136	6	,	,	PUNCT
asir-6084	136	7	z)all(y	z)all(y	PROPN
asir-6084	136	8	,	,	PUNCT
asir-6084	136	9	x)all(y	x)all(y	PROPN
asir-6084	136	10	,	,	PUNCT
asir-6084	136	11	z	z	NOUN
asir-6084	136	12	)	)	PUNCT
asir-6084	136	13	is	be	AUX
asir-6084	136	14	valid	valid	ADJ
asir-6084	136	15	.	.	PUNCT
asir-6084	137	1	that	that	PRON
asir-6084	137	2	is	is	ADV
asir-6084	137	3	,	,	PUNCT
asir-6084	137	4	aaa-1	aaa-1	PRON
asir-6084	137	5	can	can	AUX
asir-6084	137	6	be	be	AUX
asir-6084	137	7	derived	derive	VERB
asir-6084	137	8	from	from	ADP
asir-6084	137	9	iai-3	iai-3	NOUN
asir-6084	137	10	,	,	PUNCT
asir-6084	137	11	just	just	ADV
asir-6084	137	12	as	as	SCONJ
asir-6084	137	13	required	require	VERB
asir-6084	137	14	.	.	PUNCT
asir-6084	138	1	the	the	DET
asir-6084	138	2	two	two	NUM
asir-6084	138	3	others	other	NOUN
asir-6084	138	4	can	can	AUX
asir-6084	138	5	be	be	AUX
asir-6084	138	6	similarly	similarly	ADV
asir-6084	138	7	proved	prove	VERB
asir-6084	138	8	.	.	PUNCT
asir-6084	139	1	theorem	theorem	ADJ
asir-6084	139	2	8	8	NUM
asir-6084	139	3	:	:	PUNCT
asir-6084	139	4	the	the	DET
asir-6084	139	5	following	follow	VERB
asir-6084	139	6	valid	valid	ADJ
asir-6084	139	7	modal	modal	ADJ
asir-6084	139	8	syllogisms	syllogism	NOUN
asir-6084	139	9	can	can	AUX
asir-6084	139	10	be	be	AUX
asir-6084	139	11	deduced	deduce	VERB
asir-6084	139	12	from	from	ADP
asir-6084	139	13	iai-3	iai-3	NOUN
asir-6084	139	14	:	:	PUNCT
asir-6084	139	15	(	(	PUNCT
asir-6084	139	16	8.1	8.1	NUM
asir-6084	139	17	)	)	PUNCT
asir-6084	139	18	iai-3aii-3eio-3eio-3	iai-3aii-3eio-3eio-3	PROPN
asir-6084	139	19	(	(	PUNCT
asir-6084	139	20	8.2	8.2	NUM
asir-6084	139	21	)	)	PUNCT
asir-6084	139	22	iai-3aii-3eio-3eio-4eio-4	iai-3aii-3eio-3eio-4eio-4	PROPN
asir-6084	139	23	(	(	PUNCT
asir-6084	139	24	8.3	8.3	NUM
asir-6084	139	25	)	)	PUNCT
asir-6084	139	26	iai-3aii-3eio-3eio-1eio-1	iai-3aii-3eio-3eio-1eio-1	X
asir-6084	139	27	(	(	PUNCT
asir-6084	139	28	8.4	8.4	NUM
asir-6084	139	29	)	)	PUNCT
asir-6084	139	30	iai-3aii-3eio-3eio-2eio-2	iai-3aii-3eio-3eio-2eio-2	NOUN
asir-6084	139	31	proof	proof	NOUN
asir-6084	139	32	:	:	PUNCT
asir-6084	139	33	for	for	ADP
asir-6084	139	34	(	(	PUNCT
asir-6084	139	35	8.1	8.1	NUM
asir-6084	139	36	)	)	PUNCT
asir-6084	139	37	.	.	PUNCT
asir-6084	140	1	according	accord	VERB
asir-6084	140	2	to	to	ADP
asir-6084	140	3	(	(	PUNCT
asir-6084	140	4	3.2	3.2	NUM
asir-6084	140	5	)	)	PUNCT
asir-6084	140	6	iai-3aii-3eio-3	iai-3aii-3eio-3	PROPN
asir-6084	140	7	,	,	PUNCT
asir-6084	140	8	it	it	PRON
asir-6084	140	9	follows	follow	VERB
asir-6084	140	10	that	that	SCONJ
asir-6084	140	11	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	140	12	applied	apply	VERB
asir-6084	140	13	science	science	NOUN
asir-6084	140	14	and	and	CCONJ
asir-6084	140	15	innovative	innovative	ADJ
asir-6084	140	16	research	research	NOUN
asir-6084	140	17	vol	vol	NOUN
asir-6084	140	18	.	.	PUNCT
asir-6084	141	1	7	7	NUM
asir-6084	141	2	,	,	PUNCT
asir-6084	141	3	no	no	INTJ
asir-6084	141	4	.	.	NOUN
asir-6084	141	5	1	1	NUM
asir-6084	141	6	,	,	PUNCT
asir-6084	141	7	2023	2023	NUM
asir-6084	141	8	52	52	NUM
asir-6084	141	9	published	publish	VERB
asir-6084	141	10	by	by	ADP
asir-6084	141	11	scholink	scholink	PROPN
asir-6084	141	12	inc	inc	PROPN
asir-6084	141	13	.	.	PROPN
asir-6084	141	14	eio-3	eio-3	PROPN
asir-6084	141	15	is	be	AUX
asir-6084	141	16	valid	valid	ADJ
asir-6084	141	17	.	.	PUNCT
asir-6084	142	1	according	accord	VERB
asir-6084	142	2	to	to	ADP
asir-6084	142	3	fact	fact	NOUN
asir-6084	142	4	4	4	NUM
asir-6084	142	5	,	,	PUNCT
asir-6084	142	6	it	it	PRON
asir-6084	142	7	is	be	AUX
asir-6084	142	8	easily	easily	ADV
asir-6084	142	9	seen	see	VERB
asir-6084	142	10	that	that	SCONJ
asir-6084	142	11	oo	oo	PROPN
asir-6084	142	12	,	,	PUNCT
asir-6084	142	13	so	so	ADV
asir-6084	142	14	eio-3	eio-3	ADV
asir-6084	142	15	is	be	AUX
asir-6084	142	16	valid	valid	ADJ
asir-6084	142	17	.	.	PUNCT
asir-6084	143	1	in	in	ADP
asir-6084	143	2	other	other	ADJ
asir-6084	143	3	words	word	NOUN
asir-6084	143	4	,	,	PUNCT
asir-6084	143	5	it	it	PRON
asir-6084	143	6	can	can	AUX
asir-6084	143	7	be	be	AUX
asir-6084	143	8	derived	derive	VERB
asir-6084	143	9	from	from	ADP
asir-6084	143	10	iai-3	iai-3	NOUN
asir-6084	143	11	.	.	PUNCT
asir-6084	144	1	therefore	therefore	ADV
asir-6084	144	2	,	,	PUNCT
asir-6084	144	3	the	the	DET
asir-6084	144	4	proof	proof	NOUN
asir-6084	144	5	of	of	ADP
asir-6084	144	6	(	(	PUNCT
asir-6084	144	7	8.1	8.1	NUM
asir-6084	144	8	)	)	PUNCT
asir-6084	144	9	has	have	AUX
asir-6084	144	10	been	be	AUX
asir-6084	144	11	completed	complete	VERB
asir-6084	144	12	.	.	PUNCT
asir-6084	145	1	others	other	NOUN
asir-6084	145	2	can	can	AUX
asir-6084	145	3	be	be	AUX
asir-6084	145	4	similarly	similarly	ADV
asir-6084	145	5	proved	prove	VERB
asir-6084	145	6	.	.	PUNCT
asir-6084	146	1	theorem	theorem	VERB
asir-6084	146	2	9	9	NUM
asir-6084	146	3	:	:	PUNCT
asir-6084	146	4	the	the	DET
asir-6084	146	5	following	follow	VERB
asir-6084	146	6	valid	valid	ADJ
asir-6084	146	7	modal	modal	ADJ
asir-6084	146	8	syllogisms	syllogism	NOUN
asir-6084	146	9	can	can	AUX
asir-6084	146	10	be	be	AUX
asir-6084	146	11	inferred	infer	VERB
asir-6084	146	12	from	from	ADP
asir-6084	146	13	iai-3	iai-3	NOUN
asir-6084	146	14	:	:	PUNCT
asir-6084	146	15	(	(	PUNCT
asir-6084	146	16	9.1	9.1	NUM
asir-6084	146	17	)	)	PUNCT
asir-6084	146	18	iai-3aii-3eio-3eio-3aii-1	iai-3aii-3eio-3eio-3aii-1	NUM
asir-6084	146	19	(	(	PUNCT
asir-6084	146	20	9.2	9.2	NUM
asir-6084	146	21	)	)	PUNCT
asir-6084	146	22	iai-3eae-1eao-1aai-3	iai-3eae-1eao-1aai-3	NOUN
asir-6084	146	23	(	(	PUNCT
asir-6084	146	24	9.3	9.3	NUM
asir-6084	146	25	)	)	PUNCT
asir-6084	146	26	iai-3oao-3aaa-1aai-1eao-3	iai-3oao-3aaa-1aai-1eao-3	NUM
asir-6084	146	27	proof	proof	NOUN
asir-6084	146	28	:	:	PUNCT
asir-6084	146	29	for	for	ADP
asir-6084	146	30	(	(	PUNCT
asir-6084	146	31	9.1	9.1	NUM
asir-6084	146	32	)	)	PUNCT
asir-6084	146	33	.	.	PUNCT
asir-6084	147	1	according	accord	VERB
asir-6084	147	2	to	to	ADP
asir-6084	147	3	(	(	PUNCT
asir-6084	147	4	8.1	8.1	NUM
asir-6084	147	5	)	)	PUNCT
asir-6084	147	6	iai-3aii-3eio-3eio-3	iai-3aii-3eio-3eio-3	PROPN
asir-6084	147	7	,	,	PUNCT
asir-6084	147	8	it	it	PRON
asir-6084	147	9	follows	follow	VERB
asir-6084	147	10	that	that	SCONJ
asir-6084	147	11	eio-3	eio-3	PUNCT
asir-6084	147	12	is	be	AUX
asir-6084	147	13	valid	valid	ADJ
asir-6084	147	14	,	,	PUNCT
asir-6084	147	15	and	and	CCONJ
asir-6084	147	16	its	its	PRON
asir-6084	147	17	expansion	expansion	NOUN
asir-6084	147	18	is	be	AUX
asir-6084	147	19	that	that	PRON
asir-6084	147	20	no(y	no(y	PROPN
asir-6084	147	21	,	,	PUNCT
asir-6084	147	22	z)some(y	z)some(y	PROPN
asir-6084	147	23	,	,	PUNCT
asir-6084	147	24	x)not	x)not	PROPN
asir-6084	147	25	all(x	all(x	PROPN
asir-6084	147	26	,	,	PUNCT
asir-6084	147	27	z	z	NOUN
asir-6084	147	28	)	)	PUNCT
asir-6084	147	29	.	.	PUNCT
asir-6084	148	1	according	accord	VERB
asir-6084	148	2	to	to	ADP
asir-6084	148	3	rule	rule	NOUN
asir-6084	148	4	2	2	NUM
asir-6084	148	5	,	,	PUNCT
asir-6084	148	6	it	it	PRON
asir-6084	148	7	can	can	AUX
asir-6084	148	8	be	be	AUX
asir-6084	148	9	derived	derive	VERB
asir-6084	148	10	that	that	PRON
asir-6084	148	11	not	not	VERB
asir-6084	148	12	all(x	all(x	PROPN
asir-6084	148	13	,	,	PUNCT
asir-6084	148	14	z)some(y	z)some(y	NOUN
asir-6084	148	15	,	,	PUNCT
asir-6084	148	16	x)no(y	x)no(y	NOUN
asir-6084	148	17	,	,	PUNCT
asir-6084	148	18	z	z	NOUN
asir-6084	148	19	)	)	PUNCT
asir-6084	148	20	.	.	PUNCT
asir-6084	149	1	in	in	ADP
asir-6084	149	2	line	line	NOUN
asir-6084	149	3	with	with	ADP
asir-6084	149	4	the	the	DET
asir-6084	149	5	clause	clause	NOUN
asir-6084	149	6	(	(	PUNCT
asir-6084	149	7	1	1	X
asir-6084	149	8	)	)	PUNCT
asir-6084	149	9	in	in	ADP
asir-6084	149	10	fact	fact	NOUN
asir-6084	149	11	3	3	NUM
asir-6084	149	12	,	,	PUNCT
asir-6084	149	13	one	one	PRON
asir-6084	149	14	can	can	AUX
asir-6084	149	15	deduce	deduce	VERB
asir-6084	149	16	that	that	DET
asir-6084	149	17	not	not	VERB
asir-6084	149	18	all(x	all(x	PROPN
asir-6084	149	19	,	,	PUNCT
asir-6084	149	20	z)some(y	z)some(y	NOUN
asir-6084	149	21	,	,	PUNCT
asir-6084	149	22	x)no(y	x)no(y	PROPN
asir-6084	149	23	,	,	PUNCT
asir-6084	149	24	z	z	NOUN
asir-6084	149	25	)	)	PUNCT
asir-6084	149	26	.	.	PUNCT
asir-6084	150	1	in	in	ADP
asir-6084	150	2	terms	term	NOUN
asir-6084	150	3	of	of	ADP
asir-6084	150	4	the	the	DET
asir-6084	150	5	clause	clause	NOUN
asir-6084	150	6	(	(	PUNCT
asir-6084	150	7	1	1	NUM
asir-6084	150	8	)	)	PUNCT
asir-6084	150	9	and	and	CCONJ
asir-6084	150	10	(	(	PUNCT
asir-6084	150	11	3	3	X
asir-6084	150	12	)	)	PUNCT
asir-6084	150	13	in	in	ADP
asir-6084	150	14	fact	fact	NOUN
asir-6084	150	15	2	2	NUM
asir-6084	150	16	,	,	PUNCT
asir-6084	150	17	it	it	PRON
asir-6084	150	18	follows	follow	VERB
asir-6084	150	19	that	that	PRON
asir-6084	150	20	not	not	ADV
asir-6084	150	21	all(x	all(x	PROPN
asir-6084	150	22	,	,	PUNCT
asir-6084	150	23	z)=all(x	z)=all(x	PROPN
asir-6084	150	24	,	,	PUNCT
asir-6084	150	25	z	z	NOUN
asir-6084	150	26	)	)	PUNCT
asir-6084	150	27	and	and	CCONJ
asir-6084	150	28	no(y	no(y	PROPN
asir-6084	150	29	,	,	PUNCT
asir-6084	150	30	z)=some(y	z)=some(y	X
asir-6084	150	31	,	,	PUNCT
asir-6084	150	32	z	z	NOUN
asir-6084	150	33	)	)	PUNCT
asir-6084	150	34	.	.	PUNCT
asir-6084	151	1	thus	thus	ADV
asir-6084	151	2	,	,	PUNCT
asir-6084	151	3	the	the	DET
asir-6084	151	4	syllogism	syllogism	NOUN
asir-6084	151	5	all(x	all(x	PROPN
asir-6084	151	6	,	,	PUNCT
asir-6084	151	7	z)some(y	z)some(y	NOUN
asir-6084	151	8	,	,	PUNCT
asir-6084	151	9	x)some(y	x)some(y	PROPN
asir-6084	151	10	,	,	PUNCT
asir-6084	151	11	z	z	NOUN
asir-6084	151	12	)	)	PUNCT
asir-6084	151	13	is	be	AUX
asir-6084	151	14	valid	valid	ADJ
asir-6084	151	15	.	.	PUNCT
asir-6084	152	1	that	that	PRON
