id	sid	tid	token	lemma	pos
asir-56165	1	1	applied	apply	VERB
asir-56165	1	2	science	science	NOUN
asir-56165	1	3	and	and	CCONJ
asir-56165	1	4	innovative	innovative	ADJ
asir-56165	1	5	research	research	NOUN
asir-56165	1	6	issn	issn	VERB
asir-56165	1	7	2474	2474	NUM
asir-56165	1	8	-	-	SYM
asir-56165	1	9	4972	4972	NUM
asir-56165	1	10	(	(	PUNCT
asir-56165	1	11	print	print	NOUN
asir-56165	1	12	)	)	PUNCT
asir-56165	1	13	issn	issn	VERB
asir-56165	1	14	2474	2474	NUM
asir-56165	1	15	-	-	SYM
asir-56165	1	16	4980	4980	NUM
asir-56165	1	17	(	(	PUNCT
asir-56165	1	18	online	online	ADJ
asir-56165	1	19	)	)	PUNCT
asir-56165	1	20	vol	vol	NOUN
asir-56165	1	21	.	.	NOUN
asir-56165	2	1	9	9	NUM
asir-56165	2	2	,	,	PUNCT
asir-56165	2	3	no	no	INTJ
asir-56165	2	4	.	.	NOUN
asir-56165	2	5	2	2	NUM
asir-56165	2	6	,	,	PUNCT
asir-56165	2	7	2025	2025	NUM
asir-56165	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-56165	2	9	64	64	NUM
asir-56165	2	10	original	original	ADJ
asir-56165	2	11	paper	paper	NOUN
asir-56165	2	12	reducible	reducible	ADJ
asir-56165	2	13	relationships	relationship	NOUN
asir-56165	2	14	between	between	ADP
asir-56165	2	15	generalized	generalize	VERB
asir-56165	2	16	syllogisms	syllogism	NOUN
asir-56165	2	17	with	with	ADP
asir-56165	2	18	the	the	DET
asir-56165	2	19	quantifiers	quantifier	NOUN
asir-56165	2	20	in	in	ADP
asir-56165	2	21	square{at	square{at	ADV
asir-56165	2	22	least	least	ADJ
asir-56165	2	23	half	half	NOUN
asir-56165	2	24	of	of	ADP
asir-56165	2	25	the	the	DET
asir-56165	2	26	}	}	PUNCT
asir-56165	2	27	haowei	haowei	PROPN
asir-56165	2	28	shi	shi	PROPN
asir-56165	2	29	institute	institute	PROPN
asir-56165	2	30	of	of	ADP
asir-56165	2	31	logic	logic	NOUN
asir-56165	2	32	and	and	CCONJ
asir-56165	2	33	information	information	NOUN
asir-56165	2	34	technology	technology	NOUN
asir-56165	2	35	,	,	PUNCT
asir-56165	2	36	sichuan	sichuan	PROPN
asir-56165	2	37	normal	normal	ADJ
asir-56165	2	38	university	university	PROPN
asir-56165	2	39	,	,	PUNCT
asir-56165	2	40	chengdu	chengdu	PROPN
asir-56165	2	41	,	,	PUNCT
asir-56165	2	42	china	china	PROPN
asir-56165	2	43	abstract	abstract	ADJ
asir-56165	2	44	the	the	DET
asir-56165	2	45	main	main	ADJ
asir-56165	2	46	conclusions	conclusion	NOUN
asir-56165	2	47	of	of	ADP
asir-56165	2	48	this	this	DET
asir-56165	2	49	paper	paper	NOUN
asir-56165	2	50	are	be	AUX
asir-56165	2	51	as	as	SCONJ
asir-56165	2	52	follows	follow	NOUN
asir-56165	2	53	:	:	PUNCT
asir-56165	3	1	theorem	theorem	ADJ
asir-56165	3	2	1	1	NUM
asir-56165	3	3	proves	prove	VERB
asir-56165	3	4	the	the	DET
asir-56165	3	5	validity	validity	NOUN
asir-56165	3	6	of	of	ADP
asir-56165	3	7	the	the	DET
asir-56165	3	8	generalized	generalized	ADJ
asir-56165	3	9	syllogism	syllogism	NOUN
asir-56165	3	10	sai-3	sai-3	NOUN
asir-56165	3	11	.	.	PUNCT
asir-56165	4	1	theorem	theorem	NOUN
asir-56165	4	2	2	2	NUM
asir-56165	4	3	takes	take	VERB
asir-56165	4	4	the	the	DET
asir-56165	4	5	syllogism	syllogism	NOUN
asir-56165	4	6	sai-3	sai-3	PUNCT
asir-56165	4	7	as	as	ADP
asir-56165	4	8	the	the	DET
asir-56165	4	9	fundamental	fundamental	ADJ
asir-56165	4	10	axiom	axiom	NOUN
asir-56165	4	11	,	,	PUNCT
asir-56165	4	12	and	and	CCONJ
asir-56165	4	13	then	then	ADV
asir-56165	4	14	deduces	deduce	VERB
asir-56165	4	15	the	the	DET
asir-56165	4	16	other	other	ADJ
asir-56165	4	17	14	14	NUM
asir-56165	4	18	non	non	ADJ
asir-56165	4	19	-	-	ADJ
asir-56165	4	20	trivial	trivial	ADJ
asir-56165	4	21	valid	valid	ADJ
asir-56165	4	22	generalized	generalize	VERB
asir-56165	4	23	syllogisms	syllogism	NOUN
asir-56165	4	24	with	with	ADP
asir-56165	4	25	the	the	DET
asir-56165	4	26	quantifiers	quantifier	NOUN
asir-56165	4	27	in	in	ADP
asir-56165	4	28	square{at	square{at	ADV
asir-56165	4	29	least	least	ADJ
asir-56165	4	30	half	half	NOUN
asir-56165	4	31	of	of	ADP
asir-56165	4	32	the	the	PRON
asir-56165	4	33	}	}	PUNCT
asir-56165	4	34	.	.	PUNCT
asir-56165	5	1	it	it	PRON
asir-56165	5	2	means	mean	VERB
asir-56165	5	3	that	that	SCONJ
asir-56165	5	4	there	there	PRON
asir-56165	5	5	are	be	VERB
asir-56165	5	6	reducible	reducible	ADJ
asir-56165	5	7	relationships	relationship	NOUN
asir-56165	5	8	between	between	ADP
asir-56165	5	9	these	these	DET
asir-56165	5	10	15	15	NUM
asir-56165	5	11	syllogisms	syllogism	NOUN
asir-56165	5	12	,	,	PUNCT
asir-56165	5	13	and	and	CCONJ
asir-56165	5	14	that	that	SCONJ
asir-56165	5	15	the	the	DET
asir-56165	5	16	above	above	ADJ
asir-56165	5	17	knowledge	knowledge	NOUN
asir-56165	5	18	mining	mining	NOUN
asir-56165	5	19	processes	process	NOUN
asir-56165	5	20	are	be	AUX
asir-56165	5	21	consistent	consistent	ADJ
asir-56165	5	22	.	.	PUNCT
asir-56165	6	1	this	this	DET
asir-56165	6	2	innovative	innovative	ADJ
asir-56165	6	3	achievement	achievement	NOUN
asir-56165	6	4	can	can	AUX
asir-56165	6	5	promote	promote	VERB
asir-56165	6	6	in	in	ADP
asir-56165	6	7	-	-	PUNCT
asir-56165	6	8	depth	depth	NOUN
asir-56165	6	9	research	research	NOUN
asir-56165	6	10	on	on	ADP
asir-56165	6	11	generalized	generalized	ADJ
asir-56165	6	12	syllogistic	syllogistic	NOUN
asir-56165	6	13	and	and	CCONJ
asir-56165	6	14	provide	provide	VERB
asir-56165	6	15	methodological	methodological	ADJ
asir-56165	6	16	inspiration	inspiration	NOUN
asir-56165	6	17	for	for	ADP
asir-56165	6	18	knowledge	knowledge	NOUN
asir-56165	6	19	mining	mining	NOUN
asir-56165	6	20	in	in	ADP
asir-56165	6	21	artificial	artificial	ADJ
asir-56165	6	22	intelligence	intelligence	NOUN
asir-56165	6	23	.	.	PUNCT
asir-56165	7	1	keywords	keyword	VERB
asir-56165	7	2	generalized	generalized	ADJ
asir-56165	7	3	syllogisms	syllogism	NOUN
asir-56165	7	4	,	,	PUNCT
asir-56165	7	5	validity	validity	NOUN
asir-56165	7	6	,	,	PUNCT
asir-56165	7	7	reducible	reducible	ADJ
asir-56165	7	8	relationships	relationship	NOUN
asir-56165	7	9	,	,	PUNCT
asir-56165	7	10	knowledge	knowledge	NOUN
asir-56165	7	11	mining	mining	NOUN
asir-56165	7	12	1	1	NUM
asir-56165	7	13	.	.	PUNCT
asir-56165	8	1	introduction	introduction	NOUN
asir-56165	8	2	in	in	ADP
asir-56165	8	3	natural	natural	ADJ
asir-56165	8	4	language	language	NOUN
asir-56165	8	5	reasoning	reasoning	NOUN
asir-56165	8	6	,	,	PUNCT
asir-56165	8	7	in	in	ADP
asir-56165	8	8	addition	addition	NOUN
asir-56165	8	9	to	to	ADP
asir-56165	8	10	common	common	ADJ
asir-56165	8	11	classical	classical	ADJ
asir-56165	8	12	syllogism	syllogism	NOUN
asir-56165	8	13	reasoning	reasoning	NOUN
asir-56165	8	14	(	(	PUNCT
asir-56165	8	15	łukasiewicz	łukasiewicz	NOUN
asir-56165	8	16	,	,	PUNCT
asir-56165	8	17	1957	1957	NUM
asir-56165	8	18	)	)	PUNCT
asir-56165	8	19	,	,	PUNCT
asir-56165	8	20	there	there	PRON
asir-56165	8	21	is	be	VERB
asir-56165	8	22	generalized	generalized	ADJ
asir-56165	8	23	syllogism	syllogism	NOUN
asir-56165	8	24	reasoning	reasoning	NOUN
asir-56165	8	25	(	(	PUNCT
asir-56165	8	26	hao	hao	PROPN
asir-56165	8	27	,	,	PUNCT
asir-56165	8	28	2024a	2024a	NUM
asir-56165	8	29	-	-	SYM
asir-56165	8	30	b	b	NOUN
asir-56165	8	31	)	)	PUNCT
asir-56165	8	32	.	.	PUNCT
asir-56165	9	1	a	a	DET
asir-56165	9	2	non	non	ADJ
asir-56165	9	3	-	-	ADJ
asir-56165	9	4	trivial	trivial	ADJ
asir-56165	9	5	generalized	generalized	ADJ
asir-56165	9	6	syllogism	syllogism	NOUN
asir-56165	9	7	contains	contain	VERB
asir-56165	9	8	at	at	ADV
asir-56165	9	9	least	least	ADV
asir-56165	9	10	one	one	NUM
asir-56165	9	11	non	non	ADJ
asir-56165	9	12	-	-	ADJ
asir-56165	9	13	trivial	trivial	ADJ
asir-56165	9	14	generalized	generalized	ADJ
asir-56165	9	15	quantifier	quantifier	NOUN
asir-56165	9	16	(	(	PUNCT
asir-56165	9	17	peters	peters	PROPN
asir-56165	9	18	&	&	CCONJ
asir-56165	9	19	westerståhl	westerståhl	PROPN
asir-56165	9	20	,	,	PUNCT
asir-56165	9	21	2006	2006	NUM
asir-56165	9	22	;	;	PUNCT
asir-56165	9	23	xu	xu	PROPN
asir-56165	9	24	&	&	CCONJ
asir-56165	9	25	yu	yu	PROPN
asir-56165	9	26	,	,	PUNCT
asir-56165	9	27	2024	2024	NUM
asir-56165	9	28	)	)	PUNCT
asir-56165	9	29	.	.	PUNCT
asir-56165	10	1	there	there	PRON
asir-56165	10	2	are	be	VERB
asir-56165	10	3	only	only	ADV
asir-56165	10	4	four	four	NUM
asir-56165	10	5	classical	classical	ADJ
asir-56165	10	6	quantifiers	quantifier	NOUN
asir-56165	10	7	as	as	SCONJ
asir-56165	10	8	follows	follow	VERB
asir-56165	10	9	:	:	PUNCT
asir-56165	10	10	some	some	PRON
asir-56165	10	11	,	,	PUNCT
asir-56165	10	12	no	no	INTJ
asir-56165	10	13	,	,	PUNCT
asir-56165	10	14	not	not	PART
asir-56165	10	15	all	all	PRON
asir-56165	10	16	,	,	PUNCT
asir-56165	10	17	and	and	CCONJ
asir-56165	10	18	all	all	PRON
asir-56165	10	19	,	,	PUNCT
asir-56165	10	20	and	and	CCONJ
asir-56165	10	21	they	they	PRON
asir-56165	10	22	form	form	VERB
asir-56165	10	23	square{some	square{some	ADV
asir-56165	10	24	}	}	PUNCT
asir-56165	10	25	(	(	PUNCT
asir-56165	10	26	wang	wang	PROPN
asir-56165	10	27	&	&	CCONJ
asir-56165	10	28	yuan	yuan	PROPN
asir-56165	10	29	,	,	PUNCT
asir-56165	10	30	2024	2024	NUM
asir-56165	10	31	)	)	PUNCT
asir-56165	10	32	.	.	PUNCT
asir-56165	11	1	non	non	ADJ
asir-56165	11	2	-	-	ADJ
asir-56165	11	3	trivial	trivial	ADJ
asir-56165	11	4	generalized	generalized	ADJ
asir-56165	11	5	quantifiers	quantifier	NOUN
asir-56165	11	6	are	be	AUX
asir-56165	11	7	non	non	ADJ
asir-56165	11	8	-	-	ADJ
asir-56165	11	9	classical	classical	ADJ
asir-56165	11	10	ones	one	NOUN
asir-56165	11	11	,	,	PUNCT
asir-56165	11	12	such	such	ADJ
asir-56165	11	13	as	as	ADP
asir-56165	11	14	at	at	ADP
asir-56165	11	15	least	least	ADJ
asir-56165	11	16	half	half	NOUN
asir-56165	11	17	of	of	ADP
asir-56165	11	18	the	the	DET
asir-56165	11	19	,	,	PUNCT
asir-56165	11	20	fewer	few	ADJ
asir-56165	11	21	than	than	ADP
asir-56165	11	22	half	half	NOUN
asir-56165	11	23	of	of	ADP
asir-56165	11	24	the	the	DET
asir-56165	11	25	,	,	PUNCT
asir-56165	11	26	at	at	ADP
asir-56165	11	27	most	most	ADJ
asir-56165	11	28	half	half	NOUN
asir-56165	11	29	of	of	ADP
asir-56165	11	30	the	the	DET
asir-56165	11	31	,	,	PUNCT
asir-56165	11	32	most	most	ADJ
asir-56165	11	33	.	.	PUNCT
asir-56165	12	1	they	they	PRON
asir-56165	12	2	form	form	VERB
asir-56165	12	3	square{at	square{at	ADV
asir-56165	12	4	least	least	ADJ
asir-56165	12	5	half	half	NOUN
asir-56165	12	6	of	of	ADP
asir-56165	12	7	the	the	PRON
asir-56165	12	8	}	}	PUNCT
asir-56165	12	9	(	(	PUNCT
asir-56165	12	10	ma	ma	PROPN
asir-56165	12	11	&	&	CCONJ
asir-56165	12	12	cao	cao	PROPN
asir-56165	12	13	,	,	PUNCT
asir-56165	12	14	2024	2024	NUM
asir-56165	12	15	)	)	PUNCT
asir-56165	12	16	.	.	PUNCT
asir-56165	13	1	although	although	SCONJ
asir-56165	13	2	there	there	PRON
asir-56165	13	3	has	have	AUX
asir-56165	13	4	been	be	AUX
asir-56165	13	5	some	some	DET
asir-56165	13	6	works	work	NOUN
asir-56165	13	7	about	about	ADP
asir-56165	13	8	generalized	generalized	ADJ
asir-56165	13	9	syllogisms	syllogism	NOUN
asir-56165	13	10	(	(	PUNCT
asir-56165	13	11	moss	moss	NOUN
asir-56165	13	12	,	,	PUNCT
asir-56165	13	13	2010	2010	NUM
asir-56165	13	14	;	;	PUNCT
asir-56165	13	15	endrullis	endrullis	PROPN
asir-56165	13	16	&	&	CCONJ
asir-56165	13	17	moss	moss	NOUN
asir-56165	13	18	,	,	PUNCT
asir-56165	13	19	2015	2015	NUM
asir-56165	13	20	;	;	PUNCT
asir-56165	13	21	cao	cao	PROPN
asir-56165	13	22	&	&	CCONJ
asir-56165	13	23	li	li	PROPN
asir-56165	13	24	,	,	PUNCT
asir-56165	13	25	2024	2024	NUM
asir-56165	13	26	)	)	PUNCT
asir-56165	13	27	,	,	PUNCT
asir-56165	13	28	there	there	PRON
asir-56165	13	29	are	be	VERB
asir-56165	13	30	still	still	ADV
asir-56165	13	31	many	many	ADJ
asir-56165	13	32	interesting	interesting	ADJ
asir-56165	13	33	questions	question	NOUN
asir-56165	13	34	to	to	PART
asir-56165	13	35	be	be	AUX
asir-56165	13	36	studied	study	VERB
asir-56165	13	37	.	.	PUNCT
asir-56165	14	1	this	this	DET
asir-56165	14	2	paper	paper	NOUN
asir-56165	14	3	only	only	ADV
asir-56165	14	4	studies	study	VERB
asir-56165	14	5	the	the	DET
asir-56165	14	6	validity	validity	NOUN
asir-56165	14	7	and	and	CCONJ
asir-56165	14	8	reducibility	reducibility	NOUN
asir-56165	14	9	of	of	ADP
asir-56165	14	10	the	the	DET
asir-56165	14	11	generalized	generalize	VERB
asir-56165	14	12	syllogisms	syllogism	NOUN
asir-56165	14	13	involving	involve	VERB
asir-56165	14	14	the	the	DET
asir-56165	14	15	eight	eight	NUM
asir-56165	14	16	quantifiers	quantifier	NOUN
asir-56165	14	17	from	from	ADP
asir-56165	14	18	square{some	square{some	NUM
asir-56165	14	19	}	}	PUNCT
asir-56165	14	20	and	and	CCONJ
asir-56165	14	21	square{at	square{at	ADV
asir-56165	14	22	least	least	ADJ
asir-56165	14	23	half	half	NOUN
asir-56165	14	24	of	of	ADP
asir-56165	14	25	the	the	PRON
asir-56165	14	26	}	}	PUNCT
asir-56165	14	27	.	.	PUNCT
asir-56165	15	1	2	2	X
asir-56165	15	2	.	.	X
asir-56165	15	3	preliminaries	preliminary	NOUN
asir-56165	15	4	in	in	ADP
asir-56165	15	5	this	this	DET
asir-56165	15	6	paper	paper	NOUN
asir-56165	15	7	,	,	PUNCT
asir-56165	15	8	let	let	VERB
asir-56165	15	9	p	p	NOUN
asir-56165	15	10	,	,	PUNCT
asir-56165	15	11	t	t	PROPN
asir-56165	15	12	,	,	PUNCT
asir-56165	15	13	and	and	CCONJ
asir-56165	15	14	n	n	PRON
asir-56165	15	15	be	be	VERB
asir-56165	15	16	variables	variable	NOUN
asir-56165	15	17	,	,	PUNCT
asir-56165	15	18	and	and	CCONJ
asir-56165	15	19	p	p	X
asir-56165	15	20	,	,	PUNCT
asir-56165	15	21	t	t	PROPN
asir-56165	15	22	,	,	PUNCT
asir-56165	15	23	and	and	CCONJ
asir-56165	15	24	n	n	CCONJ
asir-56165	15	25	be	be	VERB
asir-56165	15	26	the	the	DET
asir-56165	15	27	sets	set	NOUN
asir-56165	15	28	that	that	PRON
asir-56165	15	29	composed	compose	VERB
asir-56165	15	30	of	of	ADP
asir-56165	15	31	p	p	PROPN
asir-56165	15	32	,	,	PUNCT
asir-56165	15	33	t	t	PROPN
asir-56165	15	34	,	,	PUNCT
asir-56165	15	35	n	n	CCONJ
asir-56165	15	36	,	,	PUNCT
asir-56165	15	37	respectively	respectively	ADV
asir-56165	15	38	.	.	PUNCT
asir-56165	16	1	d	d	X
asir-56165	16	2	be	be	AUX
asir-56165	16	3	the	the	DET
asir-56165	16	4	domain	domain	NOUN
asir-56165	16	5	of	of	ADP
asir-56165	16	6	variables	variable	NOUN
asir-56165	16	7	.	.	PUNCT
asir-56165	17	1	let	let	VERB
asir-56165	17	2			ADJ
asir-56165	17	3	,	,	PUNCT
asir-56165	17	4			X
asir-56165	17	5	,	,	PUNCT
asir-56165	17	6			NOUN
asir-56165	17	7	,	,	PUNCT
asir-56165	17	8	and	and	CCONJ
asir-56165	17	9			NUM
asir-56165	17	10	be	be	VERB
asir-56165	17	11	well	well	ADV
asir-56165	17	12	-	-	PUNCT
asir-56165	17	13	formed	form	VERB
asir-56165	17	14	formulas	formula	NOUN
asir-56165	17	15	(	(	PUNCT
asir-56165	17	16	shorted	short	VERB
asir-56165	17	17	as	as	ADP
asir-56165	17	18	wff	wff	PROPN
asir-56165	17	19	)	)	PUNCT
asir-56165	17	20	.	.	PUNCT
asir-56165	18	1	‘	'	PUNCT
asir-56165	18	2	p∩n	p∩n	NOUN
asir-56165	18	3	’	'	PUNCT
asir-56165	18	4	represents	represent	VERB
asir-56165	18	5	the	the	DET
asir-56165	18	6	cardinality	cardinality	NOUN
asir-56165	18	7	of	of	ADP
asir-56165	18	8	the	the	DET
asir-56165	18	9	intersection	intersection	NOUN
asir-56165	18	10	of	of	ADP
asir-56165	18	11	the	the	DET
asir-56165	18	12	set	set	NOUN
asir-56165	18	13	p	p	NOUN
asir-56165	18	14	and	and	CCONJ
asir-56165	18	15	n	n	CCONJ
asir-56165	18	16	,	,	PUNCT
asir-56165	18	17	‘	'	PUNCT
asir-56165	18	18	⊢	⊢	NOUN
asir-56165	18	19	’	'	PUNCT
asir-56165	18	20	says	say	VERB
asir-56165	18	21	that	that	SCONJ
asir-56165	18	22			PROPN
asir-56165	18	23	is	be	AUX
asir-56165	18	24	provable	provable	ADJ
asir-56165	18	25	,	,	PUNCT
asir-56165	18	26	and	and	CCONJ
asir-56165	18	27	‘	'	PUNCT
asir-56165	18	28	=def	=def	X
asir-56165	18	29	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-56165	18	30	applied	apply	VERB
asir-56165	18	31	science	science	NOUN
asir-56165	18	32	and	and	CCONJ
asir-56165	18	33	innovative	innovative	ADJ
asir-56165	18	34	research	research	NOUN
asir-56165	18	35	vol	vol	NOUN
asir-56165	18	36	.	.	PUNCT
asir-56165	19	1	9	9	NUM
asir-56165	19	2	,	,	PUNCT
asir-56165	19	3	no	no	INTJ
asir-56165	19	4	.	.	NOUN
asir-56165	19	5	2	2	NUM
asir-56165	19	6	,	,	PUNCT
asir-56165	19	7	2025	2025	NUM
asir-56165	19	8	65	65	NUM
asir-56165	19	9	published	publish	VERB
asir-56165	19	10	by	by	ADP
asir-56165	19	11	scholink	scholink	PROPN
asir-56165	19	12	inc	inc	PROPN
asir-56165	19	13	.	.	PUNCT
asir-56165	20	1			X
asir-56165	20	2	’	'	PUNCT
asir-56165	20	3	that	that	SCONJ
asir-56165	20	4			PROPN
asir-56165	20	5	can	can	AUX
asir-56165	20	6	be	be	AUX
asir-56165	20	7	defined	define	VERB
asir-56165	20	8	by	by	ADP
asir-56165	20	9	.	.	PROPN
asir-56165	20	10	the	the	DET
asir-56165	20	11	operators	operator	NOUN
asir-56165	20	12	(	(	PUNCT
asir-56165	20	13	such	such	ADJ
asir-56165	20	14	as	as	ADP
asir-56165	20	15			ADJ
asir-56165	20	16	,	,	PUNCT
asir-56165	20	17	→	→	SYM
asir-56165	20	18	,	,	PUNCT
asir-56165	20	19			PROPN
asir-56165	20	20	,	,	PUNCT
asir-56165	20	21			ADJ
asir-56165	20	22	)	)	PUNCT
asir-56165	20	23	are	be	AUX
asir-56165	20	24	basic	basic	ADJ
asir-56165	20	25	ones	one	NOUN
asir-56165	20	26	in	in	ADP
asir-56165	20	27	set	set	NOUN
asir-56165	20	28	theory	theory	NOUN
asir-56165	20	29	(	(	PUNCT
asir-56165	20	30	halmos	halmos	NOUN
asir-56165	20	31	,	,	PUNCT
asir-56165	20	32	1974	1974	NUM
asir-56165	20	33	)	)	PUNCT
asir-56165	20	34	.	.	PUNCT
asir-56165	21	1	let	let	VERB
asir-56165	21	2	q	q	NOUN
asir-56165	21	3	is	be	AUX
asir-56165	21	4	a	a	DET
asir-56165	21	5	quantifier	quantifier	NOUN
asir-56165	21	6	,	,	PUNCT
asir-56165	21	7	q	q	PROPN
asir-56165	21	8	,	,	PUNCT
asir-56165	21	9	q	q	PROPN
asir-56165	21	10	,	,	PUNCT
asir-56165	21	11	and	and	CCONJ
asir-56165	21	12	q	q	NOUN
asir-56165	21	13	are	be	AUX
asir-56165	21	14	respectively	respectively	ADV
asir-56165	21	15	its	its	PRON
asir-56165	21	16	outer	outer	ADJ
asir-56165	21	17	,	,	PUNCT
asir-56165	21	18	inner	inner	ADJ
asir-56165	21	19	,	,	PUNCT
asir-56165	21	20	dual	dual	ADJ
asir-56165	21	21	negative	negative	ADJ
asir-56165	21	22	quantifier	quantifier	NOUN
asir-56165	21	23	.	.	PUNCT
asir-56165	22	1	these	these	DET
asir-56165	22	2	four	four	NUM
asir-56165	22	3	quantifiers	quantifier	NOUN
asir-56165	22	4	form	form	VERB
asir-56165	22	5	a	a	DET
asir-56165	22	6	modern	modern	ADJ
asir-56165	22	7	square{q}={q	square{q}={q	ADJ
asir-56165	22	8	,	,	PUNCT
asir-56165	22	9	q	q	PROPN
asir-56165	22	10	,	,	PUNCT
asir-56165	22	11	q	q	PROPN
asir-56165	22	12	,	,	PUNCT
asir-56165	22	13	q	q	PROPN
asir-56165	22	14	}	}	PUNCT
asir-56165	22	15	(	(	PUNCT
asir-56165	22	16	hao	hao	PROPN
asir-56165	22	17	,	,	PUNCT
asir-56165	22	18	2024b	2024b	NUM
asir-56165	22	19	)	)	PUNCT
asir-56165	22	20	.	.	PUNCT
asir-56165	23	1	for	for	ADP
asir-56165	23	2	example	example	NOUN
asir-56165	23	3	,	,	PUNCT
asir-56165	23	4	square{some}={some	square{some}={some	NOUN
asir-56165	23	5	,	,	PUNCT
asir-56165	23	6	no	no	INTJ
asir-56165	23	7	,	,	PUNCT
asir-56165	23	8	not	not	PART
asir-56165	23	9	all	all	PRON
asir-56165	23	10	,	,	PUNCT
asir-56165	23	11	all	all	PRON
asir-56165	23	12	}	}	PUNCT
asir-56165	23	13	,	,	PUNCT
asir-56165	23	14	and	and	CCONJ
asir-56165	23	15	square{at	square{at	ADV
asir-56165	23	16	least	least	ADJ
asir-56165	23	17	half	half	NOUN
asir-56165	23	18	of	of	ADP
asir-56165	23	19	the}={at	the}={at	ADV
asir-56165	23	20	least	least	ADJ
asir-56165	23	21	half	half	NOUN
asir-56165	23	22	of	of	ADP
asir-56165	23	23	the	the	DET
asir-56165	23	24	,	,	PUNCT
asir-56165	23	25	fewer	few	ADJ
asir-56165	23	26	than	than	ADP
asir-56165	23	27	half	half	NOUN
asir-56165	23	28	of	of	ADP
asir-56165	23	29	the	the	DET
asir-56165	23	30	,	,	PUNCT
asir-56165	23	31	at	at	ADP
asir-56165	23	32	most	most	ADJ
asir-56165	23	33	half	half	NOUN
asir-56165	23	34	of	of	ADP
asir-56165	23	35	the	the	PRON
asir-56165	23	36	,	,	PUNCT
asir-56165	23	37	most	most	ADJ
asir-56165	23	38	}	}	PUNCT
asir-56165	23	39	.	.	PUNCT
asir-56165	24	1	the	the	DET
asir-56165	24	2	propositions	proposition	NOUN
asir-56165	24	3	containing	contain	VERB
asir-56165	24	4	these	these	DET
asir-56165	24	5	8	8	NUM
asir-56165	24	6	quantifiers	quantifier	NOUN
asir-56165	24	7	from	from	ADP
asir-56165	24	8	square{some	square{some	NUM
asir-56165	24	9	}	}	PUNCT
asir-56165	24	10	and	and	CCONJ
asir-56165	24	11	square{at	square{at	ADV
asir-56165	24	12	least	least	ADJ
asir-56165	24	13	half	half	NOUN
asir-56165	24	14	of	of	ADP
asir-56165	24	15	the	the	PRON
asir-56165	24	16	}	}	PUNCT
asir-56165	24	17	are	be	AUX
asir-56165	24	18	respectively	respectively	ADV
asir-56165	24	19	called	call	VERB
asir-56165	24	20	proposition	proposition	NOUN
asir-56165	24	21	i	i	PRON
asir-56165	24	22	,	,	PUNCT
asir-56165	24	23	e	e	PROPN
asir-56165	24	24	,	,	PUNCT
asir-56165	24	25	o	o	NOUN
asir-56165	24	26	,	,	PUNCT
asir-56165	24	27	a	a	PRON
asir-56165	24	28	,	,	PUNCT
asir-56165	24	29	s	s	PROPN
asir-56165	24	30	,	,	PUNCT
asir-56165	24	31	f	f	PROPN
asir-56165	24	32	,	,	PUNCT
asir-56165	24	33	h	h	NOUN
asir-56165	24	34	,	,	PUNCT
asir-56165	24	35	and	and	CCONJ
asir-56165	24	36	m	m	PROPN
asir-56165	24	37	(	(	PUNCT
asir-56165	24	38	ma	ma	PROPN
asir-56165	24	39	&	&	CCONJ
asir-56165	24	40	cao	cao	PROPN
asir-56165	24	41	,	,	PUNCT
asir-56165	24	42	2024	2024	NUM
asir-56165	24	43	)	)	PUNCT
asir-56165	24	44	.	.	PUNCT
asir-56165	25	1	this	this	DET
asir-56165	25	2	paper	paper	NOUN
asir-56165	25	3	only	only	ADV
asir-56165	25	4	studies	study	VERB
asir-56165	25	5	the	the	DET
asir-56165	25	6	non	non	ADJ
asir-56165	25	7	-	-	ADJ
asir-56165	25	8	trivial	trivial	ADJ
asir-56165	25	9	generalized	generalized	ADJ
asir-56165	25	10	syllogisms	syllogism	NOUN
asir-56165	25	11	composed	compose	VERB
asir-56165	25	12	of	of	ADP
asir-56165	25	13	these	these	DET
asir-56165	25	14	8	8	NUM
asir-56165	25	15	propositions	proposition	NOUN
asir-56165	25	16	,	,	PUNCT
asir-56165	25	17	and	and	CCONJ
asir-56165	25	18	these	these	DET
asir-56165	25	19	syllogisms	syllogism	NOUN
asir-56165	25	20	include	include	VERB
asir-56165	25	21	at	at	ADV
asir-56165	25	22	least	least	ADJ
asir-56165	25	23	one	one	NUM
asir-56165	25	24	of	of	ADP
asir-56165	25	25	the	the	DET
asir-56165	25	26	last	last	ADJ
asir-56165	25	27	four	four	NUM
asir-56165	25	28	propositions	proposition	NOUN
asir-56165	25	29	.	.	PUNCT
asir-56165	26	1	thus	thus	ADV
asir-56165	26	2	,	,	PUNCT
asir-56165	26	3	‘	'	PUNCT
asir-56165	26	4	at	at	ADP
asir-56165	26	5	least	least	ADJ
asir-56165	26	6	half	half	NOUN
asir-56165	26	7	of	of	ADP
asir-56165	26	8	the(t	the(t	PROPN
asir-56165	26	9	,	,	PUNCT
asir-56165	26	10	n)all(t	n)all(t	NUM
asir-56165	26	11	,	,	PUNCT
asir-56165	26	12	p)→some(p	p)→some(p	NOUN
asir-56165	26	13	,	,	PUNCT
asir-56165	26	14	n	n	CCONJ
asir-56165	26	15	)	)	PUNCT
asir-56165	26	16	’	'	PUNCT
asir-56165	26	17	is	be	AUX
asir-56165	26	18	a	a	DET
asir-56165	26	19	third	third	ADJ