asir-6084	152	2	is	is	ADV
asir-6084	152	3	,	,	PUNCT
asir-6084	152	4	aii-1	aii-1	PRON
asir-6084	152	5	can	can	AUX
asir-6084	152	6	be	be	AUX
asir-6084	152	7	derived	derive	VERB
asir-6084	152	8	from	from	ADP
asir-6084	152	9	iai-3	iai-3	NOUN
asir-6084	152	10	,	,	PUNCT
asir-6084	152	11	as	as	SCONJ
asir-6084	152	12	required	require	VERB
asir-6084	152	13	.	.	PUNCT
asir-6084	153	1	the	the	DET
asir-6084	153	2	two	two	NUM
asir-6084	153	3	others	other	NOUN
asir-6084	153	4	can	can	AUX
asir-6084	153	5	be	be	AUX
asir-6084	153	6	similarly	similarly	ADV
asir-6084	153	7	proved	prove	VERB
asir-6084	153	8	with	with	ADP
asir-6084	153	9	the	the	DET
asir-6084	153	10	help	help	NOUN
asir-6084	153	11	of	of	ADP
asir-6084	153	12	the	the	DET
asir-6084	153	13	above	above	ADJ
asir-6084	153	14	theorems	theorem	NOUN
asir-6084	153	15	,	,	PUNCT
asir-6084	153	16	facts	fact	NOUN
asir-6084	153	17	and	and	CCONJ
asir-6084	153	18	rules	rule	NOUN
asir-6084	153	19	.	.	PUNCT
asir-6084	154	1	theorem	theorem	NOUN
asir-6084	154	2	10	10	NUM
asir-6084	154	3	:	:	PUNCT
asir-6084	154	4	the	the	DET
asir-6084	154	5	following	follow	VERB
asir-6084	154	6	valid	valid	ADJ
asir-6084	154	7	modal	modal	ADJ
asir-6084	154	8	syllogisms	syllogism	NOUN
asir-6084	154	9	can	can	AUX
asir-6084	154	10	be	be	AUX
asir-6084	154	11	deduced	deduce	VERB
asir-6084	154	12	from	from	ADP
asir-6084	154	13	iai-3	iai-3	NOUN
asir-6084	154	14	:	:	PUNCT
asir-6084	154	15	(	(	PUNCT
asir-6084	154	16	10.1	10.1	NUM
asir-6084	154	17	)	)	PUNCT
asir-6084	154	18	iai-3iai-4	iai-3iai-4	NOUN
asir-6084	154	19	(	(	PUNCT
asir-6084	154	20	10.2	10.2	NUM
asir-6084	154	21	)	)	PUNCT
asir-6084	154	22	iai-3aii-3	iai-3aii-3	NOUN
asir-6084	154	23	(	(	PUNCT
asir-6084	154	24	10.3	10.3	NUM
asir-6084	154	25	)	)	PUNCT
asir-6084	154	26	iai-3aii-1	iai-3aii-1	NOUN
asir-6084	154	27	(	(	PUNCT
asir-6084	154	28	10.4	10.4	NUM
asir-6084	154	29	)	)	PUNCT
asir-6084	154	30	iai-3iai-3iai-4	iai-3iai-3iai-4	NOUN
asir-6084	154	31	(	(	PUNCT
asir-6084	154	32	10.5	10.5	NUM
asir-6084	154	33	)	)	PUNCT
asir-6084	154	34	iai-3iai-3aii-3	iai-3iai-3aii-3	NOUN
asir-6084	154	35	(	(	PUNCT
asir-6084	154	36	10.6	10.6	NUM
asir-6084	154	37	)	)	PUNCT
asir-6084	154	38	iai-3iai-3aii-1	iai-3iai-3aii-1	NUM
asir-6084	154	39	(	(	PUNCT
asir-6084	154	40	10.7	10.7	NUM
asir-6084	154	41	)	)	PUNCT
asir-6084	155	1	iai-3iai-3iai-4	iai-3iai-3iai-4	NOUN
asir-6084	155	2	(	(	PUNCT
asir-6084	155	3	10.8	10.8	NUM
asir-6084	155	4	)	)	PUNCT
asir-6084	155	5	iai-3iai-3aii-3	iai-3iai-3aii-3	PROPN
asir-6084	155	6	(	(	PUNCT
asir-6084	155	7	10.9	10.9	NUM
asir-6084	155	8	)	)	PUNCT
asir-6084	155	9	iai-3iai-3aii-1	iai-3iai-3aii-1	PROPN
asir-6084	155	10	(	(	PUNCT
asir-6084	155	11	10.10	10.10	NUM
asir-6084	155	12	)	)	PUNCT
asir-6084	155	13	iai-3eio-2eio-4	iai-3eio-2eio-4	PROPN
asir-6084	155	14	(	(	PUNCT
asir-6084	155	15	10.11	10.11	NUM
asir-6084	155	16	)	)	PUNCT
asir-6084	155	17	iai-3eio-2eio-1	iai-3eio-2eio-1	NUM
asir-6084	155	18	(	(	PUNCT
asir-6084	155	19	10.12	10.12	NUM
asir-6084	155	20	)	)	PUNCT
asir-6084	155	21	iai-3eio-2eio-3	iai-3eio-2eio-3	PROPN
asir-6084	155	22	(	(	PUNCT
asir-6084	155	23	10.13	10.13	NUM
asir-6084	155	24	)	)	PUNCT
asir-6084	155	25	iai-3eae-1eae-2	iai-3eae-1eae-2	NUM
asir-6084	155	26	(	(	PUNCT
asir-6084	155	27	10.14	10.14	NUM
asir-6084	155	28	)	)	PUNCT
asir-6084	155	29	iai-3eae-1aee-4	iai-3eae-1aee-4	NOUN
asir-6084	155	30	(	(	PUNCT
asir-6084	155	31	10.15	10.15	NUM
asir-6084	155	32	)	)	PUNCT
asir-6084	156	1	iai-3eae-1aee-2	iai-3eae-1aee-2	SYM
asir-6084	156	2	proof	proof	NOUN
asir-6084	156	3	:	:	PUNCT
asir-6084	156	4	for	for	ADP
asir-6084	156	5	(	(	PUNCT
asir-6084	156	6	10.1	10.1	NUM
asir-6084	156	7	)	)	PUNCT
asir-6084	156	8	.	.	PUNCT
asir-6084	157	1	according	accord	VERB
asir-6084	157	2	to	to	ADP
asir-6084	157	3	theorem	theorem	ADJ
asir-6084	157	4	1	1	NUM
asir-6084	157	5	,	,	PUNCT
asir-6084	157	6	iai-3	iai-3	NOUN
asir-6084	157	7	is	be	AUX
asir-6084	157	8	valid	valid	ADJ
asir-6084	157	9	,	,	PUNCT
asir-6084	157	10	and	and	CCONJ
asir-6084	157	11	its	its	PRON
asir-6084	157	12	expansion	expansion	NOUN
asir-6084	157	13	is	be	AUX
asir-6084	157	14	that	that	SCONJ
asir-6084	157	15	some(y	some(y	ADJ
asir-6084	157	16	,	,	PUNCT
asir-6084	157	17	z)all(y	z)all(y	PROPN
asir-6084	157	18	,	,	PUNCT
asir-6084	157	19	x)some(x	x)some(x	PROPN
asir-6084	157	20	,	,	PUNCT
asir-6084	157	21	z	z	NOUN
asir-6084	157	22	)	)	PUNCT
asir-6084	157	23	.	.	PUNCT
asir-6084	158	1	according	accord	VERB
asir-6084	158	2	to	to	ADP
asir-6084	158	3	the	the	DET
asir-6084	158	4	clause	clause	NOUN
asir-6084	158	5	(	(	PUNCT
asir-6084	158	6	1	1	X
asir-6084	158	7	)	)	PUNCT
asir-6084	158	8	in	in	ADP
asir-6084	158	9	fact	fact	NOUN
asir-6084	158	10	7	7	NUM
asir-6084	158	11	,	,	PUNCT
asir-6084	158	12	it	it	PRON
asir-6084	158	13	can	can	AUX
asir-6084	158	14	be	be	AUX
asir-6084	158	15	seen	see	VERB
asir-6084	158	16	that	that	SCONJ
asir-6084	158	17	some(y	some(y	ADJ
asir-6084	158	18	,	,	PUNCT
asir-6084	158	19	z)some(z	z)some(z	PROPN
asir-6084	158	20	,	,	PUNCT
asir-6084	158	21	y	y	NOUN
asir-6084	158	22	)	)	PUNCT
asir-6084	158	23	.	.	PUNCT
asir-6084	159	1	hence	hence	ADV
asir-6084	159	2	,	,	PUNCT
asir-6084	159	3	it	it	PRON
asir-6084	159	4	follows	follow	VERB
asir-6084	159	5	that	that	PRON
asir-6084	159	6	some(z	some(z	NOUN
asir-6084	159	7	,	,	PUNCT
asir-6084	159	8	y)all(y	y)all(y	ADJ
asir-6084	159	9	,	,	PUNCT
asir-6084	159	10	x)some(x	x)some(x	PROPN
asir-6084	159	11	,	,	PUNCT
asir-6084	159	12	z	z	NOUN
asir-6084	159	13	)	)	PUNCT
asir-6084	159	14	.	.	PUNCT
asir-6084	160	1	that	that	PRON
asir-6084	160	2	is	be	AUX
asir-6084	160	3	to	to	PART
asir-6084	160	4	say	say	VERB
asir-6084	160	5	that	that	SCONJ
asir-6084	160	6	iai-4	iai-4	NOUN
asir-6084	160	7	can	can	AUX
asir-6084	160	8	be	be	AUX
asir-6084	160	9	derived	derive	VERB
asir-6084	160	10	from	from	ADP
asir-6084	160	11	iai-3	iai-3	NOUN
asir-6084	160	12	,	,	PUNCT
asir-6084	160	13	the	the	DET
asir-6084	160	14	proof	proof	NOUN
asir-6084	160	15	of	of	ADP
asir-6084	160	16	(	(	PUNCT
asir-6084	160	17	10.1	10.1	NUM
asir-6084	160	18	)	)	PUNCT
asir-6084	160	19	has	have	AUX
asir-6084	160	20	been	be	AUX
asir-6084	160	21	completed	complete	VERB
asir-6084	160	22	.	.	PUNCT
asir-6084	161	1	the	the	DET
asir-6084	161	2	remaining	remain	VERB
asir-6084	161	3	syllogisms	syllogism	NOUN
asir-6084	161	4	can	can	AUX
asir-6084	161	5	be	be	AUX
asir-6084	161	6	similarly	similarly	ADV
asir-6084	161	7	deduced	deduce	VERB
asir-6084	161	8	from	from	ADP
asir-6084	161	9	iai-3	iai-3	PROPN
asir-6084	161	10	.	.	PUNCT
asir-6084	162	1	theorem	theorem	ADJ
asir-6084	162	2	11	11	NUM
asir-6084	162	3	:	:	PUNCT
asir-6084	162	4	the	the	DET
asir-6084	162	5	following	follow	VERB
asir-6084	162	6	valid	valid	ADJ
asir-6084	162	7	modal	modal	ADJ
asir-6084	162	8	syllogisms	syllogism	NOUN
asir-6084	162	9	can	can	AUX
asir-6084	162	10	be	be	AUX
asir-6084	162	11	obtained	obtain	VERB
asir-6084	162	12	from	from	ADP
asir-6084	162	13	iai-3	iai-3	NOUN
asir-6084	162	14	:	:	PUNCT
asir-6084	162	15	(	(	PUNCT
asir-6084	162	16	11.1	11.1	NUM
asir-6084	162	17	)	)	PUNCT
asir-6084	162	18	iai-3oao-3oao-3aaa-1aai-1	iai-3oao-3oao-3aaa-1aai-1	ADJ
asir-6084	162	19	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	162	20	applied	apply	VERB
asir-6084	162	21	science	science	NOUN
asir-6084	162	22	and	and	CCONJ
asir-6084	162	23	innovative	innovative	ADJ
asir-6084	162	24	research	research	NOUN
asir-6084	162	25	vol	vol	NOUN
asir-6084	162	26	.	.	PUNCT
asir-6084	163	1	7	7	NUM
asir-6084	163	2	,	,	PUNCT
asir-6084	163	3	no	no	INTJ
asir-6084	163	4	.	.	NOUN
asir-6084	163	5	1	1	NUM
asir-6084	163	6	,	,	PUNCT
asir-6084	163	7	2023	2023	NUM
asir-6084	163	8	53	53	NUM
asir-6084	163	9	published	publish	VERB
asir-6084	163	10	by	by	ADP
asir-6084	163	11	scholink	scholink	PROPN
asir-6084	163	12	inc	inc	PROPN
asir-6084	163	13	.	.	PUNCT
asir-6084	164	1	aai-4	aai-4	PROPN
asir-6084	164	2	(	(	PUNCT
asir-6084	164	3	11.2	11.2	NUM
asir-6084	164	4	)	)	PUNCT
asir-6084	164	5	iai-3oao-3oao-3aaa-1aai-1	iai-3oao-3oao-3aaa-1aai-1	NOUN
asir-6084	164	6	aai-4	aai-4	PROPN
asir-6084	164	7	(	(	PUNCT
asir-6084	164	8	11.3	11.3	NUM
asir-6084	164	9	)	)	PUNCT
asir-6084	165	1	iai-3oao-3aaa-1aai-1eao-3	iai-3oao-3aaa-1aai-1eao-3	NOUN
asir-6084	165	2	eao-4	eao-4	NOUN
asir-6084	165	3	proof	proof	NOUN
asir-6084	165	4	:	:	PUNCT
asir-6084	165	5	for	for	ADP
asir-6084	165	6	(	(	PUNCT
asir-6084	165	7	11.1	11.1	NUM
asir-6084	165	8	)	)	PUNCT
asir-6084	165	9	.	.	PUNCT
asir-6084	166	1	according	accord	VERB
asir-6084	166	2	to	to	ADP
asir-6084	166	3	(	(	PUNCT
asir-6084	166	4	10.6	10.6	NUM
asir-6084	166	5	)	)	PUNCT
asir-6084	166	6	iai-3iai-3aii-1	iai-3iai-3aii-1	NOUN
asir-6084	166	7	,	,	PUNCT
asir-6084	166	8	aai-1	aai-1	PROPN
asir-6084	166	9	is	be	AUX
asir-6084	166	10	valid	valid	ADJ
asir-6084	166	11	,	,	PUNCT
asir-6084	166	12	and	and	CCONJ
asir-6084	166	13	its	its	PRON
asir-6084	166	14	expansion	expansion	NOUN
asir-6084	166	15	is	be	AUX
asir-6084	166	16	that	that	SCONJ
asir-6084	166	17	all(y	all(y	PROPN
asir-6084	166	18	,	,	PUNCT
asir-6084	166	19	z)all(x	z)all(x	PROPN
asir-6084	166	20	,	,	PUNCT
asir-6084	166	21	y)some(x	y)some(x	PROPN
asir-6084	166	22	,	,	PUNCT
asir-6084	166	23	z	z	NOUN
asir-6084	166	24	)	)	PUNCT
asir-6084	166	25	.	.	PUNCT
asir-6084	167	1	in	in	ADP
asir-6084	167	2	terms	term	NOUN
asir-6084	167	3	of	of	ADP
asir-6084	167	4	the	the	DET
asir-6084	167	5	clause	clause	NOUN
asir-6084	167	6	(	(	PUNCT
asir-6084	167	7	1	1	X
asir-6084	167	8	)	)	PUNCT
asir-6084	167	9	in	in	ADP
asir-6084	167	10	fact	fact	NOUN
asir-6084	167	11	7	7	NUM
asir-6084	167	12	,	,	PUNCT
asir-6084	167	13	it	it	PRON
asir-6084	167	14	can	can	AUX
asir-6084	167	15	be	be	AUX
asir-6084	167	16	seen	see	VERB
asir-6084	167	17	that	that	SCONJ
asir-6084	167	18	some(x	some(x	NOUN
asir-6084	167	19	,	,	PUNCT
asir-6084	167	20	z)some(z	z)some(z	PROPN
asir-6084	167	21	,	,	PUNCT
asir-6084	167	22	x	x	NOUN
asir-6084	167	23	)	)	PUNCT
asir-6084	167	24	.	.	PUNCT
asir-6084	168	1	therefore	therefore	ADV
asir-6084	168	2	,	,	PUNCT
asir-6084	168	3	one	one	PRON
asir-6084	168	4	can	can	AUX
asir-6084	168	5	easily	easily	ADV
asir-6084	168	6	derive	derive	VERB
asir-6084	168	7	that	that	SCONJ
asir-6084	168	8	all(x	all(x	PROPN
asir-6084	168	9	,	,	PUNCT
asir-6084	168	10	y)all(y	y)all(y	NOUN
asir-6084	168	11	,	,	PUNCT
asir-6084	168	12	x)some(z	x)some(z	PROPN
asir-6084	168	13	,	,	PUNCT
asir-6084	168	14	x	x	NOUN
asir-6084	168	15	)	)	PUNCT
asir-6084	168	16	.	.	PUNCT
asir-6084	169	1	in	in	ADP
asir-6084	169	2	other	other	ADJ
asir-6084	169	3	words	word	NOUN
asir-6084	169	4	,	,	PUNCT
asir-6084	169	5	aai-4	aai-4	PROPN
asir-6084	169	6	can	can	AUX
asir-6084	169	7	be	be	AUX
asir-6084	169	8	derived	derive	VERB
asir-6084	169	9	from	from	ADP
asir-6084	169	10	iai-3	iai-3	NOUN
asir-6084	169	11	,	,	PUNCT
asir-6084	169	12	just	just	ADV
asir-6084	169	13	as	as	SCONJ
asir-6084	169	14	required	require	VERB
asir-6084	169	15	.	.	PUNCT
asir-6084	170	1	others	other	NOUN
asir-6084	170	2	can	can	AUX
asir-6084	170	3	be	be	AUX
asir-6084	170	4	similarly	similarly	ADV
asir-6084	170	5	proved	prove	VERB
asir-6084	170	6	.	.	PUNCT
asir-6084	171	1	theorem	theorem	ADJ
asir-6084	171	2	12	12	NUM
asir-6084	171	3	:	:	PUNCT
asir-6084	171	4	the	the	DET
asir-6084	171	5	following	follow	VERB
asir-6084	171	6	valid	valid	ADJ
asir-6084	171	7	modal	modal	ADJ
asir-6084	171	8	syllogisms	syllogism	NOUN
asir-6084	171	9	can	can	AUX
asir-6084	171	10	be	be	AUX
asir-6084	171	11	obtained	obtain	VERB
asir-6084	171	12	from	from	ADP
asir-6084	171	13	iai-3	iai-3	NOUN
asir-6084	171	14	:	:	PUNCT
asir-6084	171	15	(	(	PUNCT
asir-6084	171	16	12.1	12.1	NUM
asir-6084	171	17	)	)	PUNCT
asir-6084	171	18	iai-3iai-3eio-2eio-4	iai-3iai-3eio-2eio-4	NOUN
asir-6084	171	19	(	(	PUNCT
asir-6084	171	20	12.2	12.2	NUM
asir-6084	171	21	)	)	PUNCT
asir-6084	171	22	iai-3iai-3eio-2eio-1	iai-3iai-3eio-2eio-1	NOUN
asir-6084	171	23	(	(	PUNCT
asir-6084	171	24	12.3	12.3	NUM
asir-6084	171	25	)	)	PUNCT
asir-6084	171	26	iai-3iai-3eio-2eio-3	iai-3iai-3eio-2eio-3	NOUN
asir-6084	171	27	(	(	PUNCT
asir-6084	171	28	12.4	12.4	NUM
asir-6084	171	29	)	)	PUNCT
asir-6084	171	30	iai-3iai-3eae-1eae-2	iai-3iai-3eae-1eae-2	NOUN
asir-6084	171	31	(	(	PUNCT
asir-6084	171	32	12.5	12.5	NUM
asir-6084	171	33	)	)	PUNCT
asir-6084	171	34	iai-3iai-3eae-1aee-4	iai-3iai-3eae-1aee-4	NOUN
asir-6084	171	35	(	(	PUNCT
asir-6084	171	36	12.6	12.6	NUM
asir-6084	171	37	)	)	PUNCT
asir-6084	171	38	iai-3iai-3eae-1aee-2	iai-3iai-3eae-1aee-2	PROPN
asir-6084	171	39	(	(	PUNCT
asir-6084	171	40	12.7	12.7	NUM
asir-6084	171	41	)	)	PUNCT
asir-6084	171	42	iai-3iai-3eio-2eio-4	iai-3iai-3eio-2eio-4	NOUN
asir-6084	171	43	(	(	PUNCT
asir-6084	171	44	12.8	12.8	NUM
asir-6084	171	45	)	)	PUNCT
asir-6084	171	46	iai-3iai-3eio-2eio-1	iai-3iai-3eio-2eio-1	NOUN
asir-6084	171	47	(	(	PUNCT
asir-6084	171	48	12.9	12.9	NUM
asir-6084	171	49	)	)	PUNCT
asir-6084	171	50	iai-3iai-3eio-2eio-3	iai-3iai-3eio-2eio-3	NOUN
asir-6084	171	51	(	(	PUNCT
asir-6084	171	52	12.10	12.10	NUM
asir-6084	171	53	)	)	PUNCT
asir-6084	171	54	iai-3iai-3eae-1eae-2	iai-3iai-3eae-1eae-2	NOUN
asir-6084	171	55	(	(	PUNCT
asir-6084	171	56	12.11	12.11	NUM
asir-6084	171	57	)	)	PUNCT
asir-6084	171	58	iai-3iai-3eae-1aee-4	iai-3iai-3eae-1aee-4	NOUN
asir-6084	171	59	(	(	PUNCT
asir-6084	171	60	12.12	12.12	NUM
asir-6084	171	61	)	)	PUNCT
asir-6084	171	62	iai-3iai-3eae-1aee-2	iai-3iai-3eae-1aee-2	NOUN
asir-6084	171	63	(	(	PUNCT
asir-6084	171	64	12.13	12.13	NUM
asir-6084	171	65	)	)	PUNCT
asir-6084	171	66	iai-3aii-3eio-3eio-4	iai-3aii-3eio-3eio-4	NOUN
asir-6084	171	67	(	(	PUNCT
asir-6084	171	68	12.14	12.14	NUM
asir-6084	171	69	)	)	PUNCT
asir-6084	172	1	iai-3aii-3eio-3eio-1	iai-3aii-3eio-3eio-1	NOUN
asir-6084	172	2	(	(	PUNCT
asir-6084	172	3	12.15	12.15	NUM
asir-6084	172	4	)	)	PUNCT
asir-6084	172	5	iai-3aii-3eio-3eio-2	iai-3aii-3eio-3eio-2	NOUN
asir-6084	172	6	proof	proof	NOUN
asir-6084	172	7	:	:	PUNCT
asir-6084	172	8	for	for	ADP
asir-6084	172	9	(	(	PUNCT
asir-6084	172	10	12.1	12.1	NUM
asir-6084	172	11	)	)	PUNCT
asir-6084	172	12	.	.	PUNCT
asir-6084	173	1	according	accord	VERB
asir-6084	173	2	to	to	ADP
asir-6084	173	3	(	(	PUNCT
asir-6084	173	4	4.2	4.2	NUM
asir-6084	173	5	)	)	PUNCT
asir-6084	173	6	iai-3iai-3eio-2	iai-3iai-3eio-2	NOUN
asir-6084	173	7	,	,	PUNCT
asir-6084	173	8	eio-2	eio-2	NUM
asir-6084	173	9	is	be	AUX
asir-6084	173	10	valid	valid	ADJ
asir-6084	173	11	,	,	PUNCT
asir-6084	173	12	and	and	CCONJ
asir-6084	173	13	its	its	PRON
asir-6084	173	14	expansion	expansion	NOUN
asir-6084	173	15	is	be	AUX
asir-6084	173	16	that	that	SCONJ
asir-6084	173	17	no(z	no(z	NOUN
asir-6084	173	18	,	,	PUNCT
asir-6084	173	19	y)some(x	y)some(x	NOUN
asir-6084	173	20	,	,	PUNCT
asir-6084	173	21	y)not	y)not	PROPN
asir-6084	173	22	all(x	all(x	PROPN
asir-6084	173	23	,	,	PUNCT
asir-6084	173	24	z	z	NOUN
asir-6084	173	25	)	)	PUNCT
asir-6084	173	26	.	.	PUNCT
asir-6084	174	1	in	in	ADP
asir-6084	174	2	the	the	DET
asir-6084	174	3	light	light	NOUN
asir-6084	174	4	of	of	ADP
asir-6084	174	5	the	the	DET
asir-6084	174	6	clause	clause	NOUN
asir-6084	174	7	(	(	PUNCT
asir-6084	174	8	1	1	X
asir-6084	174	9	)	)	PUNCT
asir-6084	174	10	in	in	ADP
asir-6084	174	11	fact	fact	NOUN
asir-6084	174	12	7	7	NUM
asir-6084	174	13	,	,	PUNCT
asir-6084	174	14	it	it	PRON
asir-6084	174	15	follows	follow	VERB
asir-6084	174	16	that	that	SCONJ
asir-6084	174	17	some(x	some(x	NOUN
asir-6084	174	18	,	,	PUNCT
asir-6084	174	19	y)some(y	y)some(y	PROPN
asir-6084	174	20	,	,	PUNCT
asir-6084	174	21	x	x	NOUN
asir-6084	174	22	)	)	PUNCT
asir-6084	174	23	.	.	PUNCT
asir-6084	175	1	therefore	therefore	ADV
asir-6084	175	2	,	,	PUNCT
asir-6084	175	3	it	it	PRON
asir-6084	175	4	is	be	AUX
asir-6084	175	5	easily	easily	ADV
asir-6084	175	6	seen	see	VERB
asir-6084	175	7	that	that	SCONJ
asir-6084	175	8	no(z	no(z	NOUN
asir-6084	175	9	,	,	PUNCT
asir-6084	175	10	y)some(y	y)some(y	NOUN
asir-6084	175	11	,	,	PUNCT
asir-6084	175	12	x)not	x)not	PROPN
asir-6084	175	13	all(x	all(x	PROPN
asir-6084	175	14	,	,	PUNCT
asir-6084	175	15	z	z	NOUN
asir-6084	175	16	)	)	PUNCT
asir-6084	175	17	.	.	PUNCT
asir-6084	176	1	that	that	PRON
asir-6084	176	2	is	is	ADV
asir-6084	176	3	,	,	PUNCT
asir-6084	176	4	eio-4	eio-4	PROPN
asir-6084	176	5	can	can	AUX
asir-6084	176	6	be	be	AUX
asir-6084	176	7	derived	derive	VERB
asir-6084	176	8	from	from	ADP
asir-6084	176	9	iai-3	iai-3	NOUN
asir-6084	176	10	,	,	PUNCT
asir-6084	176	11	the	the	DET
asir-6084	176	12	proof	proof	NOUN
asir-6084	176	13	of	of	ADP
asir-6084	176	14	(	(	PUNCT
asir-6084	176	15	12.1	12.1	NUM
asir-6084	176	16	)	)	PUNCT
asir-6084	176	17	has	have	AUX
asir-6084	176	18	been	be	AUX
asir-6084	176	19	completed	complete	VERB
asir-6084	176	20	.	.	PUNCT
asir-6084	177	1	the	the	DET
asir-6084	177	2	others	other	NOUN
asir-6084	177	3	can	can	AUX
asir-6084	177	4	be	be	AUX
asir-6084	177	5	similarly	similarly	ADV
asir-6084	177	6	followed	follow	VERB
asir-6084	177	7	from	from	ADP
asir-6084	177	8	iai-3	iai-3	PROPN
asir-6084	177	9	.	.	PUNCT
asir-6084	178	1	theorem	theorem	ADJ
asir-6084	178	2	13	13	NUM
asir-6084	178	3	:	:	PUNCT
asir-6084	178	4	the	the	DET
asir-6084	178	5	following	follow	VERB
asir-6084	178	6	valid	valid	ADJ
asir-6084	178	7	modal	modal	ADJ
asir-6084	178	8	syllogisms	syllogism	NOUN
asir-6084	178	9	can	can	AUX
asir-6084	178	10	be	be	AUX
asir-6084	178	11	inferred	infer	VERB
asir-6084	178	12	from	from	ADP
asir-6084	178	13	iai-3	iai-3	NOUN
asir-6084	178	14	:	:	PUNCT
asir-6084	178	15	(	(	PUNCT
asir-6084	178	16	13.1	13.1	NUM
asir-6084	178	17	)	)	PUNCT
asir-6084	178	18	iai-3eae-1eao-1	iai-3eae-1eao-1	NOUN
asir-6084	178	19	(	(	PUNCT
asir-6084	178	20	13.2	13.2	NUM
asir-6084	178	21	)	)	PUNCT
asir-6084	178	22	iai-3eae-1eae-2eao-2	iai-3eae-1eae-2eao-2	PROPN
asir-6084	178	23	(	(	PUNCT
asir-6084	178	24	13.3	13.3	NUM
asir-6084	178	25	)	)	PUNCT
asir-6084	178	26	iai-3eae-1aee-4aeo-4	iai-3eae-1aee-4aeo-4	X
asir-6084	178	27	(	(	PUNCT
asir-6084	178	28	13.4	13.4	NUM
asir-6084	178	29	)	)	PUNCT
asir-6084	179	1	iai-3eae-1aee-2aeo-2	iai-3eae-1aee-2aeo-2	NOUN
asir-6084	179	2	(	(	PUNCT
asir-6084	179	3	13.5	13.5	NUM
asir-6084	179	4	)	)	PUNCT
asir-6084	179	5	iai-3iai-3eae-1eao-1	iai-3iai-3eae-1eao-1	NOUN
asir-6084	179	6	(	(	PUNCT
asir-6084	179	7	13.6	13.6	NUM
asir-6084	179	8	)	)	PUNCT
asir-6084	179	9	iai-3iai-3eae-1eae-2eao-2	iai-3iai-3eae-1eae-2eao-2	PROPN
asir-6084	179	10	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	179	11	applied	apply	VERB
asir-6084	179	12	science	science	NOUN
asir-6084	179	13	and	and	CCONJ
asir-6084	179	14	innovative	innovative	ADJ
asir-6084	179	15	research	research	NOUN
asir-6084	179	16	vol	vol	NOUN
asir-6084	179	17	.	.	PUNCT
asir-6084	180	1	7	7	NUM
asir-6084	180	2	,	,	PUNCT
asir-6084	180	3	no	no	INTJ
asir-6084	180	4	.	.	NOUN
asir-6084	180	5	1	1	NUM
asir-6084	180	6	,	,	PUNCT
asir-6084	180	7	2023	2023	NUM
asir-6084	180	8	54	54	NUM
asir-6084	180	9	published	publish	VERB
asir-6084	180	10	by	by	ADP
asir-6084	180	11	scholink	scholink	PROPN
asir-6084	180	12	inc	inc	PROPN
asir-6084	180	13	.	.	PROPN
asir-6084	181	1	(	(	PUNCT
asir-6084	181	2	13.7	13.7	NUM
asir-6084	181	3	)	)	PUNCT
asir-6084	181	4	iai-3iai-3eae-1aee-4aeo-4	iai-3iai-3eae-1aee-4aeo-4	PROPN
asir-6084	181	5	(	(	PUNCT
asir-6084	181	6	13.8	13.8	NUM
asir-6084	181	7	)	)	PUNCT
asir-6084	181	8	iai-3iai-3eae-1aee-2aeo-2	iai-3iai-3eae-1aee-2aeo-2	NOUN
asir-6084	181	9	(	(	PUNCT
asir-6084	181	10	13.9	13.9	NUM
asir-6084	181	11	)	)	PUNCT