asir-56165	26	20	figure	figure	NOUN
asir-56165	26	21	syllogism	syllogism	NOUN
asir-56165	26	22	,	,	PUNCT
asir-56165	26	23	which	which	PRON
asir-56165	26	24	can	can	AUX
asir-56165	26	25	be	be	AUX
asir-56165	26	26	abbreviated	abbreviate	VERB
asir-56165	26	27	as	as	ADP
asir-56165	26	28	sai-3	sai-3	ADJ
asir-56165	26	29	.	.	PUNCT
asir-56165	26	30	example	example	NOUN
asir-56165	27	1	1	1	NUM
asir-56165	27	2	:	:	PUNCT
asir-56165	27	3	major	major	ADJ
asir-56165	27	4	premise	premise	NOUN
asir-56165	27	5	:	:	PUNCT
asir-56165	27	6	at	at	ADP
asir-56165	27	7	least	least	ADJ
asir-56165	27	8	half	half	NOUN
asir-56165	27	9	of	of	ADP
asir-56165	27	10	my	my	PRON
asir-56165	27	11	flowers	flower	NOUN
asir-56165	27	12	are	be	AUX
asir-56165	27	13	roses	rose	NOUN
asir-56165	27	14	.	.	PUNCT
asir-56165	28	1	minor	minor	ADJ
asir-56165	28	2	premise	premise	NOUN
asir-56165	28	3	:	:	PUNCT
asir-56165	28	4	all	all	DET
asir-56165	28	5	flowers	flower	NOUN
asir-56165	28	6	are	be	AUX
asir-56165	28	7	plants	plant	NOUN
asir-56165	28	8	.	.	PUNCT
asir-56165	29	1	conclusion	conclusion	NOUN
asir-56165	29	2	:	:	PUNCT
asir-56165	29	3	some	some	DET
asir-56165	29	4	plants	plant	NOUN
asir-56165	29	5	are	be	AUX
asir-56165	29	6	roses	rose	NOUN
asir-56165	29	7	.	.	PUNCT
asir-56165	30	1	let	let	VERB
asir-56165	30	2	t	t	PROPN
asir-56165	30	3	,	,	PUNCT
asir-56165	30	4	n	n	CCONJ
asir-56165	30	5	,	,	PUNCT
asir-56165	30	6	and	and	CCONJ
asir-56165	30	7	p	p	NOUN
asir-56165	30	8	be	be	AUX
asir-56165	30	9	variables	variable	NOUN
asir-56165	30	10	that	that	PRON
asir-56165	30	11	represent	represent	VERB
asir-56165	30	12	a	a	DET
asir-56165	30	13	flower	flower	NOUN
asir-56165	30	14	,	,	PUNCT
asir-56165	30	15	a	a	DET
asir-56165	30	16	rose	rose	NOUN
asir-56165	30	17	,	,	PUNCT
asir-56165	30	18	and	and	CCONJ
asir-56165	30	19	a	a	DET
asir-56165	30	20	plant	plant	NOUN
asir-56165	30	21	,	,	PUNCT
asir-56165	30	22	respectively	respectively	ADV
asir-56165	30	23	,	,	PUNCT
asir-56165	30	24	then	then	ADV
asir-56165	30	25	this	this	DET
asir-56165	30	26	syllogism	syllogism	NOUN
asir-56165	30	27	can	can	AUX
asir-56165	30	28	be	be	AUX
asir-56165	30	29	symbolized	symbolize	VERB
asir-56165	30	30	as	as	ADP
asir-56165	30	31	‘	'	PUNCT
asir-56165	30	32	at	at	ADP
asir-56165	30	33	least	least	ADJ
asir-56165	30	34	half	half	NOUN
asir-56165	30	35	of	of	ADP
asir-56165	30	36	the(t	the(t	PROPN
asir-56165	30	37	,	,	PUNCT
asir-56165	30	38	n)all(t	n)all(t	NUM
asir-56165	30	39	,	,	PUNCT
asir-56165	30	40	p)→some(p	p)→some(p	NOUN
asir-56165	30	41	,	,	PUNCT
asir-56165	30	42	n	n	CCONJ
asir-56165	30	43	)	)	PUNCT
asir-56165	30	44	’	'	PUNCT
asir-56165	30	45	.	.	PUNCT
asir-56165	31	1	special	special	ADJ
asir-56165	31	2	note	note	NOUN
asir-56165	31	3	:	:	PUNCT
asir-56165	31	4	it	it	PRON
asir-56165	31	5	was	be	AUX
asir-56165	31	6	assumed	assume	VERB
asir-56165	31	7	that	that	SCONJ
asir-56165	31	8	the	the	DET
asir-56165	31	9	set	set	NOUN
asir-56165	31	10	composed	compose	VERB
asir-56165	31	11	of	of	ADP
asir-56165	31	12	the	the	DET
asir-56165	31	13	subject	subject	ADJ
asir-56165	31	14	variable	variable	NOUN
asir-56165	31	15	for	for	ADP
asir-56165	31	16	a	a	DET
asir-56165	31	17	categorical	categorical	ADJ
asir-56165	31	18	proposition	proposition	NOUN
asir-56165	31	19	containing	contain	VERB
asir-56165	31	20	one	one	NUM
asir-56165	31	21	of	of	ADP
asir-56165	31	22	the	the	DET
asir-56165	31	23	four	four	NUM
asir-56165	31	24	quantifiers	quantifier	NOUN
asir-56165	31	25	(	(	PUNCT
asir-56165	31	26	all	all	ADV
asir-56165	31	27	,	,	PUNCT
asir-56165	31	28	not	not	PART
asir-56165	31	29	all	all	PRON
asir-56165	31	30	,	,	PUNCT
asir-56165	31	31	most	most	ADJ
asir-56165	31	32	,	,	PUNCT
asir-56165	31	33	and	and	CCONJ
asir-56165	31	34	at	at	ADP
asir-56165	31	35	most	most	ADJ
asir-56165	31	36	half	half	NOUN
asir-56165	31	37	of	of	ADP
asir-56165	31	38	the	the	PRON
asir-56165	31	39	)	)	PUNCT
asir-56165	31	40	is	be	AUX
asir-56165	31	41	not	not	PART
asir-56165	31	42	an	an	DET
asir-56165	31	43	empty	empty	ADJ
asir-56165	31	44	set	set	NOUN
asir-56165	31	45	.	.	PUNCT
asir-56165	32	1	3	3	X
asir-56165	32	2	.	.	NUM
asir-56165	32	3	generalized	generalize	VERB
asir-56165	32	4	syllogism	syllogism	NOUN
asir-56165	32	5	system	system	NOUN
asir-56165	32	6	with	with	ADP
asir-56165	32	7	the	the	DET
asir-56165	32	8	quantifiers	quantifier	NOUN
asir-56165	32	9	‘	'	PUNCT
asir-56165	32	10	at	at	ADP
asir-56165	32	11	least	least	ADJ
asir-56165	32	12	half	half	NOUN
asir-56165	32	13	of	of	ADP
asir-56165	32	14	the	the	PRON
asir-56165	32	15	’	'	PUNCT
asir-56165	32	16	this	this	DET
asir-56165	32	17	system	system	NOUN
asir-56165	32	18	consists	consist	VERB
asir-56165	32	19	of	of	ADP
asir-56165	32	20	the	the	DET
asir-56165	32	21	following	follow	VERB
asir-56165	32	22	parts	part	NOUN
asir-56165	32	23	:	:	PUNCT
asir-56165	32	24	3.1	3.1	NUM
asir-56165	32	25	primitive	primitive	ADJ
asir-56165	32	26	symbols	symbol	NOUN
asir-56165	32	27	(	(	PUNCT
asir-56165	32	28	1	1	NUM
asir-56165	32	29	)	)	PUNCT
asir-56165	32	30	variables	variable	NOUN
asir-56165	32	31	:	:	PUNCT
asir-56165	32	32	p	p	X
asir-56165	32	33	,	,	PUNCT
asir-56165	32	34	t	t	PROPN
asir-56165	32	35	,	,	PUNCT
asir-56165	32	36	n	n	CCONJ
asir-56165	32	37	(	(	PUNCT
asir-56165	32	38	2	2	NUM
asir-56165	32	39	)	)	PUNCT
asir-56165	32	40	quantifiers	quantifier	NOUN
asir-56165	32	41	:	:	PUNCT
asir-56165	32	42	some	some	PRON
asir-56165	32	43	,	,	PUNCT
asir-56165	32	44	at	at	ADV
asir-56165	32	45	least	least	ADJ
asir-56165	32	46	half	half	NOUN
asir-56165	32	47	of	of	ADP
asir-56165	32	48	the	the	DET
asir-56165	32	49	(	(	PUNCT
asir-56165	32	50	3	3	NUM
asir-56165	32	51	)	)	PUNCT
asir-56165	32	52	operators	operator	NOUN
asir-56165	32	53	:	:	PUNCT
asir-56165	32	54			VERB
asir-56165	32	55	,	,	PUNCT
asir-56165	32	56	→	→	SYM
asir-56165	32	57	(	(	PUNCT
asir-56165	32	58	4	4	X
asir-56165	32	59	)	)	PUNCT
asir-56165	32	60	brackets	bracket	NOUN
asir-56165	32	61	:	:	PUNCT
asir-56165	32	62	(	(	PUNCT
asir-56165	32	63	,	,	PUNCT
asir-56165	32	64	)	)	PUNCT
asir-56165	32	65	3.2	3.2	NUM
asir-56165	32	66	formation	formation	NOUN
asir-56165	32	67	rules	rule	NOUN
asir-56165	32	68	(	(	PUNCT
asir-56165	32	69	1	1	X
asir-56165	32	70	)	)	PUNCT
asir-56165	32	71	if	if	SCONJ
asir-56165	32	72	q	q	NOUN
asir-56165	32	73	is	be	AUX
asir-56165	32	74	a	a	DET
asir-56165	32	75	quantifier	quantifier	NOUN
asir-56165	32	76	,	,	PUNCT
asir-56165	32	77	p	p	NOUN
asir-56165	32	78	and	and	CCONJ
asir-56165	32	79	n	n	PROPN
asir-56165	32	80	are	be	AUX
asir-56165	32	81	variables	variable	NOUN
asir-56165	32	82	,	,	PUNCT
asir-56165	32	83	then	then	ADV
asir-56165	32	84	q(p	q(p	PROPN
asir-56165	32	85	,	,	PUNCT
asir-56165	32	86	n	n	CCONJ
asir-56165	32	87	)	)	PUNCT
asir-56165	32	88	is	be	AUX
asir-56165	32	89	a	a	DET
asir-56165	32	90	wff	wff	PROPN
asir-56165	32	91	.	.	PUNCT
asir-56165	33	1	(	(	PUNCT
asir-56165	33	2	2	2	X
asir-56165	33	3	)	)	PUNCT
asir-56165	33	4	if	if	SCONJ
asir-56165	33	5			ADJ
asir-56165	33	6	and	and	CCONJ
asir-56165	33	7			PROPN
asir-56165	33	8	are	be	AUX
asir-56165	33	9	wffs	wff	NOUN
asir-56165	33	10	,	,	PUNCT
asir-56165	33	11	then	then	ADV
asir-56165	33	12	so	so	ADV
asir-56165	33	13	are	be	AUX
asir-56165	33	14			NOUN
asir-56165	33	15	and	and	CCONJ
asir-56165	33	16	→.	→.	NOUN
asir-56165	33	17	(	(	PUNCT
asir-56165	33	18	3	3	NUM
asir-56165	33	19	)	)	PUNCT
asir-56165	33	20	only	only	ADV
asir-56165	33	21	the	the	DET
asir-56165	33	22	sentences	sentence	NOUN
asir-56165	33	23	formed	form	VERB
asir-56165	33	24	on	on	ADP
asir-56165	33	25	the	the	DET
asir-56165	33	26	basis	basis	NOUN
asir-56165	33	27	of	of	ADP
asir-56165	33	28	the	the	DET
asir-56165	33	29	above	above	ADJ
asir-56165	33	30	two	two	NUM
asir-56165	33	31	rules	rule	NOUN
asir-56165	33	32	are	be	AUX
asir-56165	33	33	wffs	wff	NOUN
asir-56165	33	34	.	.	PUNCT
asir-56165	34	1	3.3	3.3	NUM
asir-56165	34	2	basic	basic	ADJ
asir-56165	34	3	axioms	axiom	NOUN
asir-56165	34	4	a1	a1	NOUN
asir-56165	34	5	:	:	PUNCT
asir-56165	34	6	if	if	SCONJ
asir-56165	34	7			ADJ
asir-56165	34	8	is	be	AUX
asir-56165	34	9	a	a	DET
asir-56165	34	10	valid	valid	ADJ
asir-56165	34	11	proposition	proposition	NOUN
asir-56165	34	12	in	in	ADP
asir-56165	34	13	classical	classical	ADJ
asir-56165	34	14	logic	logic	NOUN
asir-56165	34	15	,	,	PUNCT
asir-56165	34	16	then	then	ADV
asir-56165	34	17	⊢.	⊢.	PROPN
asir-56165	34	18	a2	a2	PROPN
asir-56165	34	19	:	:	PUNCT
asir-56165	34	20	⊢at	⊢at	X
asir-56165	34	21	least	least	ADJ
asir-56165	34	22	half	half	NOUN
asir-56165	34	23	of	of	ADP
asir-56165	34	24	the(t	the(t	PROPN
asir-56165	34	25	,	,	PUNCT
asir-56165	34	26	n)all(t	n)all(t	NUM
asir-56165	34	27	,	,	PUNCT
asir-56165	34	28	p)→some(p	p)→some(p	NOUN
asir-56165	34	29	,	,	PUNCT
asir-56165	34	30	n	n	CCONJ
asir-56165	34	31	)	)	PUNCT
asir-56165	34	32	(	(	PUNCT
asir-56165	34	33	i.e.	i.e.	X
asir-56165	34	34	the	the	DET
asir-56165	34	35	syllogism	syllogism	NOUN
asir-56165	34	36	sai-3	sai-3	PUNCT
asir-56165	34	37	)	)	PUNCT
asir-56165	34	38	.	.	PUNCT
asir-56165	35	1	3.4	3.4	NUM
asir-56165	35	2	rules	rule	NOUN
asir-56165	35	3	of	of	ADP
asir-56165	35	4	deduction	deduction	NOUN
asir-56165	35	5	rule	rule	NOUN
asir-56165	35	6	1	1	NUM
asir-56165	35	7	(	(	PUNCT
asir-56165	35	8	antecedent	antecedent	NOUN
asir-56165	35	9	strengthening	strengthening	NOUN
asir-56165	35	10	):	):	PUNCT
asir-56165	35	11	if	if	SCONJ
asir-56165	35	12	⊢(→	⊢(→	NUM
asir-56165	35	13	)	)	PUNCT
asir-56165	35	14	and	and	CCONJ
asir-56165	35	15	⊢(→	⊢(→	ADJ
asir-56165	35	16	)	)	PUNCT
asir-56165	35	17	,	,	PUNCT
asir-56165	35	18	then	then	ADV
asir-56165	35	19	⊢(→	⊢(→	NUM
asir-56165	35	20	)	)	PUNCT
asir-56165	35	21	.	.	PUNCT
asir-56165	36	1	rule	rule	NOUN
asir-56165	36	2	2	2	NUM
asir-56165	36	3	(	(	PUNCT
asir-56165	36	4	subsequent	subsequent	ADJ
asir-56165	36	5	weakening	weakening	NOUN
asir-56165	36	6	):	):	PUNCT
asir-56165	36	7	if	if	SCONJ
asir-56165	36	8	⊢(→	⊢(→	NUM
asir-56165	36	9	)	)	PUNCT
asir-56165	36	10	and	and	CCONJ
asir-56165	36	11	⊢(→	⊢(→	NOUN
asir-56165	36	12	)	)	PUNCT
asir-56165	36	13	,	,	PUNCT
asir-56165	36	14	then	then	ADV
asir-56165	36	15	⊢(→	⊢(→	NOUN
asir-56165	36	16	)	)	PUNCT
asir-56165	36	17	.	.	PUNCT
asir-56165	37	1	rule	rule	NOUN
asir-56165	37	2	3	3	NUM
asir-56165	37	3	(	(	PUNCT
asir-56165	37	4	anti	anti	ADJ
asir-56165	37	5	-	-	NOUN
asir-56165	37	6	syllogism	syllogism	NOUN
asir-56165	37	7	):	):	PUNCT
asir-56165	37	8	if	if	SCONJ
asir-56165	37	9	⊢(→	⊢(→	PROPN
asir-56165	37	10	)	)	PUNCT
asir-56165	37	11	,	,	PUNCT
asir-56165	37	12	then	then	ADV
asir-56165	37	13	⊢(→	⊢(→	NUM
asir-56165	37	14	)	)	PUNCT
asir-56165	37	15	.	.	PUNCT
asir-56165	38	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-56165	38	2	applied	apply	VERB
asir-56165	38	3	science	science	NOUN
asir-56165	38	4	and	and	CCONJ
asir-56165	38	5	innovative	innovative	ADJ
asir-56165	38	6	research	research	NOUN
asir-56165	38	7	vol	vol	NOUN
asir-56165	38	8	.	.	PUNCT
asir-56165	39	1	9	9	NUM
asir-56165	39	2	,	,	PUNCT
asir-56165	39	3	no	no	INTJ
asir-56165	39	4	.	.	NOUN
asir-56165	39	5	2	2	NUM
asir-56165	39	6	,	,	PUNCT
asir-56165	39	7	2025	2025	NUM
asir-56165	39	8	66	66	NUM
asir-56165	39	9	published	publish	VERB
asir-56165	39	10	by	by	ADP
asir-56165	39	11	scholink	scholink	PROPN
asir-56165	39	12	inc	inc	PROPN
asir-56165	39	13	.	.	PROPN
asir-56165	39	14	3.5	3.5	NUM
asir-56165	39	15	relevant	relevant	ADJ
asir-56165	39	16	definitions	definition	NOUN
asir-56165	39	17	d1	d1	NOUN
asir-56165	39	18	:	:	PUNCT
asir-56165	39	19	(	(	PUNCT
asir-56165	39	20	)=def(→	)=def(→	INTJ
asir-56165	39	21	)	)	PUNCT
asir-56165	39	22	;	;	PUNCT
asir-56165	39	23	d2	d2	PROPN
asir-56165	39	24	:	:	PUNCT
asir-56165	39	25	(	(	PUNCT
asir-56165	39	26			PROPN
asir-56165	39	27	)	)	PUNCT
asir-56165	40	1	=	=	PRON
asir-56165	40	2	def	def	ADJ
asir-56165	40	3	(	(	PUNCT
asir-56165	40	4	→)(→	→)(→	NOUN
asir-56165	40	5	)	)	PUNCT
asir-56165	40	6	;	;	PUNCT
asir-56165	40	7	d3	d3	PROPN
asir-56165	40	8	:	:	PUNCT
asir-56165	40	9	(	(	PUNCT
asir-56165	40	10	q)(p	q)(p	NOUN
asir-56165	40	11	,	,	PUNCT
asir-56165	40	12	n)=def	n)=def	ADJ
asir-56165	40	13	q(p	q(p	PROPN
asir-56165	40	14	,	,	PUNCT
asir-56165	40	15	d−n	d−n	NOUN
asir-56165	40	16	)	)	PUNCT
asir-56165	40	17	;	;	PUNCT
asir-56165	40	18	d4	d4	PROPN
asir-56165	40	19	:	:	PUNCT
asir-56165	40	20	(	(	PUNCT
asir-56165	40	21	q)(p	q)(p	ADV
asir-56165	40	22	,	,	PUNCT
asir-56165	40	23	n)=def	n)=def	VERB
asir-56165	40	24	it	it	PRON
asir-56165	40	25	is	be	AUX
asir-56165	40	26	not	not	PART
asir-56165	40	27	the	the	DET
asir-56165	40	28	case	case	NOUN
asir-56165	40	29	that	that	SCONJ
asir-56165	40	30	q(p	q(p	PROPN
asir-56165	40	31	,	,	PUNCT
asir-56165	40	32	n	n	CCONJ
asir-56165	40	33	)	)	PUNCT
asir-56165	40	34	;	;	PUNCT
asir-56165	40	35	d5	d5	NOUN
asir-56165	40	36	:	:	PUNCT
asir-56165	40	37	some(p	some(p	ADJ
asir-56165	40	38	,	,	PUNCT
asir-56165	40	39	n	n	CCONJ
asir-56165	40	40	)	)	PUNCT
asir-56165	40	41	is	be	AUX
asir-56165	40	42	true	true	ADJ
asir-56165	40	43	iff	iff	PROPN
asir-56165	40	44	p∩n	p∩n	ADJ
asir-56165	40	45	is	be	AUX
asir-56165	40	46	true	true	ADJ
asir-56165	40	47	;	;	PUNCT
asir-56165	40	48	d6	d6	NOUN
asir-56165	40	49	:	:	PUNCT
asir-56165	40	50	no(p	no(p	NOUN
asir-56165	40	51	,	,	PUNCT
asir-56165	40	52	n	n	CCONJ
asir-56165	40	53	)	)	PUNCT
asir-56165	40	54	is	be	AUX
asir-56165	40	55	true	true	ADJ
asir-56165	40	56	iff	iff	PROPN
asir-56165	40	57	p∩n=	p∩n=	NOUN
asir-56165	40	58	is	be	AUX
asir-56165	40	59	true	true	ADJ
asir-56165	40	60	;	;	PUNCT
asir-56165	40	61	d7	d7	PROPN
asir-56165	40	62	:	:	PUNCT
asir-56165	40	63	not	not	PART
asir-56165	40	64	all(p	all(p	NUM
asir-56165	40	65	,	,	PUNCT
asir-56165	40	66	n	n	CCONJ
asir-56165	40	67	)	)	PUNCT
asir-56165	40	68	is	be	AUX
asir-56165	40	69	true	true	ADJ
asir-56165	40	70	iff	iff	PROPN
asir-56165	40	71	p⊈n	p⊈n	NOUN
asir-56165	40	72	is	be	AUX
asir-56165	40	73	true	true	ADJ
asir-56165	40	74	;	;	PUNCT
asir-56165	40	75	d8	d8	ADV
asir-56165	40	76	:	:	PUNCT
asir-56165	40	77	all(p	all(p	NUM
asir-56165	40	78	,	,	PUNCT
asir-56165	40	79	n)is	n)is	ADJ
asir-56165	40	80	true	true	ADJ
asir-56165	40	81	iff	iff	PROPN
asir-56165	40	82	pn	pn	PROPN
asir-56165	40	83	is	be	AUX
asir-56165	40	84	true	true	ADJ
asir-56165	40	85	;	;	PUNCT
asir-56165	40	86	d9	d9	PROPN
asir-56165	40	87	:	:	PUNCT
asir-56165	40	88	at	at	ADP
asir-56165	40	89	least	least	ADJ
asir-56165	40	90	half	half	NOUN
asir-56165	40	91	of	of	ADP
asir-56165	40	92	the(p	the(p	NUM
asir-56165	40	93	,	,	PUNCT
asir-56165	40	94	n	n	CCONJ
asir-56165	40	95	)	)	PUNCT
asir-56165	40	96	is	be	AUX
asir-56165	40	97	true	true	ADJ
asir-56165	40	98	iff	iff	PROPN
asir-56165	40	99	p∩n0.5p	p∩n0.5p	PROPN
asir-56165	40	100	is	be	AUX
asir-56165	40	101	true	true	ADJ
asir-56165	40	102	;	;	PUNCT
asir-56165	40	103	d10	d10	PROPN
asir-56165	40	104	:	:	PUNCT
asir-56165	40	105	fewer	few	ADJ
asir-56165	40	106	than	than	ADP
asir-56165	40	107	half	half	NOUN
asir-56165	40	108	of	of	ADP
asir-56165	40	109	the(p	the(p	NUM
asir-56165	40	110	,	,	PUNCT
asir-56165	40	111	n	n	CCONJ
asir-56165	40	112	)	)	PUNCT
asir-56165	40	113	is	be	AUX
asir-56165	40	114	true	true	ADJ
asir-56165	40	115	iff	iff	PROPN
asir-56165	40	116	p∩n0.5p	p∩n0.5p	PROPN
asir-56165	40	117	is	be	AUX
asir-56165	40	118	true	true	ADJ
asir-56165	40	119	;	;	PUNCT
asir-56165	40	120	d11	d11	PROPN
asir-56165	40	121	:	:	PUNCT
asir-56165	40	122	at	at	ADP
asir-56165	40	123	most	most	ADJ
asir-56165	40	124	half	half	NOUN
asir-56165	40	125	of	of	ADP
asir-56165	40	126	the(p	the(p	NUM
asir-56165	40	127	,	,	PUNCT
asir-56165	40	128	n	n	CCONJ
asir-56165	40	129	)	)	PUNCT
asir-56165	40	130	is	be	AUX
asir-56165	40	131	true	true	ADJ
asir-56165	40	132	iff	iff	PROPN
asir-56165	40	133	p∩n0.5p	p∩n0.5p	PROPN
asir-56165	40	134	;	;	PUNCT
asir-56165	40	135	d12	d12	PROPN
asir-56165	40	136	:	:	PUNCT
asir-56165	40	137	most(p	most(p	PROPN
asir-56165	40	138	,	,	PUNCT
asir-56165	40	139	n	n	CCONJ
asir-56165	40	140	)	)	PUNCT
asir-56165	40	141	is	be	AUX
asir-56165	40	142	true	true	ADJ
asir-56165	40	143	iff	iff	PROPN
asir-56165	40	144	p∩n0.5p	p∩n0.5p	NOUN
asir-56165	40	145	is	be	AUX
asir-56165	40	146	true	true	ADJ
asir-56165	40	147	.	.	PUNCT
asir-56165	41	1	3.6	3.6	NUM
asir-56165	41	2	relevant	relevant	ADJ
asir-56165	41	3	facts	fact	NOUN
asir-56165	41	4	fact	fact	NOUN
asir-56165	41	5	1	1	NUM
asir-56165	41	6	(	(	PUNCT
asir-56165	41	7	inner	inner	ADJ
asir-56165	41	8	negation	negation	NOUN
asir-56165	41	9	):	):	PUNCT
asir-56165	41	10	(	(	PUNCT
asir-56165	41	11	1.1	1.1	NUM
asir-56165	41	12	)	)	PUNCT
asir-56165	41	13	⊢all(p	⊢all(p	PROPN
asir-56165	41	14	,	,	PUNCT
asir-56165	41	15	n)no(p	n)no(p	PROPN
asir-56165	41	16	,	,	PUNCT
asir-56165	41	17	n	n	CCONJ
asir-56165	41	18	)	)	PUNCT
asir-56165	41	19	;	;	PUNCT
asir-56165	41	20	(	(	PUNCT
asir-56165	41	21	1.2	1.2	NUM
asir-56165	41	22	)	)	PUNCT
asir-56165	41	23	⊢no(p	⊢no(p	NOUN
asir-56165	41	24	,	,	PUNCT
asir-56165	41	25	n)all(p	n)all(p	NOUN
asir-56165	41	26	,	,	PUNCT
asir-56165	41	27	n	n	CCONJ
asir-56165	41	28	)	)	PUNCT
asir-56165	41	29	;	;	PUNCT
asir-56165	41	30	(	(	PUNCT
asir-56165	41	31	1.3	1.3	NUM
asir-56165	41	32	)	)	PUNCT
asir-56165	41	33	⊢some(p	⊢some(p	NOUN
asir-56165	41	34	,	,	PUNCT
asir-56165	41	35	n)not	n)not	ADV
asir-56165	41	36	all(p	all(p	NOUN
asir-56165	41	37	,	,	PUNCT
asir-56165	41	38	n	n	CCONJ
asir-56165	41	39	)	)	PUNCT
asir-56165	41	40	;	;	PUNCT
asir-56165	41	41	(	(	PUNCT
asir-56165	41	42	1.4	1.4	X
asir-56165	41	43	)	)	PUNCT
asir-56165	41	44	⊢not	⊢not	ADV
asir-56165	41	45	all(p	all(p	PROPN
asir-56165	41	46	,	,	PUNCT
asir-56165	41	47	n)some(p	n)some(p	NOUN
asir-56165	41	48	,	,	PUNCT
asir-56165	41	49	n	n	CCONJ
asir-56165	41	50	)	)	PUNCT
asir-56165	41	51	;	;	PUNCT
asir-56165	41	52	(	(	PUNCT
asir-56165	41	53	1.5	1.5	NUM
asir-56165	41	54	)	)	PUNCT
asir-56165	41	55	⊢most(p	⊢most(p	PROPN
asir-56165	41	56	,	,	PUNCT
asir-56165	41	57	n)fewer	n)fewer	NOUN
asir-56165	41	58	than	than	ADP
asir-56165	41	59	half	half	NOUN
asir-56165	41	60	of	of	ADP
asir-56165	41	61	the(p	the(p	NOUN
asir-56165	41	62	,	,	PUNCT
asir-56165	41	63	n	n	CCONJ
asir-56165	41	64	)	)	PUNCT
asir-56165	41	65	;	;	PUNCT
asir-56165	41	66	(	(	PUNCT
asir-56165	41	67	1.6	1.6	NUM
asir-56165	41	68	)	)	PUNCT
asir-56165	41	69	⊢fewer	⊢fewer	NOUN
asir-56165	41	70	than	than	ADP
asir-56165	41	71	half	half	PRON
asir-56165	41	72	of	of	ADP
asir-56165	41	73	the(p	the(p	PROPN
asir-56165	41	74	,	,	PUNCT
asir-56165	41	75	n)most(p	n)most(p	NUM
asir-56165	41	76	,	,	PUNCT
asir-56165	41	77	n	n	CCONJ
asir-56165	41	78	)	)	PUNCT
asir-56165	41	79	;	;	PUNCT
asir-56165	41	80	(	(	PUNCT
asir-56165	41	81	1.7	1.7	NUM
asir-56165	41	82	)	)	PUNCT
asir-56165	41	83	⊢at	⊢at	NOUN
asir-56165	41	84	least	least	ADJ
asir-56165	41	85	half	half	NOUN
asir-56165	41	86	of	of	ADP
asir-56165	41	87	the(p	the(p	NOUN
asir-56165	41	88	,	,	PUNCT
asir-56165	41	89	n)at	n)at	ADV
asir-56165	41	90	most	most	ADJ
asir-56165	41	91	half	half	NOUN
asir-56165	41	92	of	of	ADP
asir-56165	41	93	the(p	the(p	NOUN
asir-56165	41	94	,	,	PUNCT
asir-56165	41	95	n	n	CCONJ
asir-56165	41	96	)	)	PUNCT
asir-56165	41	97	;	;	PUNCT
asir-56165	41	98	(	(	PUNCT
asir-56165	41	99	1.8	1.8	NUM
asir-56165	41	100	)	)	PUNCT
asir-56165	41	101	⊢at	⊢at	VERB
asir-56165	41	102	most	most	ADJ
asir-56165	41	103	half	half	NOUN
asir-56165	41	104	of	of	ADP
asir-56165	41	105	the(p	the(p	NOUN
asir-56165	41	106	,	,	PUNCT
asir-56165	41	107	n)at	n)at	ADV
asir-56165	41	108	least	least	ADJ
asir-56165	41	109	half	half	NOUN
asir-56165	41	110	of	of	ADP
asir-56165	41	111	the(p	the(p	NOUN
asir-56165	41	112	,	,	PUNCT
asir-56165	41	113	n	n	CCONJ
asir-56165	41	114	)	)	PUNCT
asir-56165	41	115	.	.	PUNCT
asir-56165	42	1	fact	fact	NOUN
asir-56165	42	2	2	2	NUM
asir-56165	42	3	(	(	PUNCT
asir-56165	42	4	outer	outer	ADJ
asir-56165	42	5	negation	negation	NOUN
asir-56165	42	6	):	):	PUNCT
asir-56165	42	7	(	(	PUNCT
asir-56165	42	8	2.1	2.1	NUM
asir-56165	42	9	)	)	PUNCT
asir-56165	42	10	⊢all(p	⊢all(p	PROPN
asir-56165	42	11	,	,	PUNCT
asir-56165	42	12	n)not	n)not	ADV
asir-56165	42	13	all(p	all(p	PROPN
asir-56165	42	14	,	,	PUNCT
asir-56165	42	15	n	n	CCONJ
asir-56165	42	16	)	)	PUNCT
asir-56165	42	17	;	;	PUNCT
asir-56165	42	18	(	(	PUNCT
asir-56165	42	19	2.2	2.2	NUM
asir-56165	42	20	)	)	PUNCT
asir-56165	42	21	⊢not	⊢not	ADJ
asir-56165	42	22	all(p	all(p	PROPN
asir-56165	42	23	,	,	PUNCT
asir-56165	42	24	n)all(p	n)all(p	NOUN
asir-56165	42	25	,	,	PUNCT
asir-56165	42	26	n	n	CCONJ
asir-56165	42	27	)	)	PUNCT
asir-56165	42	28	;	;	PUNCT
asir-56165	42	29	(	(	PUNCT
asir-56165	42	30	2.3	2.3	NUM
asir-56165	42	31	)	)	PUNCT
asir-56165	42	32	⊢no(p	⊢no(p	NOUN
asir-56165	42	33	,	,	PUNCT
asir-56165	42	34	n)some(p	n)some(p	PROPN
asir-56165	42	35	,	,	PUNCT
asir-56165	42	36	n	n	CCONJ
asir-56165	42	37	)	)	PUNCT
asir-56165	42	38	;	;	PUNCT
asir-56165	42	39	(	(	PUNCT
asir-56165	42	40	2.4	2.4	X
asir-56165	42	41	)	)	PUNCT
asir-56165	42	42	⊢some(p	⊢some(p	NOUN
asir-56165	42	43	,	,	PUNCT
asir-56165	42	44	n)no(p	n)no(p	NOUN
asir-56165	42	45	,	,	PUNCT
asir-56165	42	46	n	n	CCONJ
asir-56165	42	47	)	)	PUNCT
asir-56165	42	48	;	;	PUNCT
asir-56165	42	49	(	(	PUNCT
asir-56165	42	50	2.5	2.5	NUM
asir-56165	42	51	)	)	PUNCT
asir-56165	42	52	⊢most(p	⊢most(p	PROPN
asir-56165	42	53	,	,	PUNCT
asir-56165	42	54	n)at	n)at	ADV
asir-56165	42	55	most	most	ADJ
asir-56165	42	56	half	half	NOUN
asir-56165	42	57	of	of	ADP
asir-56165	42	58	the(p	the(p	NUM
asir-56165	42	59	,	,	PUNCT
asir-56165	42	60	n	n	CCONJ
asir-56165	42	61	)	)	PUNCT
asir-56165	42	62	;	;	PUNCT
asir-56165	42	63	(	(	PUNCT
asir-56165	42	64	2.6	2.6	NUM
asir-56165	42	65	)	)	PUNCT
asir-56165	42	66	⊢at	⊢at	ADV
asir-56165	42	67	most	most	ADJ
asir-56165	42	68	half	half	NOUN
asir-56165	42	69	of	of	ADP
asir-56165	42	70	the(p	the(p	NUM
asir-56165	42	71	,	,	PUNCT
asir-56165	42	72	n)most(p	n)most(p	PROPN
asir-56165	42	73	,	,	PUNCT
asir-56165	42	74	n	n	CCONJ
asir-56165	42	75	)	)	PUNCT
asir-56165	42	76	;	;	PUNCT
asir-56165	42	77	(	(	PUNCT
asir-56165	42	78	2.7	2.7	X
asir-56165	42	79	)	)	PUNCT
asir-56165	42	80	⊢fewer	⊢fewer	NOUN
asir-56165	42	81	than	than	ADP
asir-56165	42	82	half	half	NOUN
asir-56165	42	83	of	of	ADP
asir-56165	42	84	the(p	the(p	NOUN
asir-56165	42	85	,	,	PUNCT
asir-56165	42	86	n)at	n)at	ADV
asir-56165	42	87	least	least	ADJ
asir-56165	42	88	half	half	NOUN
asir-56165	42	89	of	of	ADP
asir-56165	42	90	the(p	the(p	NUM
asir-56165	42	91	,	,	PUNCT
asir-56165	42	92	n	n	CCONJ