asir-6084	181	12	iai-3iai-3eae-1eao-1	iai-3iai-3eae-1eao-1	NOUN
asir-6084	181	13	(	(	PUNCT
asir-6084	181	14	13.10	13.10	NUM
asir-6084	181	15	)	)	PUNCT
asir-6084	181	16	iai-3iai-3eae-1eae-2eao-2	iai-3iai-3eae-1eae-2eao-2	PROPN
asir-6084	181	17	(	(	PUNCT
asir-6084	181	18	13.11	13.11	NUM
asir-6084	181	19	)	)	PUNCT
asir-6084	181	20	iai-3iai-3eae-1aee-4aeo-4	iai-3iai-3eae-1aee-4aeo-4	PROPN
asir-6084	181	21	(	(	PUNCT
asir-6084	181	22	13.12	13.12	NUM
asir-6084	181	23	)	)	PUNCT
asir-6084	181	24	iai-3iai-3eae-1aee-2aeo-2	iai-3iai-3eae-1aee-2aeo-2	PROPN
asir-6084	181	25	(	(	PUNCT
asir-6084	181	26	13.13	13.13	NUM
asir-6084	181	27	)	)	PUNCT
asir-6084	181	28	iai-3oao-3aaa-1aai-1	iai-3oao-3aaa-1aai-1	PROPN
asir-6084	181	29	(	(	PUNCT
asir-6084	181	30	13.14	13.14	NUM
asir-6084	181	31	)	)	PUNCT
asir-6084	181	32	iai-3oao-3oao-3aaa-1aai-1	iai-3oao-3oao-3aaa-1aai-1	PROPN
asir-6084	181	33	(	(	PUNCT
asir-6084	181	34	13.15	13.15	NUM
asir-6084	181	35	)	)	PUNCT
asir-6084	181	36	iai-3oao-3oao-3aaa-1aai-1	iai-3oao-3oao-3aaa-1aai-1	PROPN
asir-6084	181	37	(	(	PUNCT
asir-6084	181	38	13.16	13.16	NUM
asir-6084	181	39	)	)	PUNCT
asir-6084	181	40	iai-3aii-3eio-3aee-2aeo-2	iai-3aii-3eio-3aee-2aeo-2	NOUN
asir-6084	181	41	(	(	PUNCT
asir-6084	181	42	13.17	13.17	NUM
asir-6084	181	43	)	)	PUNCT
asir-6084	182	1	iai-3aii-3eio-3aee-2aee-4	iai-3aii-3eio-3aee-2aee-4	ADV
asir-6084	182	2	aeo-4	aeo-4	PROPN
asir-6084	182	3	(	(	PUNCT
asir-6084	182	4	13.18	13.18	NUM
asir-6084	182	5	)	)	PUNCT
asir-6084	182	6	iai-3aii-3eio-3aee-2eae-2	iai-3aii-3eio-3aee-2eae-2	PROPN
asir-6084	182	7	eao-2	eao-2	NOUN
asir-6084	182	8	(	(	PUNCT
asir-6084	182	9	13.19	13.19	NUM
asir-6084	182	10	)	)	PUNCT
asir-6084	182	11	iai-3aii-3eio-3aee-2eae-1	iai-3aii-3eio-3aee-2eae-1	PROPN
asir-6084	182	12	eao-1	eao-1	NOUN
asir-6084	182	13	proof	proof	NOUN
asir-6084	182	14	:	:	PUNCT
asir-6084	182	15	for	for	ADP
asir-6084	182	16	(	(	PUNCT
asir-6084	182	17	13.1	13.1	NUM
asir-6084	182	18	)	)	PUNCT
asir-6084	182	19	.	.	PUNCT
asir-6084	183	1	according	accord	VERB
asir-6084	183	2	to	to	ADP
asir-6084	183	3	(	(	PUNCT
asir-6084	183	4	10.14	10.14	NUM
asir-6084	183	5	)	)	PUNCT
asir-6084	183	6	iai-3eae-1aee-4	iai-3eae-1aee-4	NOUN
asir-6084	183	7	,	,	PUNCT
asir-6084	183	8	one	one	PRON
asir-6084	183	9	can	can	AUX
asir-6084	183	10	see	see	VERB
asir-6084	183	11	that	that	SCONJ
asir-6084	183	12	eae-1	eae-1	PROPN
asir-6084	183	13	is	be	AUX
asir-6084	183	14	valid	valid	ADJ
asir-6084	183	15	.	.	PUNCT
asir-6084	184	1	with	with	ADP
asir-6084	184	2	the	the	DET
asir-6084	184	3	help	help	NOUN
asir-6084	184	4	of	of	ADP
asir-6084	184	5	fact	fact	NOUN
asir-6084	184	6	6	6	NUM
asir-6084	184	7	,	,	PUNCT
asir-6084	184	8	it	it	PRON
asir-6084	184	9	follows	follow	VERB
asir-6084	184	10	that	that	SCONJ
asir-6084	184	11	eo	eo	NOUN
asir-6084	184	12	,	,	PUNCT
asir-6084	184	13	so	so	ADV
asir-6084	184	14	eao-1	eao-1	PROPN
asir-6084	184	15	is	be	AUX
asir-6084	184	16	valid	valid	ADJ
asir-6084	184	17	.	.	PUNCT
asir-6084	185	1	in	in	ADP
asir-6084	185	2	other	other	ADJ
asir-6084	185	3	words	word	NOUN
asir-6084	185	4	,	,	PUNCT
asir-6084	185	5	eao-1	eao-1	PROPN
asir-6084	185	6	can	can	AUX
asir-6084	185	7	be	be	AUX
asir-6084	185	8	derived	derive	VERB
asir-6084	185	9	from	from	ADP
asir-6084	185	10	iai-3	iai-3	NOUN
asir-6084	185	11	,	,	PUNCT
asir-6084	185	12	as	as	SCONJ
asir-6084	185	13	required	require	VERB
asir-6084	185	14	.	.	PUNCT
asir-6084	186	1	on	on	ADP
asir-6084	186	2	the	the	DET
asir-6084	186	3	basis	basis	NOUN
asir-6084	186	4	of	of	ADP
asir-6084	186	5	the	the	DET
asir-6084	186	6	above	above	ADJ
asir-6084	186	7	theorems	theorem	NOUN
asir-6084	186	8	,	,	PUNCT
asir-6084	186	9	facts	fact	NOUN
asir-6084	186	10	and	and	CCONJ
asir-6084	186	11	rules	rule	NOUN
asir-6084	186	12	,	,	PUNCT
asir-6084	186	13	all	all	PRON
asir-6084	186	14	of	of	ADP
asir-6084	186	15	the	the	DET
asir-6084	186	16	other	other	ADJ
asir-6084	186	17	syllogisms	syllogism	NOUN
asir-6084	186	18	can	can	AUX
asir-6084	186	19	be	be	AUX
asir-6084	186	20	similarly	similarly	ADV
asir-6084	186	21	deduced	deduce	VERB
asir-6084	186	22	from	from	ADP
asir-6084	186	23	iai-3	iai-3	PROPN
asir-6084	186	24	.	.	PUNCT
asir-6084	187	1	theorem	theorem	ADJ
asir-6084	187	2	14	14	NUM
asir-6084	187	3	:	:	PUNCT
asir-6084	187	4	the	the	DET
asir-6084	187	5	following	follow	VERB
asir-6084	187	6	valid	valid	ADJ
asir-6084	187	7	modal	modal	ADJ
asir-6084	187	8	syllogisms	syllogism	NOUN
asir-6084	187	9	can	can	AUX
asir-6084	187	10	be	be	AUX
asir-6084	187	11	derived	derive	VERB
asir-6084	187	12	from	from	ADP
asir-6084	187	13	iai-3	iai-3	NOUN
asir-6084	187	14	:	:	PUNCT
asir-6084	187	15	(	(	PUNCT
asir-6084	187	16	14.1	14.1	NUM
asir-6084	187	17	)	)	PUNCT
asir-6084	187	18	iai-3aii-3eio-3aee-2aee-4	iai-3aii-3eio-3aee-2aee-4	NOUN
asir-6084	187	19	(	(	PUNCT
asir-6084	187	20	14.2	14.2	NUM
asir-6084	187	21	)	)	PUNCT
asir-6084	187	22	iai-3aii-3eio-3aee-2eae-2	iai-3aii-3eio-3aee-2eae-2	PROPN
asir-6084	187	23	(	(	PUNCT
asir-6084	187	24	14.3	14.3	NUM
asir-6084	187	25	)	)	PUNCT
asir-6084	187	26	iai-3aii-3eio-3aee-2eae-1	iai-3aii-3eio-3aee-2eae-1	NOUN
asir-6084	187	27	(	(	PUNCT
asir-6084	187	28	14.4	14.4	NUM
asir-6084	187	29	)	)	PUNCT
asir-6084	187	30	iai-3aii-3eio-3aii-1aii-3	iai-3aii-3eio-3aii-1aii-3	NOUN
asir-6084	187	31	(	(	PUNCT
asir-6084	187	32	14.5	14.5	NUM
asir-6084	187	33	)	)	PUNCT
asir-6084	187	34	iai-3aii-3eio-3aii-1iai-4	iai-3aii-3eio-3aii-1iai-4	NOUN
asir-6084	187	35	(	(	PUNCT
asir-6084	187	36	14.6	14.6	NUM
asir-6084	187	37	)	)	PUNCT
asir-6084	187	38	iai-3aii-3eio-3aii-1iai-3	iai-3aii-3eio-3aii-1iai-3	NOUN
asir-6084	187	39	(	(	PUNCT
asir-6084	187	40	14.7	14.7	NUM
asir-6084	187	41	)	)	PUNCT
asir-6084	187	42	iai-3oao-3aaa-1aai-1aai-4	iai-3oao-3aaa-1aai-1aai-4	ADJ
asir-6084	187	43	proof	proof	NOUN
asir-6084	187	44	:	:	PUNCT
asir-6084	187	45	for	for	ADP
asir-6084	187	46	(	(	PUNCT
asir-6084	187	47	14.1	14.1	NUM
asir-6084	187	48	)	)	PUNCT
asir-6084	187	49	.	.	PUNCT
asir-6084	188	1	according	accord	VERB
asir-6084	188	2	to	to	ADP
asir-6084	188	3	(	(	PUNCT
asir-6084	188	4	13.19	13.19	NUM
asir-6084	188	5	)	)	PUNCT
asir-6084	188	6	iai-3aii-3eio-3	iai-3aii-3eio-3	NOUN
asir-6084	188	7	aee-2eae-1eao-1	aee-2eae-1eao-1	PROPN
asir-6084	188	8	,	,	PUNCT
asir-6084	188	9	it	it	PRON
asir-6084	188	10	follows	follow	VERB
asir-6084	188	11	that	that	SCONJ
asir-6084	188	12	aee-2	aee-2	PROPN
asir-6084	188	13	is	be	AUX
asir-6084	188	14	valid	valid	ADJ
asir-6084	188	15	,	,	PUNCT
asir-6084	188	16	and	and	CCONJ
asir-6084	188	17	its	its	PRON
asir-6084	188	18	expansion	expansion	NOUN
asir-6084	188	19	is	be	AUX
asir-6084	188	20	that	that	PRON
asir-6084	188	21	all(z	all(z	NUM
asir-6084	188	22	,	,	PUNCT
asir-6084	188	23	y)no(x	y)no(x	PROPN
asir-6084	188	24	,	,	PUNCT
asir-6084	188	25	y)no(x	y)no(x	PROPN
asir-6084	188	26	,	,	PUNCT
asir-6084	188	27	z	z	NOUN
asir-6084	188	28	)	)	PUNCT
asir-6084	188	29	.	.	PUNCT
asir-6084	189	1	in	in	ADP
asir-6084	189	2	line	line	NOUN
asir-6084	189	3	with	with	ADP
asir-6084	189	4	the	the	DET
asir-6084	189	5	clause	clause	NOUN
asir-6084	189	6	(	(	PUNCT
asir-6084	189	7	2	2	NUM
asir-6084	189	8	)	)	PUNCT
asir-6084	189	9	in	in	ADP
asir-6084	189	10	fact	fact	NOUN
asir-6084	189	11	7	7	NUM
asir-6084	189	12	,	,	PUNCT
asir-6084	189	13	it	it	PRON
asir-6084	189	14	can	can	AUX
asir-6084	189	15	be	be	AUX
asir-6084	189	16	seen	see	VERB
asir-6084	189	17	that	that	SCONJ
asir-6084	189	18	no(x	no(x	PROPN
asir-6084	189	19	,	,	PUNCT
asir-6084	189	20	y)no(y	y)no(y	NOUN
asir-6084	189	21	,	,	PUNCT
asir-6084	189	22	x	x	NOUN
asir-6084	189	23	)	)	PUNCT
asir-6084	189	24	.	.	PUNCT
asir-6084	190	1	therefore	therefore	ADV
asir-6084	190	2	,	,	PUNCT
asir-6084	190	3	one	one	PRON
asir-6084	190	4	can	can	AUX
asir-6084	190	5	easily	easily	ADV
asir-6084	190	6	deduce	deduce	VERB
asir-6084	190	7	that	that	SCONJ
asir-6084	190	8	all(z	all(z	NOUN
asir-6084	190	9	,	,	PUNCT
asir-6084	190	10	y)no(y	y)no(y	X
asir-6084	190	11	,	,	PUNCT
asir-6084	190	12	x)no(x	x)no(x	PROPN
asir-6084	190	13	,	,	PUNCT
asir-6084	190	14	z	z	NOUN
asir-6084	190	15	)	)	PUNCT
asir-6084	190	16	.	.	PUNCT
asir-6084	191	1	that	that	PRON
asir-6084	191	2	is	be	AUX
asir-6084	191	3	,	,	PUNCT
asir-6084	191	4	aee-4	aee-4	PROPN
asir-6084	191	5	can	can	AUX
asir-6084	191	6	be	be	AUX
asir-6084	191	7	derived	derive	VERB
asir-6084	191	8	from	from	ADP
asir-6084	191	9	iai-3	iai-3	NOUN
asir-6084	191	10	.	.	PUNCT
asir-6084	192	1	so	so	ADV
asir-6084	192	2	far	far	ADV
asir-6084	192	3	,	,	PUNCT
asir-6084	192	4	the	the	DET
asir-6084	192	5	proof	proof	NOUN
asir-6084	192	6	of	of	ADP
asir-6084	192	7	(	(	PUNCT
asir-6084	192	8	14.1	14.1	NUM
asir-6084	192	9	)	)	PUNCT
asir-6084	192	10	has	have	AUX
asir-6084	192	11	been	be	AUX
asir-6084	192	12	completed	complete	VERB
asir-6084	192	13	.	.	PUNCT
asir-6084	193	1	the	the	DET
asir-6084	193	2	others	other	NOUN
asir-6084	193	3	can	can	AUX
asir-6084	193	4	be	be	AUX
asir-6084	193	5	similarly	similarly	ADV
asir-6084	193	6	proved	prove	VERB
asir-6084	193	7	on	on	ADP
asir-6084	193	8	the	the	DET
asir-6084	193	9	basis	basis	NOUN
asir-6084	193	10	of	of	ADP
asir-6084	193	11	the	the	DET
asir-6084	193	12	above	above	ADJ
asir-6084	193	13	theorems	theorem	NOUN
asir-6084	193	14	,	,	PUNCT
asir-6084	193	15	facts	fact	NOUN
asir-6084	193	16	and	and	CCONJ
asir-6084	193	17	rules	rule	NOUN
asir-6084	193	18	.	.	PUNCT
asir-6084	194	1	theorem	theorem	VERB
asir-6084	194	2	15	15	NUM
asir-6084	194	3	:	:	PUNCT
asir-6084	194	4	the	the	DET
asir-6084	194	5	following	follow	VERB
asir-6084	194	6	valid	valid	ADJ
asir-6084	194	7	modal	modal	ADJ
asir-6084	194	8	syllogisms	syllogism	NOUN
asir-6084	194	9	can	can	AUX
asir-6084	194	10	be	be	AUX
asir-6084	194	11	followed	follow	VERB
asir-6084	194	12	from	from	ADP