asir-56165	42	93	)	)	PUNCT
asir-56165	42	94	;	;	PUNCT
asir-56165	42	95	(	(	PUNCT
asir-56165	42	96	2.8	2.8	NUM
asir-56165	42	97	)	)	PUNCT
asir-56165	42	98	⊢at	⊢at	ADV
asir-56165	42	99	least	least	ADJ
asir-56165	42	100	half	half	NOUN
asir-56165	42	101	of	of	ADP
asir-56165	42	102	the(p	the(p	NUM
asir-56165	42	103	,	,	PUNCT
asir-56165	42	104	n)fewer	n)fewer	NOUN
asir-56165	42	105	than	than	ADP
asir-56165	42	106	half	half	NOUN
asir-56165	42	107	of	of	ADP
asir-56165	42	108	the(p	the(p	NUM
asir-56165	42	109	,	,	PUNCT
asir-56165	42	110	n	n	CCONJ
asir-56165	42	111	)	)	PUNCT
asir-56165	42	112	.	.	PUNCT
asir-56165	43	1	fact	fact	NOUN
asir-56165	43	2	3	3	NUM
asir-56165	43	3	(	(	PUNCT
asir-56165	43	4	symmetry	symmetry	NOUN
asir-56165	43	5	):	):	PUNCT
asir-56165	43	6	(	(	PUNCT
asir-56165	43	7	3.1	3.1	NUM
asir-56165	43	8	)	)	PUNCT
asir-56165	43	9	⊢some(p	⊢some(p	PROPN
asir-56165	43	10	,	,	PUNCT
asir-56165	43	11	n)some(n	n)some(n	PROPN
asir-56165	43	12	,	,	PUNCT
asir-56165	43	13	p	p	NOUN
asir-56165	43	14	)	)	PUNCT
asir-56165	43	15	;	;	PUNCT
asir-56165	43	16	(	(	PUNCT
asir-56165	43	17	3.2	3.2	NUM
asir-56165	43	18	)	)	PUNCT
asir-56165	43	19	⊢no(p	⊢no(p	NOUN
asir-56165	43	20	,	,	PUNCT
asir-56165	43	21	n)no(n	n)no(n	PROPN
asir-56165	43	22	,	,	PUNCT
asir-56165	43	23	p	p	NOUN
asir-56165	43	24	)	)	PUNCT
asir-56165	43	25	.	.	PUNCT
asir-56165	44	1	fact	fact	NOUN
asir-56165	44	2	4	4	NUM
asir-56165	44	3	(	(	PUNCT
asir-56165	44	4	subordination	subordination	NOUN
asir-56165	44	5	)	)	PUNCT
asir-56165	44	6	:	:	PUNCT
asir-56165	44	7	(	(	PUNCT
asir-56165	44	8	4.1	4.1	NUM
asir-56165	44	9	)	)	PUNCT
asir-56165	44	10	⊢all(p	⊢all(p	PROPN
asir-56165	44	11	,	,	PUNCT
asir-56165	44	12	n)→some(p	n)→some(p	NOUN
asir-56165	44	13	,	,	PUNCT
asir-56165	44	14	n	n	CCONJ
asir-56165	44	15	)	)	PUNCT
asir-56165	44	16	;	;	PUNCT
asir-56165	44	17	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-56165	44	18	applied	apply	VERB
asir-56165	44	19	science	science	NOUN
asir-56165	44	20	and	and	CCONJ
asir-56165	44	21	innovative	innovative	ADJ
asir-56165	44	22	research	research	NOUN
asir-56165	44	23	vol	vol	NOUN
asir-56165	44	24	.	.	PUNCT
asir-56165	45	1	9	9	NUM
asir-56165	45	2	,	,	PUNCT
asir-56165	45	3	no	no	INTJ
asir-56165	45	4	.	.	NOUN
asir-56165	45	5	2	2	NUM
asir-56165	45	6	,	,	PUNCT
asir-56165	45	7	2025	2025	NUM
asir-56165	45	8	67	67	NUM
asir-56165	45	9	published	publish	VERB
asir-56165	45	10	by	by	ADP
asir-56165	45	11	scholink	scholink	PROPN
asir-56165	45	12	inc	inc	PROPN
asir-56165	45	13	.	.	PROPN
asir-56165	46	1	(	(	PUNCT
asir-56165	46	2	4.2	4.2	NUM
asir-56165	46	3	)	)	PUNCT
asir-56165	46	4	⊢no(p	⊢no(p	NOUN
asir-56165	46	5	,	,	PUNCT
asir-56165	46	6	n)→not	n)→not	ADV
asir-56165	46	7	all(p	all(p	PROPN
asir-56165	46	8	,	,	PUNCT
asir-56165	46	9	n	n	CCONJ
asir-56165	46	10	)	)	PUNCT
asir-56165	46	11	;	;	PUNCT
asir-56165	46	12	(	(	PUNCT
asir-56165	46	13	4.3	4.3	NUM
asir-56165	46	14	)	)	PUNCT
asir-56165	46	15	⊢all(p	⊢all(p	PROPN
asir-56165	46	16	,	,	PUNCT
asir-56165	46	17	n)→most(p	n)→most(p	NOUN
asir-56165	46	18	,	,	PUNCT
asir-56165	46	19	n	n	CCONJ
asir-56165	46	20	)	)	PUNCT
asir-56165	46	21	;	;	PUNCT
asir-56165	46	22	(	(	PUNCT
asir-56165	46	23	4.4	4.4	NUM
asir-56165	46	24	)	)	PUNCT
asir-56165	46	25	⊢most(p	⊢most(p	PROPN
asir-56165	46	26	,	,	PUNCT
asir-56165	46	27	n)→some(p	n)→some(p	NOUN
asir-56165	46	28	,	,	PUNCT
asir-56165	46	29	n	n	CCONJ
asir-56165	46	30	)	)	PUNCT
asir-56165	46	31	;	;	PUNCT
asir-56165	46	32	(	(	PUNCT
asir-56165	46	33	4.5	4.5	NUM
asir-56165	46	34	)	)	PUNCT
asir-56165	46	35	⊢all(p	⊢all(p	PROPN
asir-56165	46	36	,	,	PUNCT
asir-56165	46	37	n)→at	n)→at	NOUN
asir-56165	46	38	least	least	ADJ
asir-56165	46	39	half	half	NOUN
asir-56165	46	40	of	of	ADP
asir-56165	46	41	the(p	the(p	NUM
asir-56165	46	42	,	,	PUNCT
asir-56165	46	43	n	n	CCONJ
asir-56165	46	44	)	)	PUNCT
asir-56165	46	45	;	;	PUNCT
asir-56165	46	46	(	(	PUNCT
asir-56165	46	47	4.6	4.6	X
asir-56165	46	48	)	)	PUNCT
asir-56165	46	49	⊢at	⊢at	NOUN
asir-56165	46	50	least	least	ADJ
asir-56165	46	51	half	half	NOUN
asir-56165	46	52	of	of	ADP
asir-56165	46	53	the(p	the(p	PROPN
asir-56165	46	54	,	,	PUNCT
asir-56165	46	55	n)→some(p	n)→some(p	NOUN
asir-56165	46	56	,	,	PUNCT
asir-56165	46	57	n	n	CCONJ
asir-56165	46	58	)	)	PUNCT
asir-56165	46	59	;	;	PUNCT
asir-56165	46	60	(	(	PUNCT
asir-56165	46	61	4.7	4.7	NUM
asir-56165	46	62	)	)	PUNCT
asir-56165	46	63	⊢at	⊢at	NOUN
asir-56165	46	64	least	least	ADJ
asir-56165	46	65	half	half	NOUN
asir-56165	46	66	of	of	ADP
asir-56165	46	67	the(p	the(p	PROPN
asir-56165	46	68	,	,	PUNCT
asir-56165	46	69	n)→most(p	n)→most(p	NOUN
asir-56165	46	70	,	,	PUNCT
asir-56165	46	71	n	n	CCONJ
asir-56165	46	72	)	)	PUNCT
asir-56165	46	73	;	;	PUNCT
asir-56165	46	74	(	(	PUNCT
asir-56165	46	75	4.8	4.8	NUM
asir-56165	46	76	)	)	PUNCT
asir-56165	46	77	⊢at	⊢at	VERB
asir-56165	46	78	most	most	ADJ
asir-56165	46	79	half	half	NOUN
asir-56165	46	80	of	of	ADP
asir-56165	46	81	the(p	the(p	PROPN
asir-56165	46	82	,	,	PUNCT
asir-56165	46	83	n)→fewer	n)→few	ADJ
asir-56165	46	84	than	than	ADP
asir-56165	46	85	half	half	NOUN
asir-56165	46	86	of	of	ADP
asir-56165	46	87	the(p	the(p	NUM
asir-56165	46	88	,	,	PUNCT
asir-56165	46	89	n	n	CCONJ
asir-56165	46	90	)	)	PUNCT
asir-56165	46	91	;	;	PUNCT
asir-56165	46	92	(	(	PUNCT
asir-56165	46	93	4.9	4.9	NUM
asir-56165	46	94	)	)	PUNCT
asir-56165	46	95	⊢fewer	⊢fewer	NOUN
asir-56165	46	96	than	than	ADP
asir-56165	46	97	half	half	PRON
asir-56165	46	98	of	of	ADP
asir-56165	46	99	the(p	the(p	NOUN
asir-56165	46	100	,	,	PUNCT
asir-56165	46	101	n)→not	n)→not	ADV
asir-56165	46	102	all(p	all(p	PROPN
asir-56165	46	103	,	,	PUNCT
asir-56165	46	104	n	n	CCONJ
asir-56165	46	105	)	)	PUNCT
asir-56165	46	106	;	;	PUNCT
asir-56165	46	107	(	(	PUNCT
asir-56165	46	108	4.10	4.10	NUM
asir-56165	46	109	)	)	PUNCT
asir-56165	46	110	⊢at	⊢at	VERB
asir-56165	46	111	most	most	ADJ
asir-56165	46	112	half	half	NOUN
asir-56165	46	113	of	of	ADP
asir-56165	46	114	the(p	the(p	NOUN
asir-56165	46	115	,	,	PUNCT
asir-56165	46	116	n)→not	n)→not	ADV
asir-56165	46	117	all(p	all(p	PROPN
asir-56165	46	118	,	,	PUNCT
asir-56165	46	119	n	n	CCONJ
asir-56165	46	120	)	)	PUNCT
asir-56165	46	121	;	;	PUNCT
asir-56165	46	122	(	(	PUNCT
asir-56165	46	123	4.11	4.11	NUM
asir-56165	46	124	)	)	PUNCT
asir-56165	46	125	⊢no(p	⊢no(p	NOUN
asir-56165	46	126	,	,	PUNCT
asir-56165	46	127	n)→fewer	n)→fewer	X
asir-56165	46	128	than	than	ADP
asir-56165	46	129	half	half	NOUN
asir-56165	46	130	of	of	ADP
asir-56165	46	131	the(p	the(p	NUM
asir-56165	46	132	,	,	PUNCT
asir-56165	46	133	n	n	CCONJ
asir-56165	46	134	)	)	PUNCT
asir-56165	46	135	;	;	PUNCT
asir-56165	46	136	(	(	PUNCT
asir-56165	46	137	4.12	4.12	NUM
asir-56165	46	138	)	)	PUNCT
asir-56165	46	139	⊢no(p	⊢no(p	NOUN
asir-56165	46	140	,	,	PUNCT
asir-56165	46	141	n)→at	n)→at	NOUN
asir-56165	46	142	most	most	ADJ
asir-56165	46	143	half	half	NOUN
asir-56165	46	144	of	of	ADP
asir-56165	46	145	the(p	the(p	NUM
asir-56165	46	146	,	,	PUNCT
asir-56165	46	147	n	n	CCONJ
asir-56165	46	148	)	)	PUNCT
asir-56165	46	149	.	.	PUNCT
asir-56165	47	1	the	the	DET
asir-56165	47	2	above	above	ADJ
asir-56165	47	3	facts	fact	NOUN
asir-56165	47	4	are	be	AUX
asir-56165	47	5	the	the	DET
asir-56165	47	6	basis	basis	NOUN
asir-56165	47	7	facts	fact	NOUN
asir-56165	47	8	in	in	ADP
asir-56165	47	9	generalized	generalized	ADJ
asir-56165	47	10	quantifier	quantifier	NOUN
asir-56165	47	11	theory	theory	NOUN
asir-56165	47	12	(	(	PUNCT
asir-56165	47	13	peters	peters	PROPN
asir-56165	47	14	&	&	CCONJ
asir-56165	47	15	westerståhl	westerståhl	PROPN
asir-56165	47	16	,	,	PUNCT
asir-56165	47	17	2006	2006	NUM
asir-56165	47	18	)	)	PUNCT
asir-56165	47	19	.	.	PUNCT
asir-56165	48	1	4	4	X
asir-56165	48	2	.	.	X
asir-56165	48	3	knowledge	knowledge	NOUN
asir-56165	48	4	mining	mining	NOUN
asir-56165	48	5	about	about	ADP
asir-56165	48	6	valid	valid	ADJ
asir-56165	48	7	generalized	generalized	ADJ
asir-56165	48	8	syllogisms	syllogism	NOUN
asir-56165	48	9	the	the	DET
asir-56165	48	10	following	follow	VERB
asir-56165	48	11	theorem	theorem	ADJ
asir-56165	48	12	1	1	NUM
asir-56165	48	13	proves	prove	VERB
asir-56165	48	14	the	the	DET
asir-56165	48	15	validity	validity	NOUN
asir-56165	48	16	of	of	ADP
asir-56165	48	17	the	the	DET
asir-56165	48	18	generalized	generalized	ADJ
asir-56165	48	19	syllogism	syllogism	NOUN
asir-56165	48	20	sai-3	sai-3	NOUN
asir-56165	48	21	.	.	PUNCT
asir-56165	49	1	taking	take	VERB
asir-56165	49	2	the	the	DET
asir-56165	49	3	syllogism	syllogism	NOUN
asir-56165	49	4	sai-3	sai-3	PUNCT
asir-56165	49	5	as	as	ADP
asir-56165	49	6	the	the	DET
asir-56165	49	7	fundamental	fundamental	ADJ
asir-56165	49	8	axiom	axiom	NOUN
asir-56165	49	9	in	in	ADP
asir-56165	49	10	theorem	theorem	NOUN
asir-56165	49	11	2	2	NUM
asir-56165	49	12	,	,	PUNCT
asir-56165	49	13	the	the	DET
asir-56165	49	14	other	other	ADJ
asir-56165	49	15	14	14	NUM
asir-56165	49	16	valid	valid	ADJ
asir-56165	49	17	generalized	generalize	VERB
asir-56165	49	18	syllogisms	syllogism	NOUN
asir-56165	49	19	can	can	AUX
asir-56165	49	20	be	be	AUX
asir-56165	49	21	derived	derive	VERB
asir-56165	49	22	by	by	ADP
asir-56165	49	23	the	the	DET
asir-56165	49	24	above	above	ADJ
asir-56165	49	25	facts	fact	NOUN
asir-56165	49	26	and	and	CCONJ
asir-56165	49	27	definitions	definition	NOUN
asir-56165	49	28	.	.	PUNCT
asir-56165	50	1	theorem	theorem	ADJ
asir-56165	50	2	1	1	NUM
asir-56165	50	3	(	(	PUNCT
asir-56165	50	4	sai-3	sai-3	X
asir-56165	50	5	):	):	PUNCT
asir-56165	50	6	the	the	DET
asir-56165	50	7	generalized	generalized	ADJ
asir-56165	50	8	syllogism	syllogism	NOUN
asir-56165	50	9	at	at	ADP
asir-56165	50	10	least	least	ADJ
asir-56165	50	11	half	half	NOUN
asir-56165	50	12	of	of	ADP
asir-56165	50	13	the(t	the(t	PROPN
asir-56165	50	14	,	,	PUNCT
asir-56165	50	15	n)all(t	n)all(t	NUM
asir-56165	50	16	,	,	PUNCT
asir-56165	50	17	p)→some(p	p)→some(p	NOUN
asir-56165	50	18	,	,	PUNCT
asir-56165	50	19	n	n	CCONJ
asir-56165	50	20	)	)	PUNCT
asir-56165	50	21	is	be	AUX
asir-56165	50	22	valid	valid	ADJ
asir-56165	50	23	.	.	PUNCT
asir-56165	51	1	proof	proof	NOUN
asir-56165	51	2	:	:	PUNCT
asir-56165	51	3	suppose	suppose	VERB
asir-56165	51	4	that	that	SCONJ
asir-56165	51	5	at	at	ADV
asir-56165	51	6	least	least	ADJ
asir-56165	51	7	half	half	NOUN
asir-56165	51	8	of	of	ADP
asir-56165	51	9	the(t	the(t	PROPN
asir-56165	51	10	,	,	PUNCT
asir-56165	51	11	n	n	CCONJ
asir-56165	51	12	)	)	PUNCT
asir-56165	51	13	and	and	CCONJ
asir-56165	51	14	all(t	all(t	PROPN
asir-56165	51	15	,	,	PUNCT
asir-56165	51	16	p	p	NOUN
asir-56165	51	17	)	)	PUNCT
asir-56165	51	18	are	be	AUX
asir-56165	51	19	true	true	ADJ
asir-56165	51	20	,	,	PUNCT
asir-56165	51	21	thus	thus	ADV
asir-56165	51	22	t∩n0.5t	t∩n0.5t	PROPN
asir-56165	51	23	is	be	AUX
asir-56165	51	24	true	true	ADJ
asir-56165	51	25	according	accord	VERB
asir-56165	51	26	to	to	ADP
asir-56165	51	27	definition	definition	NOUN
asir-56165	51	28	d9	d9	PROPN
asir-56165	51	29	,	,	PUNCT
asir-56165	51	30	and	and	CCONJ
asir-56165	51	31	tp	tp	NOUN
asir-56165	51	32	is	be	AUX
asir-56165	51	33	true	true	ADJ
asir-56165	51	34	with	with	SCONJ
asir-56165	51	35	the	the	DET
asir-56165	51	36	help	help	NOUN