asir-6084	194	13	iai-3	iai-3	NOUN
asir-6084	194	14	:	:	PUNCT
asir-6084	194	15	(	(	PUNCT
asir-6084	194	16	15.1	15.1	NUM
asir-6084	194	17	)	)	PUNCT
asir-6084	194	18	iai-3oao-3aaa-1aai-1eao-3	iai-3oao-3aaa-1aai-1eao-3	NOUN
asir-6084	194	19	eao-3	eao-3	PROPN
asir-6084	194	20	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	194	21	applied	apply	VERB
asir-6084	194	22	science	science	NOUN
asir-6084	194	23	and	and	CCONJ
asir-6084	194	24	innovative	innovative	ADJ
asir-6084	194	25	research	research	NOUN
asir-6084	194	26	vol	vol	NOUN
asir-6084	194	27	.	.	PUNCT
asir-6084	195	1	7	7	NUM
asir-6084	195	2	,	,	PUNCT
asir-6084	195	3	no	no	INTJ
asir-6084	195	4	.	.	NOUN
asir-6084	195	5	1	1	NUM
asir-6084	195	6	,	,	PUNCT
asir-6084	195	7	2023	2023	NUM
asir-6084	195	8	55	55	NUM
asir-6084	195	9	published	publish	VERB
asir-6084	195	10	by	by	ADP
asir-6084	195	11	scholink	scholink	PROPN
asir-6084	195	12	inc	inc	PROPN
asir-6084	195	13	.	.	PROPN
asir-6084	196	1	(	(	PUNCT
asir-6084	196	2	15.2	15.2	NUM
asir-6084	196	3	)	)	PUNCT
asir-6084	196	4	iai-3oao-3aaa-1aai-1eao-3	iai-3oao-3aaa-1aai-1eao-3	NOUN
asir-6084	196	5	eao-4eao-4	eao-4eao-4	NOUN
asir-6084	196	6	(	(	PUNCT
asir-6084	196	7	15.3	15.3	NUM
asir-6084	196	8	)	)	PUNCT
asir-6084	196	9	iai-3eae-1eao-1aai-3aai-3	iai-3eae-1eao-1aai-3aai-3	PROPN
asir-6084	196	10	(	(	PUNCT
asir-6084	196	11	15.4	15.4	NUM
asir-6084	196	12	)	)	PUNCT
asir-6084	196	13	iai-3eae-1eao-1aai-3aai-3	iai-3eae-1eao-1aai-3aai-3	PROPN
asir-6084	196	14	(	(	PUNCT
asir-6084	196	15	15.5	15.5	NUM
asir-6084	196	16	)	)	PUNCT
asir-6084	196	17	iai-3oao-3aaa-1aai-1eao-3	iai-3oao-3aaa-1aai-1eao-3	PROPN
asir-6084	196	18	eao-3	eao-3	PROPN
asir-6084	196	19	(	(	PUNCT
asir-6084	196	20	15.6	15.6	NUM
asir-6084	196	21	)	)	PUNCT
asir-6084	196	22	iai-3oao-3aaa-1aai-1eao-3	iai-3oao-3aaa-1aai-1eao-3	NOUN
asir-6084	196	23	eao-4eao-4	eao-4eao-4	NOUN
asir-6084	196	24	proof	proof	NOUN
asir-6084	196	25	:	:	PUNCT
asir-6084	196	26	for	for	ADP
asir-6084	196	27	(	(	PUNCT
asir-6084	196	28	15.1	15.1	NUM
asir-6084	196	29	)	)	PUNCT
asir-6084	196	30	.	.	PUNCT
asir-6084	197	1	in	in	ADP
asir-6084	197	2	terms	term	NOUN
asir-6084	197	3	of	of	ADP
asir-6084	197	4	(	(	PUNCT
asir-6084	197	5	11.3	11.3	NUM
asir-6084	197	6	)	)	PUNCT
asir-6084	197	7	iai-3oao-3aaa-1	iai-3oao-3aaa-1	NOUN
asir-6084	197	8	aai-1	aai-1	NOUN
asir-6084	197	9	eao-3eao-4	eao-3eao-4	PROPN
asir-6084	197	10	,	,	PUNCT
asir-6084	197	11	it	it	PRON
asir-6084	197	12	follows	follow	VERB
asir-6084	197	13	that	that	SCONJ
asir-6084	197	14	eao-3	eao-3	PROPN
asir-6084	197	15	is	be	AUX
asir-6084	197	16	valid	valid	ADJ
asir-6084	197	17	.	.	PUNCT
asir-6084	198	1	according	accord	VERB
asir-6084	198	2	to	to	ADP
asir-6084	198	3	fact	fact	NOUN
asir-6084	198	4	4	4	NUM
asir-6084	198	5	,	,	PUNCT
asir-6084	198	6	it	it	PRON
asir-6084	198	7	is	be	AUX
asir-6084	198	8	easily	easily	ADV
asir-6084	198	9	seen	see	VERB
asir-6084	198	10	that	that	SCONJ
asir-6084	198	11	oo	oo	PROPN
asir-6084	198	12	,	,	PUNCT
asir-6084	198	13	thus	thus	ADV
asir-6084	198	14	eao-3	eao-3	PROPN
asir-6084	198	15	is	be	AUX
asir-6084	198	16	valid	valid	ADJ
asir-6084	198	17	.	.	PUNCT
asir-6084	199	1	that	that	PRON
asir-6084	199	2	is	be	AUX
asir-6084	199	3	to	to	PART
asir-6084	199	4	say	say	VERB
asir-6084	199	5	that	that	SCONJ
asir-6084	199	6	eao-3	eao-3	PROPN
asir-6084	199	7	can	can	AUX
asir-6084	199	8	be	be	AUX
asir-6084	199	9	derived	derive	VERB
asir-6084	199	10	from	from	ADP
asir-6084	199	11	iai-3	iai-3	NOUN
asir-6084	199	12	,	,	PUNCT
asir-6084	199	13	just	just	ADV
asir-6084	199	14	as	as	SCONJ
asir-6084	199	15	required	require	VERB
asir-6084	199	16	.	.	PUNCT
asir-6084	200	1	making	make	VERB
asir-6084	200	2	the	the	DET
asir-6084	200	3	best	good	ADJ
asir-6084	200	4	of	of	ADP
asir-6084	200	5	the	the	DET
asir-6084	200	6	above	above	ADJ
asir-6084	200	7	theorems	theorem	NOUN
asir-6084	200	8	,	,	PUNCT
asir-6084	200	9	facts	fact	NOUN
asir-6084	200	10	and	and	CCONJ
asir-6084	200	11	rules	rule	NOUN
asir-6084	200	12	,	,	PUNCT
asir-6084	200	13	all	all	PRON
asir-6084	200	14	of	of	ADP
asir-6084	200	15	the	the	DET
asir-6084	200	16	other	other	ADJ
asir-6084	200	17	modal	modal	ADJ
asir-6084	200	18	syllogisms	syllogism	NOUN
asir-6084	200	19	can	can	AUX
asir-6084	200	20	be	be	AUX
asir-6084	200	21	inferred	infer	VERB
asir-6084	200	22	from	from	ADP
asir-6084	200	23	iai-3	iai-3	NOUN
asir-6084	200	24	.	.	PROPN
asir-6084	200	25	4	4	X
asir-6084	200	26	.	.	X
asir-6084	200	27	conclusion	conclusion	NOUN
asir-6084	200	28	making	make	VERB
asir-6084	200	29	full	full	ADJ
asir-6084	200	30	use	use	NOUN
asir-6084	200	31	of	of	ADP
asir-6084	200	32	the	the	DET
asir-6084	200	33	truth	truth	NOUN
asir-6084	200	34	value	value	NOUN
asir-6084	200	35	definition	definition	NOUN
asir-6084	200	36	of	of	ADP
asir-6084	200	37	(	(	PUNCT
asir-6084	200	38	modal	modal	NOUN
asir-6084	200	39	)	)	PUNCT
asir-6084	200	40	categorical	categorical	ADJ
asir-6084	200	41	propositions	proposition	NOUN
asir-6084	200	42	,	,	PUNCT
asir-6084	200	43	the	the	DET
asir-6084	200	44	transformable	transformable	ADJ
asir-6084	200	45	relations	relation	NOUN
asir-6084	200	46	between	between	ADP
asir-6084	200	47	an	an	DET
asir-6084	200	48	aristotelian	aristotelian	ADJ
asir-6084	200	49	quantifier	quantifier	NOUN
asir-6084	200	50	and	and	CCONJ
asir-6084	200	51	their	their	PRON
asir-6084	200	52	three	three	NUM
asir-6084	200	53	negative	negative	ADJ
asir-6084	200	54	quantifiers	quantifier	NOUN
asir-6084	200	55	,	,	PUNCT
asir-6084	200	56	the	the	DET
asir-6084	200	57	reasoning	reasoning	NOUN
asir-6084	200	58	rules	rule	NOUN
asir-6084	200	59	of	of	ADP
asir-6084	200	60	classical	classical	ADJ
asir-6084	200	61	propositional	propositional	ADJ
asir-6084	200	62	logic	logic	NOUN
asir-6084	200	63	,	,	PUNCT
asir-6084	200	64	and	and	CCONJ
asir-6084	200	65	the	the	DET
asir-6084	200	66	symmetry	symmetry	NOUN
asir-6084	200	67	of	of	ADP
asir-6084	200	68	the	the	DET
asir-6084	200	69	two	two	NUM
asir-6084	200	70	aristotelian	aristotelian	ADJ
asir-6084	200	71	quantifiers	quantifier	NOUN
asir-6084	200	72	(	(	PUNCT
asir-6084	200	73	i.e.	i.e.	X
asir-6084	200	74	some	some	PRON
asir-6084	200	75	and	and	CCONJ
asir-6084	200	76	no	no	NOUN
asir-6084	200	77	)	)	PUNCT
asir-6084	200	78	,	,	PUNCT
asir-6084	200	79	this	this	DET
asir-6084	200	80	paper	paper	NOUN
asir-6084	200	81	shows	show	VERB
asir-6084	200	82	that	that	SCONJ
asir-6084	200	83	at	at	ADV
asir-6084	200	84	least	least	ADV
asir-6084	200	85	91	91	NUM
asir-6084	200	86	valid	valid	ADJ
asir-6084	200	87	aristotelian	aristotelian	ADJ
asir-6084	200	88	modal	modal	NOUN
asir-6084	200	89	syllogisms	syllogism	NOUN
asir-6084	200	90	can	can	AUX
asir-6084	200	91	be	be	AUX
asir-6084	200	92	deduced	deduce	VERB
asir-6084	200	93	from	from	ADP
asir-6084	200	94	iai-3	iai-3	NOUN
asir-6084	200	95	.	.	PUNCT
asir-6084	201	1	the	the	DET
asir-6084	201	2	reason	reason	NOUN
asir-6084	201	3	why	why	SCONJ
asir-6084	201	4	the	the	DET
asir-6084	201	5	above	above	ADJ
asir-6084	201	6	91	91	NUM
asir-6084	201	7	valid	valid	ADJ
asir-6084	201	8	aristotelian	aristotelian	PROPN
asir-6084	201	9	modal	modal	NOUN
asir-6084	201	10	syllogisms	syllogism	NOUN
asir-6084	201	11	can	can	AUX
asir-6084	201	12	be	be	AUX
asir-6084	201	13	reduced	reduce	VERB
asir-6084	201	14	is	be	AUX
asir-6084	201	15	that	that	SCONJ
asir-6084	201	16	any	any	DET
asir-6084	201	17	aristotelian	aristotelian	ADJ
asir-6084	201	18	quantifier	quantifier	NOUN
asir-6084	201	19	can	can	AUX
asir-6084	201	20	be	be	AUX
asir-6084	201	21	defined	define	VERB
asir-6084	201	22	by	by	ADP
asir-6084	201	23	the	the	DET
asir-6084	201	24	other	other	ADJ
asir-6084	201	25	three	three	NUM
asir-6084	201	26	aristotelian	aristotelian	ADJ
asir-6084	201	27	quantifiers	quantifier	NOUN
asir-6084	201	28	,	,	PUNCT
asir-6084	201	29	and	and	CCONJ
asir-6084	201	30	the	the	DET
asir-6084	201	31	necessary	necessary	ADJ
asir-6084	201	32	modality	modality	NOUN
asir-6084	201	33	(	(	PUNCT
asir-6084	201	34			NUM
asir-6084	201	35	)	)	PUNCT
asir-6084	201	36	and	and	CCONJ
asir-6084	201	37	possible	possible	ADJ
asir-6084	201	38	modality	modality	NOUN
asir-6084	201	39	(	(	PUNCT
asir-6084	201	40			NOUN
asir-6084	201	41	)	)	PUNCT
asir-6084	201	42	can	can	AUX
asir-6084	201	43	also	also	ADV
asir-6084	201	44	be	be	AUX
asir-6084	201	45	defined	define	VERB
asir-6084	201	46	mutually	mutually	ADV
asir-6084	201	47	.	.	PUNCT
asir-6084	202	1	this	this	DET
asir-6084	202	2	research	research	NOUN
asir-6084	202	3	method	method	NOUN
asir-6084	202	4	is	be	AUX
asir-6084	202	5	universal	universal	ADJ
asir-6084	202	6	.	.	PUNCT
asir-6084	203	1	that	that	PRON
asir-6084	203	2	is	be	AUX
asir-6084	203	3	to	to	PART
asir-6084	203	4	say	say	VERB
asir-6084	203	5	that	that	SCONJ
asir-6084	203	6	other	other	ADJ
asir-6084	203	7	valid	valid	ADJ
asir-6084	203	8	aristotelian	aristotelian	PROPN
asir-6084	203	9	modal	modal	NOUN
asir-6084	203	10	syllogisms	syllogism	NOUN
asir-6084	203	11	can	can	AUX
asir-6084	203	12	also	also	ADV
asir-6084	203	13	be	be	AUX
asir-6084	203	14	deduced	deduce	VERB
asir-6084	203	15	similarly	similarly	ADV
asir-6084	203	16	from	from	ADP
asir-6084	203	17	some	some	DET
asir-6084	203	18	valid	valid	ADJ
asir-6084	203	19	syllogisms	syllogism	NOUN
asir-6084	203	20	other	other	ADJ
asir-6084	203	21	than	than	ADP
asir-6084	203	22	iai-3	iai-3	ADJ
asir-6084	203	23	,	,	PUNCT
asir-6084	203	24	such	such	ADJ
asir-6084	203	25	as	as	ADP
asir-6084	203	26	iai-3	iai-3	PROPN
asir-6084	203	27	,	,	PUNCT
asir-6084	203	28	iai-3	iai-3	NOUN
asir-6084	203	29	,	,	PUNCT
asir-6084	203	30	and	and	CCONJ
asir-6084	203	31	iai-3	iai-3	NOUN
asir-6084	203	32	.	.	PUNCT
asir-6084	204	1	all	all	DET
asir-6084	204	2	valid	valid	ADJ
asir-6084	204	3	aristotelian	aristotelian	ADJ
asir-6084	204	4	modal	modal	NOUN
asir-6084	204	5	syllogisms	syllogism	NOUN
asir-6084	204	6	obtained	obtain	VERB
asir-6084	204	7	by	by	ADP
asir-6084	204	8	adding	add	VERB
asir-6084	204	9	modal	modal	ADJ
asir-6084	204	10	operators	operator	NOUN
asir-6084	204	11	to	to	ADP
asir-6084	204	12	the	the	DET
asir-6084	204	13	valid	valid	ADJ
asir-6084	204	14	aristotelian	aristotelian	PROPN
asir-6084	204	15	syllogism	syllogism	NOUN
asir-6084	204	16	iai-3	iai-3	NUM
asir-6084	204	17	are	be	AUX
asir-6084	204	18	as	as	SCONJ
asir-6084	204	19	follows	follow	VERB
asir-6084	204	20	:	:	PUNCT
asir-6084	204	21	iai-3	iai-3	ADJ
asir-6084	204	22	,	,	PUNCT
asir-6084	204	23	iai-3	iai-3	ADJ
asir-6084	204	24	,	,	PUNCT
asir-6084	204	25	iai-3	iai-3	PROPN
asir-6084	204	26	,	,	PUNCT
asir-6084	204	27	iai-3	iai-3	PROPN
asir-6084	204	28	,	,	PUNCT
asir-6084	204	29	iai-3	iai-3	NOUN
asir-6084	204	30	,	,	PUNCT
asir-6084	204	31	iai-3	iai-3	PROPN
asir-6084	204	32	,	,	PUNCT
asir-6084	204	33	iai-3	iai-3	PROPN
asir-6084	204	34	,	,	PUNCT
asir-6084	204	35	iai-3	iai-3	NOUN
asir-6084	204	36	,	,	PUNCT
asir-6084	204	37	iai-3	iai-3	NOUN
asir-6084	204	38	,	,	PUNCT
asir-6084	204	39	iai-3	iai-3	NOUN
asir-6084	204	40	,	,	PUNCT
asir-6084	204	41	iai-3	iai-3	PROPN
asir-6084	204	42	and	and	CCONJ
asir-6084	204	43	iai-3	iai-3	NOUN
asir-6084	204	44	.	.	PUNCT
asir-6084	205	1	the	the	DET
asir-6084	205	2	validity	validity	NOUN
asir-6084	205	3	of	of	ADP
asir-6084	205	4	these	these	DET
asir-6084	205	5	syllogisms	syllogism	NOUN
asir-6084	205	6	can	can	AUX
asir-6084	205	7	be	be	AUX
asir-6084	205	8	proved	prove	VERB
asir-6084	205	9	in	in	ADP
asir-6084	205	10	the	the	DET
asir-6084	205	11	same	same	ADJ
asir-6084	205	12	way	way	NOUN
asir-6084	205	13	that	that	PRON
asir-6084	205	14	theorem	theorem	VERB
asir-6084	205	15	1	1	NUM
asir-6084	205	16	proves	prove	VERB
asir-6084	205	17	the	the	DET
asir-6084	205	18	validity	validity	NOUN
asir-6084	205	19	of	of	ADP
asir-6084	205	20	iai-3	iai-3	NOUN
asir-6084	205	21	.	.	PUNCT
asir-6084	206	1	if	if	SCONJ
asir-6084	206	2	one	one	PRON
asir-6084	206	3	can	can	AUX
asir-6084	206	4	use	use	VERB
asir-6084	206	5	the	the	DET
asir-6084	206	6	reduction	reduction	NOUN
asir-6084	206	7	method	method	NOUN
asir-6084	206	8	in	in	ADP
asir-6084	206	9	this	this	DET
asir-6084	206	10	paper	paper	NOUN
asir-6084	206	11	to	to	PART
asir-6084	206	12	derive	derive	VERB
asir-6084	206	13	all	all	DET
asir-6084	206	14	the	the	DET
asir-6084	206	15	other	other	ADJ
asir-6084	206	16	valid	valid	ADJ
asir-6084	206	17	aristotelian	aristotelian	PROPN
asir-6084	206	18	modal	modal	NOUN
asir-6084	206	19	syllogisms	syllogism	NOUN
asir-6084	206	20	from	from	ADP
asir-6084	206	21	these	these	DET
asir-6084	206	22	12	12	NUM
asir-6084	206	23	valid	valid	ADJ
asir-6084	206	24	syllogisms	syllogism	NOUN
asir-6084	206	25	,	,	PUNCT
asir-6084	206	26	then	then	ADV
asir-6084	206	27	it	it	PRON
asir-6084	206	28	is	be	AUX
asir-6084	206	29	possible	possible	ADJ
asir-6084	206	30	to	to	PART
asir-6084	206	31	establish	establish	VERB
asir-6084	206	32	a	a	DET
asir-6084	206	33	formal	formal	ADJ
asir-6084	206	34	axiom	axiom	NOUN
asir-6084	206	35	system	system	NOUN
asir-6084	206	36	for	for	ADP
asir-6084	206	37	aristotelian	aristotelian	ADJ
asir-6084	206	38	modal	modal	ADJ
asir-6084	206	39	syllogistic	syllogistic	NOUN
asir-6084	206	40	.	.	PUNCT
asir-6084	207	1	this	this	DET
asir-6084	207	2	issue	issue	NOUN
asir-6084	207	3	needs	need	VERB
asir-6084	207	4	further	further	ADJ
asir-6084	207	5	study	study	NOUN
asir-6084	207	6	.	.	PUNCT
asir-6084	208	1	acknowledgements	acknowledgement	NOUN
asir-6084	208	2	this	this	DET
asir-6084	208	3	work	work	NOUN
asir-6084	208	4	was	be	AUX
asir-6084	208	5	supported	support	VERB
asir-6084	208	6	by	by	ADP
asir-6084	208	7	science	science	NOUN
asir-6084	208	8	and	and	CCONJ
asir-6084	208	9	technology	technology	NOUN
asir-6084	208	10	philosophy	philosophy	NOUN
asir-6084	208	11	and	and	CCONJ
asir-6084	208	12	logic	logic	NOUN
asir-6084	208	13	teaching	teaching	NOUN
asir-6084	208	14	team	team	NOUN
asir-6084	208	15	project	project	NOUN
asir-6084	208	16	of	of	ADP
asir-6084	208	17	anhui	anhui	PROPN
asir-6084	208	18	university	university	PROPN
asir-6084	208	19	under	under	ADP
asir-6084	208	20	grant	grant	NOUN
asir-6084	208	21	no	no	NOUN
asir-6084	208	22	.	.	PUNCT
asir-6084	208	23	2022xjzlgc071	2022xjzlgc071	NUM
asir-6084	208	24	.	.	NOUN
asir-6084	209	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-6084	209	2	applied	apply	VERB
asir-6084	209	3	science	science	NOUN
asir-6084	209	4	and	and	CCONJ
asir-6084	209	5	innovative	innovative	ADJ
asir-6084	209	6	research	research	NOUN
asir-6084	209	7	vol	vol	NOUN
asir-6084	209	8	.	.	PUNCT
asir-6084	210	1	7	7	NUM
asir-6084	210	2	,	,	PUNCT
asir-6084	210	3	no	no	INTJ
asir-6084	210	4	.	.	NOUN
asir-6084	210	5	1	1	NUM
asir-6084	210	6	,	,	PUNCT
asir-6084	210	7	2023	2023	NUM
asir-6084	210	8	56	56	NUM
asir-6084	210	9	published	publish	VERB
asir-6084	210	10	by	by	ADP
asir-6084	210	11	scholink	scholink	PROPN
asir-6084	210	12	inc	inc	PROPN
asir-6084	210	13	.	.	PROPN
asir-6084	210	14	references	reference	NOUN
asir-6084	210	15	chagrov	chagrov	PROPN
asir-6084	210	16	,	,	PUNCT
asir-6084	210	17	f.	f.	PROPN
asir-6084	210	18	,	,	PUNCT
asir-6084	210	19	&	&	CCONJ
asir-6084	210	20	zakharyaschev	zakharyaschev	PROPN
asir-6084	210	21	,	,	PUNCT
asir-6084	210	22	m.	m.	NOUN
asir-6084	210	23	(	(	PUNCT
asir-6084	210	24	1997	1997	NUM
asir-6084	210	25	)	)	PUNCT
asir-6084	210	26	.	.	PUNCT
asir-6084	211	1	modal	modal	ADJ
asir-6084	211	2	logic	logic	NOUN
asir-6084	211	3	.	.	PUNCT
asir-6084	212	1	oxford	oxford	NOUN
asir-6084	212	2	:	:	PUNCT
asir-6084	212	3	clarendon	clarendon	PROPN
asir-6084	212	4	press	press	PROPN
asir-6084	212	5	.	.	PUNCT
asir-6084	213	1	chellas	chellas	PROPN
asir-6084	213	2	,	,	PUNCT
asir-6084	213	3	f.	f.	PROPN
asir-6084	213	4	(	(	PUNCT
asir-6084	213	5	1980	1980	NUM
asir-6084	213	6	)	)	PUNCT
asir-6084	213	7	.	.	PUNCT
asir-6084	214	1	modal	modal	ADJ
asir-6084	214	2	logic	logic	NOUN
asir-6084	214	3	:	:	PUNCT
asir-6084	214	4	an	an	DET
asir-6084	214	5	introduction	introduction	NOUN
asir-6084	214	6	.	.	PUNCT
asir-6084	215	1	cambridge	cambridge	PROPN
asir-6084	215	2	:	:	PUNCT
asir-6084	215	3	cambridge	cambridge	PROPN
asir-6084	215	4	university	university	PROPN
asir-6084	215	5	press	press	NOUN
asir-6084	215	6	.	.	PUNCT
asir-6084	216	1	endrullis	endrullis	PROPN
asir-6084	216	2	,	,	PUNCT
asir-6084	216	3	&	&	CCONJ
asir-6084	216	4	moss	moss	PROPN
asir-6084	216	5	,	,	PUNCT
asir-6084	216	6	l.	l.	PROPN
asir-6084	216	7	s.	s.	PROPN
asir-6084	216	8	(	(	PUNCT
asir-6084	216	9	2015	2015	NUM
asir-6084	216	10	)	)	PUNCT
asir-6084	216	11	.	.	PUNCT
asir-6084	217	1	syllogistic	syllogistic	ADJ
asir-6084	217	2	logic	logic	NOUN
asir-6084	217	3	with	with	ADP
asir-6084	217	4	‘	'	PUNCT
asir-6084	217	5	most	most	ADJ
asir-6084	217	6	’	'	PUNCT
asir-6084	217	7	.	.	PUNCT
asir-6084	218	1	in	in	ADP
asir-6084	218	2	v.	v.	PROPN
asir-6084	218	3	de	de	PROPN
asir-6084	218	4	paiva	paiva	PROPN
asir-6084	218	5	et	et	PROPN
asir-6084	218	6	al	al	PROPN
asir-6084	218	7	.	.	PROPN
asir-6084	219	1	(	(	PUNCT
asir-6084	219	2	eds	ed	NOUN
asir-6084	219	3	.	.	PUNCT
asir-6084	219	4	)	)	PUNCT
asir-6084	219	5	,	,	PUNCT
asir-6084	219	6	logic	logic	NOUN
asir-6084	219	7	,	,	PUNCT
asir-6084	219	8	language	language	NOUN
asir-6084	219	9	,	,	PUNCT
asir-6084	219	10	information	information	NOUN
asir-6084	219	11	,	,	PUNCT
asir-6084	219	12	and	and	CCONJ
asir-6084	219	13	computation	computation	NOUN
asir-6084	219	14	(	(	PUNCT
asir-6084	219	15	pp	pp	ADJ
asir-6084	219	16	.	.	PUNCT
asir-6084	220	1	124	124	NUM
asir-6084	220	2	-	-	SYM
asir-6084	220	3	139	139	NUM
asir-6084	220	4	)	)	PUNCT
asir-6084	220	5	.	.	PUNCT
asir-6084	221	1	https://doi.org/10.1007/978	https://doi.org/10.1007/978	PROPN
asir-6084	221	2	-3	-3	PUNCT
asir-6084	221	3	-	-	PUNCT
asir-6084	221	4	662	662	NUM
asir-6084	221	5	-	-	PUNCT
asir-6084	221	6	47709	47709	NUM
asir-6084	221	7	-	-	PUNCT
asir-6084	221	8	0_10	0_10	NUM
asir-6084	221	9	geach	geach	NOUN
asir-6084	221	10	,	,	PUNCT
asir-6084	221	11	p.	p.	NOUN
asir-6084	221	12	t.	t.	PROPN
asir-6084	221	13	(	(	PUNCT
asir-6084	221	14	1964	1964	NUM
asir-6084	221	15	)	)	PUNCT
asir-6084	221	16	.	.	PUNCT
asir-6084	222	1	review	review	NOUN
asir-6084	222	2	of	of	ADP
asir-6084	222	3	mccall	mccall	PROPN
asir-6084	222	4	(	(	PUNCT
asir-6084	222	5	1963	1963	NUM
asir-6084	222	6	)	)	PUNCT
asir-6084	222	7	.	.	PUNCT
asir-6084	223	1	ratio	ratio	NOUN
asir-6084	223	2	,	,	PUNCT
asir-6084	223	3	(	(	PUNCT
asir-6084	223	4	6	6	NUM
asir-6084	223	5	)	)	PUNCT
asir-6084	223	6	,	,	PUNCT
asir-6084	223	7	200	200	NUM
asir-6084	223	8	-	-	SYM
asir-6084	223	9	206	206	NUM
asir-6084	223	10	.	.	PUNCT
asir-6084	224	1	hamilton	hamilton	PROPN
asir-6084	224	2	,	,	PUNCT
asir-6084	224	3	a.	a.	PROPN
asir-6084	224	4	g.	g.	PROPN
asir-6084	224	5	(	(	PUNCT
asir-6084	224	6	1978	1978	NUM
asir-6084	224	7	)	)	PUNCT
asir-6084	224	8	.	.	PUNCT
asir-6084	225	1	logic	logic	NOUN
asir-6084	225	2	for	for	ADP
asir-6084	225	3	mathematicians	mathematician	NOUN
asir-6084	225	4	.	.	PUNCT
asir-6084	226	1	cambridge	cambridge	PROPN
asir-6084	226	2	:	:	PUNCT
asir-6084	226	3	cambridge	cambridge	PROPN
asir-6084	226	4	university	university	PROPN
asir-6084	226	5	press	press	NOUN
asir-6084	226	6	.	.	PUNCT
asir-6084	227	1	ivanov	ivanov	PROPN
asir-6084	227	2	,	,	PUNCT
asir-6084	227	3	n.	n.	NOUN
asir-6084	227	4	,	,	PUNCT
asir-6084	227	5	&	&	CCONJ
asir-6084	227	6	vakarelov	vakarelov	PROPN
asir-6084	227	7	,	,	PUNCT
asir-6084	227	8	d.	d.	PROPN
asir-6084	227	9	(	(	PUNCT
asir-6084	227	10	2012	2012	NUM
asir-6084	227	11	)	)	PUNCT
asir-6084	227	12	.	.	PUNCT