asir-56165	51	37	of	of	ADP
asir-56165	51	38	definition	definition	NOUN
asir-56165	51	39	d8	d8	ADV
asir-56165	51	40	.	.	PUNCT
asir-56165	52	1	it	it	PRON
asir-56165	52	2	follows	follow	VERB
asir-56165	52	3	that	that	SCONJ
asir-56165	52	4	p∩n.	p∩n.	PROPN
asir-56165	52	5	this	this	PRON
asir-56165	52	6	can	can	AUX
asir-56165	52	7	be	be	AUX
asir-56165	52	8	proven	prove	VERB
asir-56165	52	9	using	use	VERB
asir-56165	52	10	the	the	DET
asir-56165	52	11	method	method	NOUN
asir-56165	52	12	of	of	ADP
asir-56165	52	13	contradiction	contradiction	NOUN
asir-56165	52	14	.	.	PUNCT
asir-56165	53	1	suppose	suppose	VERB
asir-56165	53	2	that	that	SCONJ
asir-56165	53	3	p∩n=	p∩n=	NOUN
asir-56165	53	4	,	,	PUNCT
asir-56165	53	5	thus	thus	ADV
asir-56165	53	6	t∩n=	t∩n=	VERB
asir-56165	53	7	in	in	ADP
asir-56165	53	8	line	line	NOUN
asir-56165	53	9	with	with	ADP
asir-56165	53	10	tp	tp	PROPN
asir-56165	53	11	.	.	PUNCT
asir-56165	54	1	this	this	PRON
asir-56165	54	2	contradicts	contradict	VERB
asir-56165	54	3	t∩n0.5t.	t∩n0.5t.	PROPN
asir-56165	54	4	therefore	therefore	ADV
asir-56165	54	5	,	,	PUNCT
asir-56165	54	6	p∩n	p∩n	PROPN
asir-56165	54	7	holds	hold	VERB
asir-56165	54	8	.	.	PUNCT
asir-56165	55	1	it	it	PRON
asir-56165	55	2	can	can	AUX
asir-56165	55	3	be	be	AUX
asir-56165	55	4	concluded	conclude	VERB
asir-56165	55	5	that	that	SCONJ
asir-56165	55	6	some(p	some(p	NOUN
asir-56165	55	7	,	,	PUNCT
asir-56165	55	8	n	n	CCONJ
asir-56165	55	9	)	)	PUNCT
asir-56165	55	10	is	be	AUX
asir-56165	55	11	true	true	ADJ
asir-56165	55	12	in	in	ADP
asir-56165	55	13	the	the	DET
asir-56165	55	14	light	light	NOUN
asir-56165	55	15	of	of	ADP
asir-56165	55	16	definition	definition	NOUN
asir-56165	55	17	d5	d5	NOUN
asir-56165	55	18	,	,	PUNCT
asir-56165	55	19	just	just	ADV
asir-56165	55	20	as	as	SCONJ
asir-56165	55	21	desired	desire	VERB
asir-56165	55	22	.	.	PUNCT
asir-56165	56	1	theorem	theorem	VERB
asir-56165	56	2	2	2	NUM
asir-56165	56	3	:	:	PUNCT
asir-56165	56	4	there	there	PRON
asir-56165	56	5	are	be	VERB
asir-56165	56	6	14	14	NUM
asir-56165	56	7	valid	valid	ADJ
asir-56165	56	8	generalized	generalize	VERB
asir-56165	56	9	syllogisms	syllogism	NOUN
asir-56165	56	10	inferred	infer	VERB
asir-56165	56	11	from	from	ADP
asir-56165	56	12	sai-3	sai-3	ADV
asir-56165	56	13	:	:	PUNCT
asir-56165	56	14	(	(	PUNCT
asir-56165	56	15	1	1	X
asir-56165	56	16	)	)	PUNCT
asir-56165	56	17	⊢sai-3→asi-3	⊢sai-3→asi-3	NOUN
asir-56165	56	18	(	(	PUNCT
asir-56165	56	19	2	2	NUM
asir-56165	56	20	)	)	PUNCT
asir-56165	56	21	⊢sai-3→hao-3	⊢sai-3→hao-3	PROPN
asir-56165	56	22	(	(	PUNCT
asir-56165	56	23	3	3	X
asir-56165	56	24	)	)	PUNCT
asir-56165	56	25	⊢sai-3→eaf-1	⊢sai-3→eaf-1	NOUN
asir-56165	56	26	(	(	PUNCT
asir-56165	56	27	4	4	NUM
asir-56165	56	28	)	)	PUNCT
asir-56165	56	29	⊢sai-3→eaf-1→eaf-2	⊢sai-3→eaf-1→eaf-2	NOUN
asir-56165	56	30	(	(	PUNCT
asir-56165	56	31	5	5	NUM
asir-56165	56	32	)	)	PUNCT
asir-56165	56	33	⊢sai-3→eso-2	⊢sai-3→eso-2	PROPN
asir-56165	56	34	(	(	PUNCT
asir-56165	56	35	6	6	NUM
asir-56165	56	36	)	)	PUNCT
asir-56165	56	37	⊢sai-3→eso-2→eso-1	⊢sai-3→eso-2→eso-1	NOUN
asir-56165	56	38	(	(	PUNCT
asir-56165	56	39	7	7	X
asir-56165	56	40	)	)	PUNCT
asir-56165	56	41	⊢sai-3→asi-3→eso-3	⊢sai-3→asi-3→eso-3	NOUN
asir-56165	56	42	(	(	PUNCT
asir-56165	56	43	8)	8)	NUM
asir-56165	56	44	⊢sai-3→asi-3→eso-3→eso-4	⊢sai-3→asi-3→eso-3→eso-4	NOUN
asir-56165	56	45	(	(	PUNCT
asir-56165	56	46	9	9	NUM
asir-56165	56	47	)	)	PUNCT
asir-56165	57	1	⊢sai-3→eaf-1→aam-1	⊢sai-3→eaf-1→aam-1	NOUN
asir-56165	57	2	(	(	PUNCT
asir-56165	57	3	10	10	NUM
asir-56165	57	4	)	)	PUNCT
asir-56165	57	5	⊢sai-3→eaf-1→eaf-2→aef-2	⊢sai-3→eaf-1→eaf-2→aef-2	NOUN
asir-56165	57	6	(	(	PUNCT
asir-56165	57	7	11	11	NUM
asir-56165	57	8	)	)	PUNCT
asir-56165	57	9	⊢sai-3→eaf-1→eaf-2→aef-2→aef-4	⊢sai-3→eaf-1→eaf-2→aef-2→aef-4	PROPN
asir-56165	57	10	(	(	PUNCT
asir-56165	57	11	12	12	NUM
asir-56165	57	12	)	)	PUNCT
asir-56165	57	13	⊢sai-3→eso-2→aho-2	⊢sai-3→eso-2→aho-2	NOUN
asir-56165	57	14	(	(	PUNCT
asir-56165	57	15	13	13	NUM
asir-56165	57	16	)	)	PUNCT
asir-56165	57	17	⊢sai-3→eso-2→eso-1→asi-1	⊢sai-3→eso-2→eso-1→asi-1	X
asir-56165	57	18	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-56165	57	19	applied	apply	VERB
asir-56165	57	20	science	science	NOUN
asir-56165	57	21	and	and	CCONJ
asir-56165	57	22	innovative	innovative	ADJ
asir-56165	57	23	research	research	NOUN
asir-56165	57	24	vol	vol	NOUN
asir-56165	57	25	.	.	PUNCT
asir-56165	58	1	9	9	NUM
asir-56165	58	2	,	,	PUNCT
asir-56165	58	3	no	no	INTJ
asir-56165	58	4	.	.	NOUN
asir-56165	58	5	2	2	NUM
asir-56165	58	6	,	,	PUNCT
asir-56165	58	7	2025	2025	NUM
asir-56165	58	8	68	68	NUM
asir-56165	58	9	published	publish	VERB
asir-56165	58	10	by	by	ADP
asir-56165	58	11	scholink	scholink	PROPN
asir-56165	58	12	inc	inc	PROPN
asir-56165	58	13	.	.	PROPN
asir-56165	59	1	(	(	PUNCT
asir-56165	59	2	14	14	NUM
asir-56165	59	3	)	)	PUNCT
asir-56165	59	4	⊢sai-3→eso-2→eso-1→asi-1→sai-4	⊢sai-3→eso-2→eso-1→asi-1→sai-4	NOUN
asir-56165	59	5	proof	proof	NOUN
asir-56165	59	6	:	:	PUNCT
asir-56165	60	1	[	[	X
asir-56165	60	2	1	1	X
asir-56165	60	3	]	]	X
asir-56165	60	4	⊢at	⊢at	VERB
asir-56165	60	5	least	least	ADJ
asir-56165	60	6	half	half	NOUN
asir-56165	60	7	of	of	ADP
asir-56165	60	8	the(t	the(t	PROPN
asir-56165	60	9	,	,	PUNCT
asir-56165	60	10	n)all(t	n)all(t	NUM
asir-56165	60	11	,	,	PUNCT
asir-56165	60	12	p)→some(p	p)→some(p	NOUN
asir-56165	60	13	,	,	PUNCT
asir-56165	60	14	n	n	CCONJ
asir-56165	60	15	)	)	PUNCT
asir-56165	60	16	(	(	PUNCT
asir-56165	60	17	i.e.	i.e.	X
asir-56165	60	18	sai-3	sai-3	ADP
asir-56165	60	19	,	,	PUNCT
asir-56165	60	20	basic	basic	ADJ
asir-56165	60	21	axiom	axiom	NOUN
asir-56165	60	22	a2	a2	PROPN
asir-56165	60	23	)	)	PUNCT
asir-56165	61	1	[	[	X
asir-56165	61	2	2	2	X
asir-56165	61	3	]	]	X
asir-56165	61	4	⊢at	⊢at	X
asir-56165	61	5	least	least	ADJ
asir-56165	61	6	half	half	NOUN
asir-56165	61	7	of	of	ADP
asir-56165	61	8	the(t	the(t	PROPN
asir-56165	61	9	,	,	PUNCT
asir-56165	61	10	n)all(t	n)all(t	NUM
asir-56165	61	11	,	,	PUNCT
asir-56165	61	12	p)→some(n	p)→some(n	PROPN
asir-56165	61	13	,	,	PUNCT
asir-56165	61	14	p	p	NOUN
asir-56165	61	15	)	)	PUNCT
asir-56165	61	16	(	(	PUNCT
asir-56165	61	17	i.e.	i.e.	X
asir-56165	61	18	asi-3	asi-3	NUM
asir-56165	61	19	,	,	PUNCT
asir-56165	61	20	by	by	ADP
asir-56165	61	21	[	[	X
asir-56165	61	22	1	1	NUM
asir-56165	61	23	]	]	PUNCT
asir-56165	61	24	and	and	CCONJ
asir-56165	61	25	fact	fact	NOUN
asir-56165	61	26	(	(	PUNCT
asir-56165	61	27	3.1	3.1	NUM
asir-56165	61	28	)	)	PUNCT
asir-56165	61	29	)	)	PUNCT
asir-56165	62	1	[	[	X
asir-56165	62	2	3	3	X
asir-56165	62	3	]	]	X
asir-56165	62	4	⊢at	⊢at	VERB
asir-56165	62	5	most	most	ADJ
asir-56165	62	6	half	half	NOUN
asir-56165	62	7	of	of	ADP
asir-56165	62	8	the	the	DET
asir-56165	62	9	(	(	PUNCT
asir-56165	62	10	t	t	PROPN
asir-56165	62	11	,	,	PUNCT
asir-56165	62	12	n)all(t	n)all(t	NUM
asir-56165	62	13	,	,	PUNCT
asir-56165	62	14	p)→not	p)→not	PROPN
asir-56165	62	15	all(p	all(p	NOUN
asir-56165	62	16	,	,	PUNCT
asir-56165	62	17	n	n	CCONJ
asir-56165	62	18	)	)	PUNCT
asir-56165	62	19	(	(	PUNCT
asir-56165	62	20	by	by	ADP
asir-56165	62	21	[	[	X
asir-56165	62	22	1	1	NUM
asir-56165	62	23	]	]	PUNCT
asir-56165	62	24	,	,	PUNCT
asir-56165	62	25	fact	fact	NOUN
asir-56165	62	26	(	(	PUNCT
asir-56165	62	27	1.7	1.7	NUM
asir-56165	62	28	)	)	PUNCT
asir-56165	62	29	and	and	CCONJ
asir-56165	62	30	(	(	PUNCT
asir-56165	62	31	1.3	1.3	NUM
asir-56165	62	32	)	)	PUNCT
asir-56165	62	33	)	)	PUNCT
asir-56165	63	1	[	[	X
asir-56165	63	2	4	4	X
asir-56165	63	3	]	]	X
asir-56165	63	4	⊢at	⊢at	VERB
asir-56165	63	5	most	most	ADJ
asir-56165	63	6	half	half	NOUN
asir-56165	63	7	of	of	ADP
asir-56165	63	8	the(t	the(t	PROPN
asir-56165	63	9	,	,	PUNCT
asir-56165	63	10	d−n)all(t	d−n)all(t	NOUN
asir-56165	63	11	,	,	PUNCT
asir-56165	63	12	p)→not	p)→not	PROPN
asir-56165	63	13	all(p	all(p	NOUN
asir-56165	63	14	,	,	PUNCT
asir-56165	63	15	d−n	d−n	NOUN
asir-56165	63	16	)	)	PUNCT
asir-56165	63	17	(	(	PUNCT
asir-56165	63	18	i.e.	i.e.	X
asir-56165	63	19	hao-3	hao-3	NUM
asir-56165	63	20	,	,	PUNCT
asir-56165	63	21	by	by	ADP
asir-56165	63	22	[	[	X
asir-56165	63	23	1	1	NUM
asir-56165	63	24	]	]	PUNCT
asir-56165	63	25	and	and	CCONJ
asir-56165	63	26	definition	definition	NOUN
asir-56165	63	27	d3	d3	PROPN
asir-56165	63	28	)	)	PUNCT
asir-56165	64	1	[	[	X
asir-56165	64	2	5	5	NUM
asir-56165	64	3	]	]	X
asir-56165	64	4	⊢some(p	⊢some(p	NOUN
asir-56165	64	5	,	,	PUNCT
asir-56165	64	6	n)all(t	n)all(t	NUM
asir-56165	64	7	,	,	PUNCT
asir-56165	64	8	p)→at	p)→at	NOUN
asir-56165	64	9	least	least	ADJ
asir-56165	64	10	half	half	NOUN
asir-56165	64	11	of	of	ADP
asir-56165	64	12	the(t	the(t	PROPN
asir-56165	64	13	,	,	PUNCT
asir-56165	64	14	n	n	CCONJ
asir-56165	64	15	)	)	PUNCT
asir-56165	64	16	(	(	PUNCT
asir-56165	64	17	by	by	ADP
asir-56165	64	18	[	[	X
asir-56165	64	19	1	1	NUM
asir-56165	64	20	]	]	PUNCT
asir-56165	64	21	and	and	CCONJ
asir-56165	64	22	rule	rule	VERB
asir-56165	64	23	3	3	NUM
asir-56165	64	24	)	)	PUNCT
asir-56165	65	1	[	[	X
asir-56165	65	2	6	6	NUM
asir-56165	65	3	]	]	PUNCT
asir-56165	65	4	⊢no(p	⊢no(p	NOUN
asir-56165	65	5	,	,	PUNCT
asir-56165	65	6	n)all(t	n)all(t	NUM
asir-56165	65	7	,	,	PUNCT
asir-56165	65	8	p)→fewer	p)→few	ADJ
asir-56165	65	9	than	than	ADP
asir-56165	65	10	half	half	NOUN
asir-56165	65	11	of	of	ADP
asir-56165	65	12	the(t	the(t	PROPN
asir-56165	65	13	,	,	PUNCT
asir-56165	65	14	n	n	CCONJ
asir-56165	65	15	)	)	PUNCT
asir-56165	65	16	(	(	PUNCT
asir-56165	65	17	i.e.	i.e.	X
asir-56165	65	18	eaf-1	eaf-1	NUM
asir-56165	65	19	,	,	PUNCT
asir-56165	65	20	by	by	ADP
asir-56165	65	21	[	[	X
asir-56165	65	22	5	5	NUM
asir-56165	65	23	]	]	PUNCT
asir-56165	65	24	,	,	PUNCT
asir-56165	65	25	fact	fact	NOUN
asir-56165	65	26	(	(	PUNCT
asir-56165	65	27	2.4	2.4	NUM
asir-56165	65	28	)	)	PUNCT
asir-56165	65	29	and	and	CCONJ
asir-56165	65	30	(	(	PUNCT
asir-56165	65	31	2.8	2.8	NUM
asir-56165	65	32	)	)	PUNCT
asir-56165	65	33	)	)	PUNCT
asir-56165	66	1	[	[	X
asir-56165	66	2	7	7	NUM
asir-56165	66	3	]	]	X
asir-56165	66	4	⊢no(n	⊢no(n	NOUN
asir-56165	66	5	,	,	PUNCT
asir-56165	66	6	p)all(t	p)all(t	PROPN
asir-56165	66	7	,	,	PUNCT
asir-56165	66	8	p)→fewer	p)→few	ADJ
asir-56165	66	9	than	than	ADP
asir-56165	66	10	half	half	NOUN
asir-56165	66	11	of	of	ADP
asir-56165	66	12	the(t	the(t	PROPN
asir-56165	66	13	,	,	PUNCT
asir-56165	66	14	n	n	CCONJ
asir-56165	66	15	)	)	PUNCT
asir-56165	66	16	(	(	PUNCT
asir-56165	66	17	i.e.	i.e.	X
asir-56165	66	18	eaf-2	eaf-2	NUM
asir-56165	66	19	,	,	PUNCT
asir-56165	66	20	by	by	ADP
asir-56165	66	21	[	[	X
asir-56165	66	22	6	6	NUM
asir-56165	66	23	]	]	PUNCT
asir-56165	66	24	and	and	CCONJ
asir-56165	66	25	fact	fact	NOUN
asir-56165	66	26	(	(	PUNCT
asir-56165	66	27	3.2	3.2	NUM
asir-56165	66	28	)	)	PUNCT
asir-56165	66	29	)	)	PUNCT
asir-56165	67	1	[	[	X
asir-56165	67	2	8	8	NUM
asir-56165	67	3	]	]	X
asir-56165	67	4	⊢some(p	⊢some(p	NOUN
asir-56165	67	5	,	,	PUNCT
asir-56165	67	6	n)at	n)at	PRON
asir-56165	67	7	least	least	ADJ
asir-56165	67	8	half	half	NOUN
asir-56165	67	9	of	of	ADP
asir-56165	67	10	the(t	the(t	PROPN
asir-56165	67	11	,	,	PUNCT
asir-56165	67	12	n)→all(t	n)→all(t	PROPN
asir-56165	67	13	,	,	PUNCT
asir-56165	67	14	p	p	NOUN
asir-56165	67	15	)	)	PUNCT
asir-56165	67	16	(	(	PUNCT
asir-56165	67	17	by	by	ADP
asir-56165	67	18	[	[	X
asir-56165	67	19	1	1	NUM
asir-56165	67	20	]	]	PUNCT
asir-56165	67	21	and	and	CCONJ
asir-56165	67	22	rule	rule	VERB
asir-56165	67	23	3	3	NUM
asir-56165	67	24	)	)	PUNCT
asir-56165	68	1	[	[	X
asir-56165	68	2	9	9	NUM
asir-56165	68	3	]	]	SYM
asir-56165	68	4	⊢no(p	⊢no(p	NOUN
asir-56165	68	5	,	,	PUNCT
asir-56165	68	6	n)at	n)at	PRON
asir-56165	68	7	least	least	ADJ
asir-56165	68	8	half	half	NOUN
asir-56165	68	9	of	of	ADP
asir-56165	68	10	the(t	the(t	PROPN
asir-56165	68	11	,	,	PUNCT
asir-56165	68	12	n)→not	n)→not	PROPN
asir-56165	68	13	all(t	all(t	PROPN
asir-56165	68	14	,	,	PUNCT
asir-56165	68	15	p	p	NOUN
asir-56165	68	16	)	)	PUNCT
asir-56165	68	17	(	(	PUNCT
asir-56165	68	18	i.e.	i.e.	X
asir-56165	68	19	eso-2	eso-2	NUM
asir-56165	68	20	,	,	PUNCT
asir-56165	68	21	by	by	ADP
asir-56165	68	22	[	[	X
asir-56165	68	23	8	8	NUM
asir-56165	68	24	]	]	PUNCT
asir-56165	68	25	,	,	PUNCT
asir-56165	68	26	fact	fact	NOUN
asir-56165	68	27	(	(	PUNCT
asir-56165	68	28	2.4	2.4	NUM
asir-56165	68	29	)	)	PUNCT
asir-56165	68	30	and	and	CCONJ
asir-56165	68	31	(	(	PUNCT
asir-56165	68	32	2.1	2.1	NUM
asir-56165	68	33	)	)	PUNCT
asir-56165	68	34	)	)	PUNCT
asir-56165	69	1	[	[	X
asir-56165	69	2	10	10	NUM
asir-56165	69	3	]	]	X
asir-56165	69	4	⊢no(n	⊢no(n	NOUN
asir-56165	69	5	,	,	PUNCT
asir-56165	69	6	p)at	p)at	ADV
asir-56165	69	7	least	least	ADJ
asir-56165	69	8	half	half	NOUN
asir-56165	69	9	of	of	ADP
asir-56165	69	10	the(t	the(t	PROPN
asir-56165	69	11	,	,	PUNCT
asir-56165	69	12	n)→not	n)→not	PROPN
asir-56165	69	13	all(t	all(t	PROPN
asir-56165	69	14	,	,	PUNCT
asir-56165	69	15	p	p	NOUN
asir-56165	69	16	)	)	PUNCT
asir-56165	69	17	(	(	PUNCT
asir-56165	69	18	i.e.	i.e.	X
asir-56165	69	19	eso-1	eso-1	NUM
asir-56165	69	20	,	,	PUNCT
asir-56165	69	21	by	by	ADP
asir-56165	69	22	[	[	X
asir-56165	69	23	9	9	NUM
asir-56165	69	24	]	]	PUNCT
asir-56165	69	25	and	and	CCONJ
asir-56165	69	26	fact	fact	NOUN
asir-56165	69	27	(	(	PUNCT
asir-56165	69	28	3.2	3.2	NUM
asir-56165	69	29	)	)	PUNCT
asir-56165	69	30	)	)	PUNCT
asir-56165	70	1	[	[	X
asir-56165	70	2	11	11	NUM
asir-56165	70	3	]	]	X
asir-56165	70	4	⊢at	⊢at	VERB
asir-56165	70	5	least	least	ADJ
asir-56165	70	6	half	half	NOUN
asir-56165	70	7	of	of	ADP
asir-56165	70	8	the(t	the(t	PROPN
asir-56165	70	9	,	,	PUNCT
asir-56165	70	10	n)no(t	n)no(t	NOUN
asir-56165	70	11	,	,	PUNCT
asir-56165	70	12	p)→not	p)→not	PROPN
asir-56165	70	13	all(n	all(n	NOUN
asir-56165	70	14	,	,	PUNCT
asir-56165	70	15	p	p	NOUN
asir-56165	70	16	)	)	PUNCT
asir-56165	70	17	(	(	PUNCT
asir-56165	70	18	by	by	ADP
asir-56165	70	19	[	[	X
asir-56165	70	20	2	2	NUM
asir-56165	70	21	]	]	PUNCT
asir-56165	70	22	,	,	PUNCT
asir-56165	70	23	fact	fact	NOUN
asir-56165	70	24	(	(	PUNCT
asir-56165	70	25	1.1	1.1	NUM
asir-56165	70	26	)	)	PUNCT
asir-56165	70	27	and	and	CCONJ
asir-56165	70	28	(	(	PUNCT
asir-56165	70	29	1.3	1.3	NUM
asir-56165	70	30	)	)	PUNCT
asir-56165	70	31	)	)	PUNCT
asir-56165	71	1	[	[	X
asir-56165	71	2	12	12	NUM
asir-56165	71	3	]	]	X
asir-56165	71	4	⊢at	⊢at	X
asir-56165	71	5	least	least	ADJ
asir-56165	71	6	half	half	NOUN
asir-56165	71	7	of	of	ADP
asir-56165	71	8	the(t	the(t	PRON
asir-56165	71	9	,	,	PUNCT
asir-56165	71	10	n)no(t	n)no(t	PRON
asir-56165	71	11	,	,	PUNCT
asir-56165	71	12	d−p)→not	d−p)→not	PROPN
asir-56165	71	13	all(n	all(n	PROPN
asir-56165	71	14	,	,	PUNCT
asir-56165	71	15	d−p	d−p	NUM
asir-56165	71	16	)	)	PUNCT
asir-56165	71	17	(	(	PUNCT
asir-56165	71	18	i.e.	i.e.	X
asir-56165	71	19	eso-3	eso-3	ADV
asir-56165	71	20	,	,	PUNCT
asir-56165	71	21	by	by	ADP
asir-56165	71	22	[	[	PUNCT
asir-56165	71	23	11	11	NUM
asir-56165	71	24	]	]	PUNCT
asir-56165	71	25	and	and	CCONJ
asir-56165	71	26	definition	definition	NOUN
asir-56165	71	27	d3	d3	PROPN
asir-56165	71	28	)	)	PUNCT
asir-56165	72	1	[	[	X
asir-56165	72	2	13	13	NUM
asir-56165	72	3	]	]	SYM
asir-56165	72	4	⊢at	⊢at	VERB
asir-56165	72	5	least	least	ADJ
asir-56165	72	6	half	half	NOUN
asir-56165	72	7	of	of	ADP
asir-56165	72	8	the(t	the(t	PROPN
asir-56165	72	9	,	,	PUNCT
asir-56165	72	10	n)no(d−p	n)no(d−p	PROPN
asir-56165	72	11	,	,	PUNCT
asir-56165	72	12	t)→not	t)→not	ADV
asir-56165	72	13	all(n	all(n	PROPN
asir-56165	72	14	,	,	PUNCT
asir-56165	72	15	d−p	d−p	NUM
asir-56165	72	16	)	)	PUNCT
asir-56165	72	17	(	(	PUNCT
asir-56165	72	18	i.e.	i.e.	X
asir-56165	72	19	eso-4	eso-4	X
asir-56165	72	20	,	,	PUNCT
asir-56165	72	21	by	by	ADP
asir-56165	72	22	[	[	X
asir-56165	72	23	12	12	NUM
asir-56165	72	24	]	]	PUNCT
asir-56165	72	25	and	and	CCONJ
asir-56165	72	26	fact	fact	NOUN
asir-56165	72	27	(	(	PUNCT
asir-56165	72	28	3.2	3.2	NUM
asir-56165	72	29	)	)	PUNCT
asir-56165	72	30	)	)	PUNCT
asir-56165	73	1	[	[	X
asir-56165	73	2	14	14	NUM
asir-56165	73	3	]	]	X
asir-56165	73	4	⊢all(p	⊢all(p	PROPN
asir-56165	73	5	,	,	PUNCT
asir-56165	73	6	n)all(t	n)all(t	NUM
asir-56165	73	7	,	,	PUNCT
asir-56165	73	8	p)→most(t	p)→most(t	NOUN
asir-56165	73	9	,	,	PUNCT
asir-56165	73	10	n	n	CCONJ
asir-56165	73	11	)	)	PUNCT
asir-56165	73	12	(	(	PUNCT
asir-56165	73	13	by	by	ADP
asir-56165	73	14	[	[	X
asir-56165	73	15	6	6	NUM
asir-56165	73	16	]	]	PUNCT
asir-56165	73	17	,	,	PUNCT
asir-56165	73	18	fact	fact	NOUN
asir-56165	73	19	(	(	PUNCT
asir-56165	73	20	1.2	1.2	NUM
asir-56165	73	21	)	)	PUNCT
asir-56165	73	22	and	and	CCONJ
asir-56165	73	23	(	(	PUNCT
asir-56165	73	24	1.6	1.6	NUM
asir-56165	73	25	)	)	PUNCT
asir-56165	73	26	)	)	PUNCT
asir-56165	74	1	[	[	X
asir-56165	74	2	15	15	NUM
asir-56165	74	3	]	]	X
asir-56165	74	4	⊢all(p	⊢all(p	PROPN
asir-56165	74	5	,	,	PUNCT
asir-56165	74	6	d−n)all(t	d−n)all(t	NOUN
asir-56165	74	7	,	,	PUNCT
asir-56165	74	8	p)→most(t	p)→most(t	NOUN
asir-56165	74	9	,	,	PUNCT
asir-56165	74	10	d−n	d−n	NOUN
asir-56165	74	11	)	)	PUNCT
asir-56165	74	12	(	(	PUNCT
asir-56165	74	13	i.e.	i.e.	X
asir-56165	74	14	aam-1	aam-1	NUM
asir-56165	74	15	,	,	PUNCT
asir-56165	74	16	by	by	ADP
asir-56165	74	17	[	[	X
asir-56165	74	18	14	14	NUM
asir-56165	74	19	]	]	PUNCT
asir-56165	74	20	and	and	CCONJ
asir-56165	74	21	definition	definition	NOUN
asir-56165	74	22	d3	d3	PROPN
asir-56165	74	23	)	)	PUNCT
asir-56165	75	1	[	[	X
asir-56165	75	2	16	16	NUM
asir-56165	75	3	]	]	X
asir-56165	75	4	⊢all(n	⊢all(n	PROPN
asir-56165	75	5	,	,	PUNCT
asir-56165	75	6	p)no(t	p)no(t	NOUN
asir-56165	75	7	,	,	PUNCT
asir-56165	75	8	p)→fewer	p)→few	ADJ
asir-56165	75	9	than	than	ADP
asir-56165	75	10	half	half	NOUN
asir-56165	75	11	of	of	ADP
asir-56165	75	12	the(t	the(t	PROPN
asir-56165	75	13	,	,	PUNCT
asir-56165	75	14	n	n	CCONJ
asir-56165	75	15	)	)	PUNCT
asir-56165	75	16	(	(	PUNCT
asir-56165	75	17	by	by	ADP
asir-56165	75	18	[	[	X
asir-56165	75	19	7	7	NUM
asir-56165	75	20	]	]	PUNCT
asir-56165	75	21	,	,	PUNCT
asir-56165	75	22	fact	fact	NOUN
asir-56165	75	23	(	(	PUNCT
asir-56165	75	24	1.1	1.1	NUM
asir-56165	75	25	)	)	PUNCT
asir-56165	75	26	and	and	CCONJ
asir-56165	75	27	(	(	PUNCT
asir-56165	75	28	1.2	1.2	NUM
asir-56165	75	29	)	)	PUNCT
asir-56165	75	30	)	)	PUNCT
asir-56165	76	1	[	[	X
asir-56165	76	2	17	17	NUM
asir-56165	76	3	]	]	X
asir-56165	76	4	⊢all(n	⊢all(n	NOUN
asir-56165	76	5	,	,	PUNCT
asir-56165	76	6	d−p)no(t	d−p)no(t	NOUN
asir-56165	76	7	,	,	PUNCT
asir-56165	76	8	d−p)→fewer	d−p)→fewer	NOUN
asir-56165	76	9	than	than	ADP
asir-56165	76	10	half	half	NOUN
asir-56165	76	11	of	of	ADP
asir-56165	76	12	the(t	the(t	PROPN
asir-56165	76	13	,	,	PUNCT
asir-56165	76	14	n	n	CCONJ
asir-56165	76	15	)	)	PUNCT
asir-56165	76	16	(	(	PUNCT
asir-56165	76	17	i.e.	i.e.	X
asir-56165	76	18	aef-2	aef-2	NUM
asir-56165	76	19	,	,	PUNCT
asir-56165	76	20	by	by	ADP
asir-56165	76	21	[	[	X
asir-56165	76	22	16	16	NUM
asir-56165	76	23	]	]	PUNCT
asir-56165	76	24	and	and	CCONJ
asir-56165	76	25	definition	definition	NOUN
asir-56165	76	26	d3	d3	PROPN
asir-56165	76	27	)	)	PUNCT
asir-56165	77	1	[	[	X
asir-56165	77	2	18	18	NUM
asir-56165	77	3	]	]	X
asir-56165	77	4	⊢all(n	⊢all(n	PROPN
asir-56165	77	5	,	,	PUNCT
asir-56165	77	6	d−p)no(d−p	d−p)no(d−p	PROPN
asir-56165	77	7	,	,	PUNCT
asir-56165	77	8	t)→fewer	t)→fewer	NUM
asir-56165	77	9	than	than	ADP
asir-56165	77	10	half	half	NOUN
asir-56165	77	11	of	of	ADP
asir-56165	77	12	the(t	the(t	PROPN
asir-56165	77	13	,	,	PUNCT
asir-56165	77	14	n	n	CCONJ
asir-56165	77	15	)	)	PUNCT
asir-56165	77	16	(	(	PUNCT
asir-56165	77	17	i.e.	i.e.	X
asir-56165	77	18	aef-4	aef-4	NUM
asir-56165	77	19	,	,	PUNCT
asir-56165	77	20	by	by	ADP
asir-56165	77	21	[	[	X
asir-56165	77	22	17	17	NUM
asir-56165	77	23	]	]	PUNCT
asir-56165	77	24	and	and	CCONJ
asir-56165	77	25	fact	fact	NOUN
asir-56165	77	26	(	(	PUNCT
asir-56165	77	27	3.2	3.2	NUM
asir-56165	77	28	)	)	PUNCT
asir-56165	77	29	)	)	PUNCT
asir-56165	78	1	[	[	X
asir-56165	78	2	19	19	NUM
asir-56165	78	3	]	]	X
asir-56165	78	4	⊢all(p	⊢all(p	PROPN
asir-56165	78	5	,	,	PUNCT
asir-56165	78	6	n)at	n)at	PRON
asir-56165	78	7	most	most	ADV
asir-56165	78	8	half	half	NOUN
asir-56165	78	9	of	of	ADP
asir-56165	78	10	the(t	the(t	NOUN
asir-56165	78	11	,	,	PUNCT
asir-56165	78	12	n)→not	n)→not	PROPN
asir-56165	78	13	all(t	all(t	PROPN
asir-56165	78	14	,	,	PUNCT
asir-56165	78	15	p	p	NOUN
asir-56165	78	16	)	)	PUNCT
asir-56165	78	17	(	(	PUNCT
asir-56165	78	18	by	by	ADP
asir-56165	78	19	[	[	PUNCT
asir-56165	78	20	9	9	NUM
asir-56165	78	21	]	]	PUNCT
asir-56165	78	22	,	,	PUNCT
asir-56165	78	23	fact	fact	NOUN
asir-56165	78	24	(	(	PUNCT
asir-56165	78	25	1.2	1.2	NUM
asir-56165	78	26	)	)	PUNCT
asir-56165	78	27	and	and	CCONJ
asir-56165	78	28	(	(	PUNCT
asir-56165	78	29	1.7	1.7	NUM
asir-56165	78	30	)	)	PUNCT
asir-56165	78	31	)	)	PUNCT
asir-56165	79	1	[	[	X
asir-56165	79	2	20	20	NUM
asir-56165	79	3	]	]	X
asir-56165	79	4	⊢all(p	⊢all(p	PROPN
asir-56165	79	5	,	,	PUNCT
asir-56165	79	6	d−n)at	d−n)at	PROPN
asir-56165	79	7	most	most	ADV
asir-56165	79	8	half	half	NOUN
asir-56165	79	9	of	of	ADP
asir-56165	79	10	the(t	the(t	PROPN
asir-56165	79	11	,	,	PUNCT
asir-56165	79	12	d−n)→not	d−n)→not	PROPN
asir-56165	79	13	all(t	all(t	PROPN
asir-56165	79	14	,	,	PUNCT
asir-56165	79	15	p	p	NOUN
asir-56165	79	16	)	)	PUNCT
asir-56165	79	17	(	(	PUNCT
asir-56165	79	18	i.e.	i.e.	X
asir-56165	79	19	aho-2	aho-2	NOUN
asir-56165	79	20	,	,	PUNCT
asir-56165	79	21	by	by	ADP
asir-56165	79	22	[	[	X
asir-56165	79	23	19	19	NUM
asir-56165	79	24	]	]	PUNCT
asir-56165	79	25	and	and	CCONJ
asir-56165	79	26	definition	definition	NOUN
asir-56165	79	27	d3	d3	PROPN
asir-56165	79	28	)	)	PUNCT
asir-56165	80	1	[	[	X
asir-56165	80	2	21	21	NUM
asir-56165	80	3	]	]	X
asir-56165	80	4	⊢all(n	⊢all(n	PROPN
asir-56165	80	5	,	,	PUNCT
asir-56165	80	6	p)at	p)at	ADV
asir-56165	80	7	least	least	ADJ
asir-56165	80	8	half	half	NOUN
asir-56165	80	9	of	of	ADP
asir-56165	80	10	the(t	the(t	PROPN
asir-56165	80	11	,	,	PUNCT
asir-56165	80	12	n)→some(t	n)→some(t	PROPN
asir-56165	80	13	,	,	PUNCT
asir-56165	80	14	p	p	NOUN
asir-56165	80	15	)	)	PUNCT
asir-56165	80	16	(	(	PUNCT
asir-56165	80	17	by	by	ADP
asir-56165	80	18	[	[	X
asir-56165	80	19	10	10	NUM
asir-56165	80	20	]	]	PUNCT
asir-56165	80	21	,	,	PUNCT
asir-56165	80	22	fact	fact	NOUN
asir-56165	80	23	(	(	PUNCT
asir-56165	80	24	1.2	1.2	NUM
asir-56165	80	25	)	)	PUNCT
asir-56165	80	26	and	and	CCONJ