asir-6084	228	1	a	a	DET
asir-6084	228	2	system	system	NOUN
asir-6084	228	3	of	of	ADP
asir-6084	228	4	relational	relational	ADJ
asir-6084	228	5	syllogistic	syllogistic	NOUN
asir-6084	228	6	incorporating	incorporate	VERB
asir-6084	228	7	full	full	ADJ
asir-6084	228	8	boolean	boolean	ADJ
asir-6084	228	9	reasoning	reasoning	NOUN
asir-6084	228	10	.	.	PUNCT
asir-6084	229	1	journal	journal	NOUN
asir-6084	229	2	of	of	ADP
asir-6084	229	3	logic	logic	NOUN
asir-6084	229	4	,	,	PUNCT
asir-6084	229	5	language	language	NOUN
asir-6084	229	6	and	and	CCONJ
asir-6084	229	7	information	information	NOUN
asir-6084	229	8	,	,	PUNCT
asir-6084	229	9	(	(	PUNCT
asir-6084	229	10	21	21	NUM
asir-6084	229	11	)	)	PUNCT
asir-6084	229	12	,	,	PUNCT
asir-6084	229	13	433	433	NUM
asir-6084	229	14	-	-	SYM
asir-6084	229	15	459	459	NUM
asir-6084	229	16	.	.	PUNCT
asir-6084	230	1	https://doi.org/	https://doi.org/	VERB
asir-6084	230	2	10.1007	10.1007	NUM
asir-6084	230	3	/	/	SYM
asir-6084	230	4	s10849	s10849	NOUN
asir-6084	230	5	-	-	NOUN
asir-6084	230	6	012	012	NUM
asir-6084	230	7	-	-	PUNCT
asir-6084	230	8	9165	9165	NUM
asir-6084	230	9	-	-	PUNCT
asir-6084	230	10	1	1	NUM
asir-6084	230	11	johnson	johnson	PROPN
asir-6084	230	12	,	,	PUNCT
asir-6084	230	13	f.	f.	PROPN
asir-6084	230	14	(	(	PUNCT
asir-6084	230	15	1989	1989	NUM
asir-6084	230	16	)	)	PUNCT
asir-6084	230	17	.	.	PUNCT
asir-6084	231	1	models	model	NOUN
asir-6084	231	2	for	for	ADP
asir-6084	231	3	modal	modal	ADJ
asir-6084	231	4	syllogisms	syllogism	NOUN
asir-6084	231	5	.	.	PUNCT
asir-6084	232	1	notre	notre	PROPN
asir-6084	232	2	dame	dame	PROPN
asir-6084	232	3	journal	journal	NOUN
asir-6084	232	4	of	of	ADP
asir-6084	232	5	formal	formal	ADJ
asir-6084	232	6	logic	logic	NOUN
asir-6084	232	7	,	,	PUNCT
asir-6084	232	8	(	(	PUNCT
asir-6084	232	9	30	30	NUM
asir-6084	232	10	)	)	PUNCT
asir-6084	232	11	,	,	PUNCT
asir-6084	232	12	271	271	NUM
asir-6084	232	13	-	-	SYM
asir-6084	232	14	284	284	NUM
asir-6084	232	15	.	.	PUNCT
asir-6084	233	1	johnson	johnson	PROPN
asir-6084	233	2	,	,	PUNCT
asir-6084	233	3	f.	f.	PROPN
asir-6084	233	4	(	(	PUNCT
asir-6084	233	5	2004	2004	NUM
asir-6084	233	6	)	)	PUNCT
asir-6084	233	7	.	.	PUNCT
asir-6084	234	1	aristotle	aristotle	PROPN
asir-6084	234	2	’s	’s	PART
asir-6084	234	3	modal	modal	ADJ
asir-6084	234	4	syllogisms	syllogism	NOUN
asir-6084	234	5	.	.	PUNCT
asir-6084	235	1	handbook	handbook	NOUN
asir-6084	235	2	of	of	ADP
asir-6084	235	3	the	the	DET
asir-6084	235	4	history	history	NOUN
asir-6084	235	5	of	of	ADP
asir-6084	235	6	logic	logic	NOUN
asir-6084	235	7	,	,	PUNCT
asir-6084	235	8	i	i	PRON
asir-6084	235	9	,	,	PUNCT
asir-6084	235	10	247	247	NUM
asir-6084	235	11	-	-	SYM
asir-6084	235	12	338	338	NUM
asir-6084	235	13	.	.	PUNCT
asir-6084	236	1	https://doi.org/10.1016/s1874-5857(04)80006-2	https://doi.org/10.1016/s1874-5857(04)80006-2	NOUN
asir-6084	236	2	łukasiewicz	łukasiewicz	NOUN
asir-6084	236	3	,	,	PUNCT
asir-6084	236	4	j.	j.	PROPN
asir-6084	236	5	(	(	PUNCT
asir-6084	236	6	1957	1957	NUM
asir-6084	236	7	)	)	PUNCT
asir-6084	236	8	.	.	PUNCT
asir-6084	237	1	aristotle	aristotle	PROPN
asir-6084	237	2	’s	’s	PROPN
asir-6084	237	3	syllogistic	syllogistic	NOUN
asir-6084	237	4	:	:	PUNCT
asir-6084	237	5	from	from	ADP
asir-6084	237	6	the	the	DET
asir-6084	237	7	standpoint	standpoint	NOUN
asir-6084	237	8	of	of	ADP
asir-6084	237	9	modern	modern	ADJ
asir-6084	237	10	formal	formal	ADJ
asir-6084	237	11	logic	logic	NOUN
asir-6084	237	12	.	.	PUNCT
asir-6084	238	1	second	second	ADJ
asir-6084	238	2	edition	edition	NOUN
asir-6084	238	3	,	,	PUNCT
asir-6084	238	4	oxford	oxford	PROPN
asir-6084	238	5	:	:	PUNCT
asir-6084	238	6	clerndon	clerndon	NOUN
asir-6084	238	7	press	press	PROPN
asir-6084	238	8	.	.	PUNCT
asir-6084	239	1	malink	malink	PROPN
asir-6084	239	2	,	,	PUNCT
asir-6084	239	3	m.	m.	NOUN
asir-6084	239	4	(	(	PUNCT
asir-6084	239	5	2006	2006	NUM
asir-6084	239	6	)	)	PUNCT
asir-6084	239	7	.	.	PUNCT
asir-6084	240	1	a	a	DET
asir-6084	240	2	reconstruction	reconstruction	NOUN
asir-6084	240	3	of	of	ADP
asir-6084	240	4	aristotle	aristotle	PROPN
asir-6084	240	5	’s	’s	PART
asir-6084	240	6	modal	modal	ADJ
asir-6084	240	7	syllogistic	syllogistic	NOUN
asir-6084	240	8	.	.	PUNCT
asir-6084	241	1	history	history	NOUN
asir-6084	241	2	and	and	CCONJ
asir-6084	241	3	philosophy	philosophy	NOUN
asir-6084	241	4	of	of	ADP
asir-6084	241	5	logic	logic	NOUN
asir-6084	241	6	,	,	PUNCT
asir-6084	241	7	(	(	PUNCT
asir-6084	241	8	27	27	NUM
asir-6084	241	9	)	)	PUNCT
asir-6084	241	10	,	,	PUNCT
asir-6084	241	11	95	95	NUM
asir-6084	241	12	-	-	SYM
asir-6084	241	13	141	141	NUM
asir-6084	241	14	.	.	PUNCT
asir-6084	242	1	malink	malink	NOUN
asir-6084	242	2	,	,	PUNCT
asir-6084	242	3	m.	m.	NOUN
asir-6084	242	4	(	(	PUNCT
asir-6084	242	5	2013	2013	NUM
asir-6084	242	6	)	)	PUNCT
asir-6084	242	7	.	.	PUNCT
asir-6084	243	1	aristotle	aristotle	PROPN
asir-6084	243	2	’s	’s	PART
asir-6084	243	3	modal	modal	ADJ
asir-6084	243	4	syllogistic	syllogistic	NOUN
asir-6084	243	5	.	.	PUNCT
asir-6084	244	1	cambridge	cambridge	PROPN
asir-6084	244	2	,	,	PUNCT
asir-6084	244	3	ma	ma	PROPN
asir-6084	244	4	:	:	PUNCT
asir-6084	244	5	harvard	harvard	PROPN
asir-6084	244	6	university	university	PROPN
asir-6084	244	7	press	press	NOUN
asir-6084	244	8	.	.	PUNCT
asir-6084	245	1	mccall	mccall	PROPN
asir-6084	245	2	,	,	PUNCT
asir-6084	245	3	s.	s.	PROPN
asir-6084	245	4	(	(	PUNCT
asir-6084	245	5	1963	1963	NUM
asir-6084	245	6	)	)	PUNCT
asir-6084	245	7	.	.	PUNCT
asir-6084	246	1	studies	study	NOUN
asir-6084	246	2	in	in	ADP
asir-6084	246	3	logic	logic	NOUN
asir-6084	246	4	and	and	CCONJ
asir-6084	246	5	the	the	DET
asir-6084	246	6	foundations	foundation	NOUN
asir-6084	246	7	of	of	ADP
asir-6084	246	8	mathematics	mathematic	NOUN
asir-6084	246	9	.	.	PUNCT
asir-6084	247	1	aristotle	aristotle	PROPN
asir-6084	247	2	’s	’s	PART
asir-6084	247	3	modal	modal	ADJ
asir-6084	247	4	syllogisms	syllogism	NOUN
asir-6084	247	5	.	.	PUNCT
asir-6084	248	1	north	north	NOUN
asir-6084	248	2	-	-	PUNCT
asir-6084	248	3	holland	holland	PROPN
asir-6084	248	4	publishing	publishing	PROPN
asir-6084	248	5	company	company	NOUN
asir-6084	248	6	,	,	PUNCT
asir-6084	248	7	amsterdam	amsterdam	PROPN
asir-6084	248	8	.	.	PUNCT
asir-6084	249	1	moss	moss	PROPN
asir-6084	249	2	,	,	PUNCT
asir-6084	249	3	l.	l.	PROPN
asir-6084	249	4	s.	s.	PROPN
asir-6084	249	5	(	(	PUNCT
asir-6084	249	6	2008	2008	NUM
asir-6084	249	7	)	)	PUNCT
asir-6084	249	8	.	.	PUNCT
asir-6084	250	1	completeness	completeness	NOUN
asir-6084	250	2	theorems	theorem	VERB
asir-6084	250	3	for	for	ADP
asir-6084	250	4	syllogistic	syllogistic	ADJ
asir-6084	250	5	fragments	fragment	NOUN
asir-6084	250	6	.	.	PUNCT
asir-6084	251	1	in	in	ADP
asir-6084	251	2	f.	f.	PROPN
asir-6084	251	3	hamm	hamm	PROPN
asir-6084	251	4	,	,	PUNCT
asir-6084	251	5	&	&	CCONJ
asir-6084	251	6	s.	s.	PROPN
asir-6084	251	7	kepser	kepser	PROPN
asir-6084	251	8	(	(	PUNCT
asir-6084	251	9	eds	ed	NOUN
asir-6084	251	10	.	.	PUNCT
asir-6084	251	11	)	)	PUNCT
asir-6084	251	12	,	,	PUNCT
asir-6084	251	13	logics	logic	NOUN
asir-6084	251	14	for	for	ADP
asir-6084	251	15	linguistic	linguistic	ADJ
asir-6084	251	16	structures	structure	NOUN
asir-6084	251	17	(	(	PUNCT
asir-6084	251	18	pp	pp	ADJ
asir-6084	251	19	.	.	PUNCT
asir-6084	251	20	143	143	NUM
asir-6084	251	21	-	-	SYM
asir-6084	251	22	173	173	NUM
asir-6084	251	23	)	)	PUNCT
asir-6084	251	24	.	.	PUNCT
asir-6084	252	1	mouton	mouton	PROPN
asir-6084	252	2	de	de	PROPN
asir-6084	252	3	gruyter	gruyter	PROPN
asir-6084	252	4	,	,	PUNCT
asir-6084	252	5	berlin	berlin	PROPN
asir-6084	252	6	.	.	PUNCT
asir-6084	253	1	moss	moss	PROPN
asir-6084	253	2	,	,	PUNCT
asir-6084	253	3	l.	l.	PROPN
asir-6084	253	4	s.	s.	PROPN
asir-6084	253	5	(	(	PUNCT
asir-6084	253	6	2010	2010	NUM
asir-6084	253	7	)	)	PUNCT
asir-6084	253	8	.	.	PUNCT
asir-6084	254	1	syllogistic	syllogistic	ADJ
asir-6084	254	2	logics	logic	NOUN
asir-6084	254	3	with	with	ADP
asir-6084	254	4	verbs	verbs	PROPN
asir-6084	254	5	.	.	PROPN
asir-6084	254	6	journal	journal	PROPN
asir-6084	254	7	of	of	ADP
asir-6084	254	8	logic	logic	NOUN
asir-6084	254	9	and	and	CCONJ
asir-6084	254	10	computation	computation	NOUN
asir-6084	254	11	,	,	PUNCT
asir-6084	254	12	20(4	20(4	NOUN
asir-6084	254	13	)	)	PUNCT
asir-6084	254	14	,	,	PUNCT
asir-6084	254	15	947	947	NUM
asir-6084	254	16	-	-	SYM
asir-6084	254	17	967	967	NUM
asir-6084	254	18	.	.	PUNCT
asir-6084	255	1	https://doi.org/10.1093/logcom/exn086	https://doi.org/10.1093/logcom/exn086	NOUN
asir-6084	255	2	murinová	murinová	PROPN
asir-6084	255	3	,	,	PUNCT
asir-6084	255	4	p.	p.	NOUN
asir-6084	255	5	,	,	PUNCT
asir-6084	255	6	&	&	CCONJ
asir-6084	255	7	novák	novák	PROPN
asir-6084	255	8	,	,	PUNCT
asir-6084	255	9	v.	v.	PROPN
asir-6084	255	10	(	(	PUNCT
asir-6084	255	11	2012	2012	NUM
asir-6084	255	12	)	)	PUNCT
asir-6084	255	13	.	.	PUNCT
asir-6084	256	1	a	a	DET
asir-6084	256	2	formal	formal	ADJ
asir-6084	256	3	theory	theory	NOUN
asir-6084	256	4	of	of	ADP
asir-6084	256	5	generalized	generalized	ADJ
asir-6084	256	6	intermediate	intermediate	ADJ
asir-6084	256	7	syllogisms	syllogism	NOUN
asir-6084	256	8	.	.	PUNCT
asir-6084	257	1	fuzzy	fuzzy	ADJ
asir-6084	257	2	sets	set	NOUN
asir-6084	257	3	and	and	CCONJ
asir-6084	257	4	systems	system	NOUN
asir-6084	257	5	,	,	PUNCT
asir-6084	257	6	186	186	NUM
asir-6084	257	7	,	,	PUNCT
asir-6084	257	8	47	47	NUM
asir-6084	257	9	-	-	SYM
asir-6084	257	10	80	80	NUM
asir-6084	257	11	.	.	PUNCT
asir-6084	258	1	https://doi.org/10.1016/j.fss.2011.07.004	https://doi.org/10.1016/j.fss.2011.07.004	PROPN
asir-6084	258	2	patzig	patzig	PROPN
asir-6084	258	3	,	,	PUNCT
asir-6084	258	4	g.	g.	PROPN
asir-6084	258	5	(	(	PUNCT
asir-6084	258	6	1969	1969	NUM
asir-6084	258	7	)	)	PUNCT
asir-6084	258	8	.	.	PUNCT
asir-6084	259	1	aristotle	aristotle	PROPN
asir-6084	259	2	's	's	PART
asir-6084	259	3	theory	theory	NOUN
asir-6084	259	4	of	of	ADP
asir-6084	259	5	the	the	DET
asir-6084	259	6	syllogism	syllogism	NOUN
asir-6084	259	7	.	.	PUNCT
asir-6084	260	1	j.	j.	PROPN
asir-6084	260	2	barnes	barnes	PROPN
asir-6084	260	3	(	(	PUNCT
asir-6084	260	4	trans	trans	PROPN
asir-6084	260	5	.	.	PUNCT
asir-6084	260	6	)	)	PUNCT
asir-6084	260	7	,	,	PUNCT
asir-6084	260	8	dordrecht	dordrecht	PROPN
asir-6084	260	9	:	:	PUNCT
asir-6084	260	10	d.	d.	PROPN
asir-6084	260	11	reidel	reidel	PROPN
asir-6084	260	12	.	.	PUNCT
asir-6084	261	1	https://doi.org/10.1007/978-94-017-0787-9	https://doi.org/10.1007/978-94-017-0787-9	PROPN
asir-6084	261	2	peters	peters	PROPN
asir-6084	261	3	,	,	PUNCT
asir-6084	261	4	s.	s.	PROPN
asir-6084	261	5	,	,	PUNCT
asir-6084	261	6	&	&	CCONJ
asir-6084	261	7	westerståhl	westerståhl	PROPN
asir-6084	261	8	,	,	PUNCT
asir-6084	261	9	d.	d.	PROPN
asir-6084	261	10	(	(	PUNCT
asir-6084	261	11	2006	2006	NUM
asir-6084	261	12	)	)	PUNCT
asir-6084	261	13	.	.	PUNCT
asir-6084	262	1	quantifiers	quantifier	NOUN
asir-6084	262	2	in	in	ADP
asir-6084	262	3	language	language	NOUN
asir-6084	262	4	and	and	CCONJ
asir-6084	262	5	logic	logic	NOUN
asir-6084	262	6	.	.	PUNCT
asir-6084	263	1	claredon	claredon	PROPN
asir-6084	263	2	press	press	PROPN
asir-6084	263	3	,	,	PUNCT
asir-6084	263	4	oxford	oxford	PROPN
asir-6084	263	5	.	.	PUNCT
asir-6084	264	1	pratt	pratt	PROPN
asir-6084	264	2	-	-	PUNCT
asir-6084	264	3	hartmann	hartmann	PROPN
asir-6084	264	4	,	,	PUNCT
asir-6084	264	5	i.	i.	PROPN
asir-6084	264	6	(	(	PUNCT
asir-6084	264	7	2014	2014	NUM
asir-6084	264	8	)	)	PUNCT
asir-6084	264	9	.	.	PUNCT
asir-6084	265	1	the	the	DET
asir-6084	265	2	relational	relational	ADJ
asir-6084	265	3	syllogistic	syllogistic	NOUN
asir-6084	265	4	revisited	revisit	VERB
asir-6084	265	5	.	.	PUNCT
asir-6084	266	1	perspectives	perspective	NOUN
asir-6084	266	2	on	on	ADP
asir-6084	266	3	semantic	semantic	ADJ
asir-6084	266	4	representations	representation	NOUN
asir-6084	266	5	for	for	ADP
asir-6084	266	6	textual	textual	ADJ
asir-6084	266	7	inference	inference	NOUN
asir-6084	266	8	(	(	PUNCT
asir-6084	266	9	pp	pp	ADJ
asir-6084	266	10	.	.	PUNCT
asir-6084	267	1	195	195	NUM
asir-6084	267	2	-	-	SYM
asir-6084	267	3	227	227	NUM
asir-6084	267	4	)	)	PUNCT
asir-6084	267	5	.	.	PUNCT
asir-6084	268	1	csli	csli	PROPN
asir-6084	268	2	publications	publication	NOUN
asir-6084	268	3	.	.	PUNCT
asir-6084	269	1	thom	thom	PROPN
asir-6084	269	2	,	,	PUNCT
asir-6084	269	3	p.	p.	NOUN
asir-6084	269	4	(	(	PUNCT
asir-6084	269	5	1996	1996	NUM
asir-6084	269	6	)	)	PUNCT
asir-6084	269	7	.	.	PUNCT
asir-6084	270	1	the	the	DET
asir-6084	270	2	logic	logic	NOUN
asir-6084	270	3	of	of	ADP
asir-6084	270	4	essentialism	essentialism	NOUN
asir-6084	270	5	:	:	PUNCT
asir-6084	270	6	an	an	DET
asir-6084	270	7	interpretation	interpretation	NOUN
asir-6084	270	8	of	of	ADP
asir-6084	270	9	aristotle	aristotle	PROPN
asir-6084	270	10	’s	’s	PART
asir-6084	270	11	modal	modal	ADJ
asir-6084	270	12	syllogistic	syllogistic	NOUN
asir-6084	270	13	.	.	PUNCT
asir-6084	271	1	(	(	PUNCT
asir-6084	271	2	synthese	synthese	ADJ
asir-6084	271	3	historical	historical	ADJ
asir-6084	271	4	library	library	NOUN
asir-6084	271	5	43	43	NUM
asir-6084	271	6	)	)	PUNCT
asir-6084	271	7	,	,	PUNCT
asir-6084	271	8	dordrecht	dordrecht	PROPN
asir-6084	271	9	:	:	PUNCT
asir-6084	271	10	kluwer	kluwer	PROPN
asir-6084	271	11	.	.	PUNCT
asir-6084	272	1	thomason	thomason	PROPN
asir-6084	272	2	,	,	PUNCT
asir-6084	272	3	s.	s.	PROPN
asir-6084	272	4	k.	k.	PROPN
asir-6084	272	5	(	(	PUNCT
asir-6084	272	6	1993	1993	NUM
asir-6084	272	7	)	)	PUNCT
asir-6084	272	8	.	.	PUNCT
asir-6084	273	1	semantic	semantic	ADJ
asir-6084	273	2	analysis	analysis	NOUN
asir-6084	273	3	of	of	ADP
asir-6084	273	4	the	the	DET
asir-6084	273	5	modal	modal	ADJ
asir-6084	273	6	syllogistic	syllogistic	NOUN
asir-6084	273	7	.	.	PUNCT
asir-6084	274	1	journal	journal	NOUN
asir-6084	274	2	of	of	ADP
asir-6084	274	3	philosophical	philosophical	ADJ
asir-6084	274	4	logic	logic	NOUN
asir-6084	274	5	,	,	PUNCT
asir-6084	274	6	(	(	PUNCT
asir-6084	274	7	22	22	NUM
asir-6084	274	8	)	)	PUNCT
asir-6084	274	9	,	,	PUNCT
asir-6084	274	10	111	111	NUM
asir-6084	274	11	-	-	SYM
asir-6084	274	12	128	128	NUM
asir-6084	274	13	.	.	PUNCT
asir-6084	275	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-6084	275	2	applied	apply	VERB
asir-6084	275	3	science	science	NOUN
asir-6084	275	4	and	and	CCONJ
asir-6084	275	5	innovative	innovative	ADJ
asir-6084	275	6	research	research	NOUN
asir-6084	275	7	vol	vol	NOUN
asir-6084	275	8	.	.	PUNCT
asir-6084	276	1	7	7	NUM
asir-6084	276	2	,	,	PUNCT
asir-6084	276	3	no	no	INTJ
asir-6084	276	4	.	.	NOUN
asir-6084	276	5	1	1	NUM
asir-6084	276	6	,	,	PUNCT
asir-6084	276	7	2023	2023	NUM
asir-6084	276	8	57	57	NUM
asir-6084	276	9	published	publish	VERB
asir-6084	276	10	by	by	ADP
asir-6084	276	11	scholink	scholink	PROPN
asir-6084	276	12	inc	inc	PROPN
asir-6084	276	13	.	.	PROPN
asir-6084	276	14	thomason	thomason	PROPN
asir-6084	276	15	,	,	PUNCT
asir-6084	276	16	s.	s.	PROPN
asir-6084	276	17	k.	k.	PROPN
asir-6084	276	18	(	(	PUNCT
asir-6084	276	19	1997	1997	NUM
asir-6084	276	20	)	)	PUNCT
asir-6084	276	21	,	,	PUNCT
asir-6084	276	22	relational	relational	ADJ
asir-6084	276	23	modal	modal	NOUN
asir-6084	276	24	for	for	ADP
asir-6084	276	25	the	the	DET
asir-6084	276	26	modal	modal	ADJ
asir-6084	276	27	syllogistic	syllogistic	NOUN
asir-6084	276	28	.	.	PUNCT
asir-6084	277	1	journal	journal	NOUN
asir-6084	277	2	of	of	ADP
asir-6084	277	3	philosophical	philosophical	ADJ
asir-6084	277	4	logic	logic	NOUN
asir-6084	277	5	,	,	PUNCT
asir-6084	277	6	(	(	PUNCT
asir-6084	277	7	26	26	NUM
asir-6084	277	8	)	)	PUNCT
asir-6084	277	9	,	,	PUNCT
asir-6084	277	10	129	129	NUM
asir-6084	277	11	-	-	SYM
asir-6084	277	12	1141	1141	NUM
asir-6084	277	13	.	.	PUNCT
asir-6084	278	1	zhang	zhang	PROPN
asir-6084	278	2	,	,	PUNCT
asir-6084	278	3	x.	x.	PROPN
asir-6084	278	4	j.	j.	PROPN
asir-6084	278	5	(	(	PUNCT
asir-6084	278	6	2014	2014	NUM
asir-6084	278	7	)	)	PUNCT
asir-6084	278	8	.	.	PUNCT
asir-6084	279	1	a	a	DET
asir-6084	279	2	study	study	NOUN
asir-6084	279	3	of	of	ADP
asir-6084	279	4	generalized	generalized	ADJ
asir-6084	279	5	quantifier	quantifier	NOUN
asir-6084	279	6	theory	theory	NOUN
asir-6084	279	7	.	.	PUNCT
asir-6084	280	1	xiamen	xiamen	PROPN
asir-6084	280	2	university	university	PROPN
asir-6084	280	3	press	press	NOUN
asir-6084	280	4	.	.	PUNCT
asir-6084	281	1	(	(	PUNCT
asir-6084	281	2	in	in	ADP
asir-6084	281	3	chinese	chinese	PROPN
asir-6084	281	4	)	)	PUNCT
asir-6084	281	5	zhang	zhang	PROPN
asir-6084	281	6	,	,	PUNCT
asir-6084	281	7	x.	x.	PROPN
asir-6084	281	8	j.	j.	PROPN
asir-6084	281	9	(	(	PUNCT
asir-6084	281	10	2018	2018	NUM
asir-6084	281	11	)	)	PUNCT
asir-6084	281	12	.	.	PUNCT
asir-6084	282	1	axiomatization	axiomatization	NOUN
asir-6084	282	2	of	of	ADP
asir-6084	282	3	aristotelian	aristotelian	ADJ
asir-6084	282	4	syllogistic	syllogistic	ADJ
asir-6084	282	5	logic	logic	NOUN
asir-6084	282	6	based	base	VERB
asir-6084	282	7	on	on	ADP
asir-6084	282	8	generalized	generalized	ADJ
asir-6084	282	9	quantifier	quantifier	NOUN
asir-6084	282	10	theory	theory	NOUN
asir-6084	282	11	.	.	PUNCT
asir-6084	283	1	applied	apply	VERB
asir-6084	283	2	and	and	CCONJ
asir-6084	283	3	computational	computational	ADJ
asir-6084	283	4	mathematics	mathematic	NOUN
asir-6084	283	5	,	,	PUNCT
asir-6084	283	6	7(3	7(3	NUM
asir-6084	283	7	)	)	PUNCT
asir-6084	283	8	,	,	PUNCT
asir-6084	283	9	167	167	NUM
asir-6084	283	10	-	-	SYM
asir-6084	283	11	172	172	NUM
asir-6084	283	12	.	.	PUNCT
asir-6084	283	13	https://doi.org/	https://doi.org/	PROPN
asir-6084	283	14	10.11648	10.11648	NUM
asir-6084	283	15	/	/	SYM
asir-6084	283	16	j.acm.20180703.23	j.acm.20180703.23	PROPN
asir-6084	283	17	zhang	zhang	PROPN
asir-6084	283	18	,	,	PUNCT
asir-6084	283	19	x.	x.	PROPN
asir-6084	283	20	j.	j.	PROPN
asir-6084	283	21	(	(	PUNCT
asir-6084	283	22	2020a	2020a	NUM
asir-6084	283	23	)	)	PUNCT
asir-6084	283	24	.	.	PUNCT
asir-6084	284	1	research	research	NOUN
asir-6084	284	2	on	on	ADP
asir-6084	284	3	extended	extended	ADJ
asir-6084	284	4	syllogism	syllogism	NOUN
asir-6084	284	5	for	for	ADP
asir-6084	284	6	natural	natural	ADJ
asir-6084	284	7	language	language	NOUN
asir-6084	284	8	information	information	NOUN
asir-6084	284	9	processing	processing	NOUN
asir-6084	284	10	.	.	PUNCT
asir-6084	285	1	beijing	beijing	PROPN
asir-6084	285	2	:	:	PUNCT
asir-6084	285	3	science	science	NOUN
asir-6084	285	4	press	press	PROPN
asir-6084	285	5	.	.	PUNCT
asir-6084	286	1	(	(	PUNCT
asir-6084	286	2	in	in	ADP
asir-6084	286	3	chinese	chinese	PROPN
asir-6084	286	4	)	)	PUNCT
asir-6084	286	5	zhang	zhang	PROPN
asir-6084	286	6	,	,	PUNCT
asir-6084	286	7	x.	x.	PROPN
asir-6084	286	8	j.	j.	PROPN
asir-6084	286	9	(	(	PUNCT
asir-6084	286	10	2020b	2020b	NUM
asir-6084	286	11	)	)	PUNCT
asir-6084	286	12	.	.	PUNCT
asir-6084	287	1	screening	screen	VERB
asir-6084	287	2	out	out	ADP
asir-6084	287	3	all	all	DET
asir-6084	287	4	valid	valid	ADJ
asir-6084	287	5	aristotelian	aristotelian	ADJ
asir-6084	287	6	modal	modal	NOUN
asir-6084	287	7	syllogisms	syllogism	NOUN
asir-6084	287	8	.	.	PUNCT
asir-6084	288	1	applied	apply	VERB
asir-6084	288	2	and	and	CCONJ
asir-6084	288	3	computational	computational	ADJ
asir-6084	288	4	mathematics	mathematic	NOUN
asir-6084	288	5	,	,	PUNCT
asir-6084	288	6	8(6	8(6	NUM
asir-6084	288	7	)	)	PUNCT
asir-6084	288	8	,	,	PUNCT
asir-6084	288	9	95	95	NUM
asir-6084	288	10	-	-	SYM
asir-6084	288	11	104	104	NUM
asir-6084	288	12	.	.	PUNCT
asir-6084	289	1	https://doi.org/10.11648/j.acm.20190806.12	https://doi.org/10.11648/j.acm.20190806.12	VERB