asir-56165	80	27	(	(	PUNCT
asir-56165	80	28	1.4	1.4	NUM
asir-56165	80	29	)	)	PUNCT
asir-56165	80	30	)	)	PUNCT
asir-56165	81	1	[	[	X
asir-56165	81	2	22	22	NUM
asir-56165	81	3	]	]	X
asir-56165	81	4	⊢all(n	⊢all(n	NOUN
asir-56165	81	5	,	,	PUNCT
asir-56165	81	6	d−p)at	d−p)at	PROPN
asir-56165	81	7	least	least	ADJ
asir-56165	81	8	half	half	NOUN
asir-56165	81	9	of	of	ADP
asir-56165	81	10	the(t	the(t	NOUN
asir-56165	81	11	,	,	PUNCT
asir-56165	81	12	n)→some(t	n)→some(t	ADJ
asir-56165	81	13	,	,	PUNCT
asir-56165	81	14	d−p	d−p	NUM
asir-56165	81	15	)	)	PUNCT
asir-56165	81	16	(	(	PUNCT
asir-56165	81	17	i.e.	i.e.	X
asir-56165	81	18	asi-1	asi-1	NUM
asir-56165	81	19	,	,	PUNCT
asir-56165	81	20	by	by	ADP
asir-56165	81	21	[	[	X
asir-56165	81	22	21	21	NUM
asir-56165	81	23	]	]	PUNCT
asir-56165	81	24	and	and	CCONJ
asir-56165	81	25	definition	definition	NOUN
asir-56165	81	26	d3	d3	PROPN
asir-56165	81	27	)	)	PUNCT
asir-56165	82	1	[	[	X
asir-56165	82	2	23	23	NUM
asir-56165	82	3	]	]	X
asir-56165	82	4	⊢all(n	⊢all(n	NOUN
asir-56165	82	5	,	,	PUNCT
asir-56165	82	6	d−p)at	d−p)at	PROPN
asir-56165	82	7	least	least	ADJ
asir-56165	82	8	half	half	NOUN
asir-56165	82	9	of	of	ADP
asir-56165	82	10	the(t	the(t	PRON
asir-56165	82	11	,	,	PUNCT
asir-56165	82	12	n)→some(d−p	n)→some(d−p	PROPN
asir-56165	82	13	,	,	PUNCT
asir-56165	82	14	t	t	PROPN
asir-56165	82	15	)	)	PUNCT
asir-56165	82	16	(	(	PUNCT
asir-56165	82	17	i.e.	i.e.	X
asir-56165	82	18	sai-4	sai-4	ADV
asir-56165	82	19	,	,	PUNCT
asir-56165	82	20	by	by	ADP
asir-56165	82	21	[	[	X
asir-56165	82	22	22	22	NUM
asir-56165	82	23	]	]	PUNCT
asir-56165	82	24	and	and	CCONJ
asir-56165	82	25	fact	fact	NOUN
asir-56165	82	26	(	(	PUNCT
asir-56165	82	27	3.1	3.1	NUM
asir-56165	82	28	)	)	PUNCT
asir-56165	82	29	)	)	PUNCT
asir-56165	83	1	the	the	DET
asir-56165	83	2	above	above	ADJ
asir-56165	83	3	proof	proof	NOUN
asir-56165	83	4	processes	process	NOUN
asir-56165	83	5	are	be	AUX
asir-56165	83	6	logical	logical	ADJ
asir-56165	83	7	deduction	deduction	NOUN
asir-56165	83	8	ones	one	NOUN
asir-56165	83	9	.	.	PUNCT
asir-56165	84	1	therefore	therefore	ADV
asir-56165	84	2	,	,	PUNCT
asir-56165	84	3	the	the	DET
asir-56165	84	4	above	above	ADJ
asir-56165	84	5	knowledge	knowledge	NOUN
asir-56165	84	6	mining	mining	NOUN
asir-56165	84	7	processes	process	NOUN
asir-56165	84	8	are	be	AUX
asir-56165	84	9	consistent	consistent	ADJ
asir-56165	84	10	.	.	PUNCT
asir-56165	85	1	theorem	theorem	ADJ
asir-56165	85	2	2	2	NUM
asir-56165	85	3	demonstrates	demonstrate	VERB
asir-56165	85	4	that	that	SCONJ
asir-56165	85	5	the	the	DET
asir-56165	85	6	validity	validity	NOUN
asir-56165	85	7	of	of	ADP
asir-56165	85	8	the	the	DET
asir-56165	85	9	above	above	ADJ
asir-56165	85	10	14	14	NUM
asir-56165	85	11	non	non	ADJ
asir-56165	85	12	-	-	ADJ
asir-56165	85	13	trivial	trivial	ADJ
asir-56165	85	14	generalized	generalized	ADJ
asir-56165	85	15	syllogisms	syllogism	NOUN
asir-56165	85	16	can	can	AUX
asir-56165	85	17	be	be	AUX
asir-56165	85	18	derived	derive	VERB
asir-56165	85	19	from	from	ADP
asir-56165	85	20	the	the	DET
asir-56165	85	21	validity	validity	NOUN
asir-56165	85	22	of	of	ADP
asir-56165	85	23	the	the	DET
asir-56165	85	24	syllogism	syllogism	NOUN
asir-56165	85	25	sai-3	sai-3	NOUN
asir-56165	85	26	.	.	PUNCT
asir-56165	86	1	in	in	ADP
asir-56165	86	2	other	other	ADJ
asir-56165	86	3	words	word	NOUN
asir-56165	86	4	,	,	PUNCT
asir-56165	86	5	there	there	PRON
asir-56165	86	6	are	be	VERB
asir-56165	86	7	reducible	reducible	ADJ
asir-56165	86	8	relationships	relationship	NOUN
asir-56165	86	9	between	between	ADP
asir-56165	86	10	these	these	DET
asir-56165	86	11	15	15	NUM
asir-56165	86	12	syllogisms	syllogism	NOUN
asir-56165	86	13	with	with	ADP
asir-56165	86	14	the	the	DET
asir-56165	86	15	quantifiers	quantifier	NOUN
asir-56165	86	16	in	in	ADP
asir-56165	86	17	square{at	square{at	ADV
asir-56165	86	18	least	least	ADJ
asir-56165	86	19	half	half	NOUN
asir-56165	86	20	of	of	ADP
asir-56165	86	21	the	the	PRON
asir-56165	86	22	}	}	PUNCT
asir-56165	86	23	.	.	PUNCT
asir-56165	87	1	5	5	X
asir-56165	87	2	.	.	X
asir-56165	87	3	conclusion	conclusion	VERB
asir-56165	87	4	the	the	DET
asir-56165	87	5	main	main	ADJ
asir-56165	87	6	conclusions	conclusion	NOUN
asir-56165	87	7	of	of	ADP
asir-56165	87	8	this	this	DET
asir-56165	87	9	paper	paper	NOUN
asir-56165	87	10	are	be	AUX
asir-56165	87	11	as	as	SCONJ
asir-56165	87	12	follows	follow	NOUN
asir-56165	87	13	:	:	PUNCT
asir-56165	87	14	theorem	theorem	ADJ
asir-56165	87	15	1	1	NUM
asir-56165	87	16	proves	prove	VERB
asir-56165	87	17	the	the	DET
asir-56165	87	18	validity	validity	NOUN
asir-56165	87	19	of	of	ADP
asir-56165	87	20	the	the	DET
asir-56165	87	21	generalized	generalized	ADJ
asir-56165	87	22	syllogism	syllogism	NOUN
asir-56165	87	23	sai-3	sai-3	NOUN
asir-56165	87	24	.	.	PUNCT
asir-56165	88	1	theorem	theorem	NOUN
asir-56165	88	2	2	2	NUM
asir-56165	88	3	takes	take	VERB
asir-56165	88	4	the	the	DET
asir-56165	88	5	syllogism	syllogism	NOUN
asir-56165	88	6	sai-3	sai-3	PUNCT
asir-56165	88	7	as	as	ADP
asir-56165	88	8	the	the	DET
asir-56165	88	9	fundamental	fundamental	ADJ
asir-56165	88	10	axiom	axiom	NOUN
asir-56165	88	11	,	,	PUNCT
asir-56165	88	12	and	and	CCONJ
asir-56165	88	13	then	then	ADV
asir-56165	88	14	deduces	deduce	VERB
asir-56165	88	15	the	the	DET
asir-56165	88	16	other	other	ADJ
asir-56165	88	17	14	14	NUM
asir-56165	88	18	non	non	ADJ
asir-56165	88	19	-	-	ADJ
asir-56165	88	20	trivial	trivial	ADJ
asir-56165	88	21	valid	valid	ADJ
asir-56165	88	22	generalized	generalize	VERB
asir-56165	88	23	syllogisms	syllogism	NOUN
asir-56165	88	24	with	with	ADP
asir-56165	88	25	the	the	DET
asir-56165	88	26	quantifiers	quantifier	NOUN
asir-56165	88	27	in	in	ADP
asir-56165	88	28	square{at	square{at	ADV
asir-56165	88	29	least	least	ADJ
asir-56165	88	30	half	half	NOUN
asir-56165	88	31	of	of	ADP
asir-56165	88	32	the	the	PRON
asir-56165	88	33	}	}	PUNCT
asir-56165	88	34	.	.	PUNCT
asir-56165	89	1	it	it	PRON
asir-56165	89	2	means	mean	VERB
asir-56165	89	3	that	that	SCONJ
asir-56165	89	4	there	there	PRON
asir-56165	89	5	are	be	VERB
asir-56165	89	6	reducible	reducible	ADJ
asir-56165	89	7	relationships	relationship	NOUN
asir-56165	89	8	between	between	ADP
asir-56165	89	9	these	these	DET
asir-56165	89	10	15	15	NUM
asir-56165	89	11	syllogisms	syllogism	NOUN
asir-56165	89	12	,	,	PUNCT
asir-56165	89	13	and	and	CCONJ
asir-56165	89	14	that	that	SCONJ
asir-56165	89	15	the	the	DET
asir-56165	89	16	above	above	ADJ
asir-56165	89	17	knowledge	knowledge	NOUN
asir-56165	89	18	mining	mining	NOUN
asir-56165	89	19	processes	process	NOUN
asir-56165	89	20	are	be	AUX
asir-56165	89	21	consistent	consistent	ADJ
asir-56165	89	22	.	.	PUNCT
asir-56165	90	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-56165	90	2	applied	apply	VERB
asir-56165	90	3	science	science	NOUN
asir-56165	90	4	and	and	CCONJ
asir-56165	90	5	innovative	innovative	ADJ
asir-56165	90	6	research	research	NOUN
asir-56165	90	7	vol	vol	NOUN
asir-56165	90	8	.	.	PUNCT
asir-56165	91	1	9	9	NUM
asir-56165	91	2	,	,	PUNCT
asir-56165	91	3	no	no	INTJ
asir-56165	91	4	.	.	NOUN
asir-56165	91	5	2	2	NUM
asir-56165	91	6	,	,	PUNCT
asir-56165	91	7	2025	2025	NUM
asir-56165	91	8	69	69	NUM
asir-56165	91	9	published	publish	VERB
asir-56165	91	10	by	by	ADP
asir-56165	91	11	scholink	scholink	PROPN
asir-56165	91	12	inc	inc	PROPN
asir-56165	91	13	.	.	PROPN
asir-56165	91	14	acknowledgement	acknowledgement	NOUN
asir-56165	91	15	this	this	DET
asir-56165	91	16	work	work	NOUN
asir-56165	91	17	was	be	AUX
asir-56165	91	18	supported	support	VERB
asir-56165	91	19	by	by	ADP
asir-56165	91	20	the	the	DET
asir-56165	91	21	national	national	ADJ
asir-56165	91	22	social	social	PROPN
asir-56165	91	23	science	science	PROPN
asir-56165	91	24	fund	fund	NOUN
asir-56165	91	25	of	of	ADP
asir-56165	91	26	china	china	PROPN
asir-56165	91	27	under	under	ADP
asir-56165	91	28	grant	grant	PROPN
asir-56165	91	29	no	no	NOUN
asir-56165	91	30	.	.	PUNCT
asir-56165	92	1	22fzxb092	22fzxb092	X
asir-56165	92	2	.	.	PUNCT
asir-56165	93	1	references	reference	NOUN
asir-56165	93	2	cao	cao	PROPN
asir-56165	93	3	,	,	PUNCT
asir-56165	93	4	q.	q.	PROPN
asir-56165	93	5	,	,	PUNCT
asir-56165	93	6	&	&	CCONJ
asir-56165	93	7	li	li	PROPN
asir-56165	93	8	,	,	PUNCT
asir-56165	93	9	h.	h.	PROPN
asir-56165	93	10	(	(	PUNCT
asir-56165	93	11	2024	2024	NUM
asir-56165	93	12	)	)	PUNCT
asir-56165	93	13	.	.	PUNCT
asir-56165	94	1	the	the	DET
asir-56165	94	2	reducible	reducible	ADJ
asir-56165	94	3	relations	relation	NOUN
asir-56165	94	4	between	between	ADP
asir-56165	94	5	/	/	PUNCT
asir-56165	94	6	among	among	ADP
asir-56165	94	7	valid	valid	ADJ
asir-56165	94	8	generalized	generalize	VERB
asir-56165	94	9	syllogisms	syllogism	NOUN
asir-56165	94	10	with	with	ADP
asir-56165	94	11	the	the	DET
asir-56165	94	12	generalized	generalized	ADJ
asir-56165	94	13	quantifiers	quantifier	NOUN
asir-56165	94	14	in	in	ADP
asir-56165	94	15	square{most	square{most	ADJ
asir-56165	94	16	}	}	PUNCT
asir-56165	94	17	.	.	PUNCT
asir-56165	95	1	scirea	scirea	PROPN
asir-56165	95	2	journal	journal	PROPN
asir-56165	95	3	of	of	ADP
asir-56165	95	4	philosophy	philosophy	NOUN
asir-56165	95	5	,	,	PUNCT
asir-56165	95	6	4(2	4(2	NUM
asir-56165	95	7	)	)	PUNCT
asir-56165	95	8	,	,	PUNCT
asir-56165	95	9	34	34	NUM
asir-56165	95	10	-	-	SYM
asir-56165	95	11	42	42	NUM
asir-56165	95	12	.	.	PUNCT
asir-56165	96	1	https://www	https://www	PROPN
asir-56165	96	2	.	.	PUNCT
asir-56165	96	3	scirea.org/journal/philosophy	scirea.org/journal/philosophy	PROPN
asir-56165	96	4	endrullis	endrullis	PROPN
asir-56165	96	5	,	,	PUNCT
asir-56165	96	6	j.	j.	PROPN
asir-56165	96	7	,	,	PUNCT
asir-56165	96	8	&	&	CCONJ
asir-56165	96	9	moss	moss	PROPN
asir-56165	96	10	,	,	PUNCT
asir-56165	96	11	l.	l.	PROPN
asir-56165	96	12	s.	s.	PROPN
asir-56165	96	13	(	(	PUNCT
asir-56165	96	14	2015	2015	NUM
asir-56165	96	15	)	)	PUNCT
asir-56165	96	16	.	.	PUNCT
asir-56165	97	1	syllogistic	syllogistic	ADJ
asir-56165	97	2	logic	logic	NOUN
asir-56165	97	3	with	with	ADP
asir-56165	97	4	‘	'	PUNCT
asir-56165	97	5	most	most	ADJ
asir-56165	97	6	’	'	PUNCT
asir-56165	97	7	.	.	PUNCT
asir-56165	98	1	in	in	ADP
asir-56165	98	2	de	de	PROPN
asir-56165	98	3	paiva	paiva	PROPN
asir-56165	98	4	,	,	PUNCT
asir-56165	98	5	v.	v.	ADP
asir-56165	98	6	et	et	PROPN
asir-56165	98	7	al	al	PROPN
asir-56165	98	8	.	.	PROPN
asir-56165	99	1	(	(	PUNCT
asir-56165	99	2	eds	ed	NOUN
asir-56165	99	3	.	.	PUNCT
asir-56165	99	4	)	)	PUNCT
asir-56165	99	5	,	,	PUNCT
asir-56165	99	6	logic	logic	NOUN
asir-56165	99	7	,	,	PUNCT
asir-56165	99	8	language	language	NOUN
asir-56165	99	9	,	,	PUNCT
asir-56165	99	10	information	information	NOUN
asir-56165	99	11	,	,	PUNCT
asir-56165	99	12	and	and	CCONJ
asir-56165	99	13	computation	computation	NOUN
asir-56165	99	14	(	(	PUNCT
asir-56165	99	15	pp	pp	ADJ
asir-56165	99	16	.	.	PUNCT
asir-56165	100	1	124	124	NUM
asir-56165	100	2	-	-	SYM
asir-56165	100	3	139	139	NUM
asir-56165	100	4	)	)	PUNCT
asir-56165	100	5	.	.	PUNCT
asir-56165	101	1	https://doi.org/10.1007/978-3-662	https://doi.org/10.1007/978-3-662	NOUN
asir-56165	101	2	47709	47709	NUM
asir-56165	101	3	-	-	PUNCT
asir-56165	101	4	0_10	0_10	NUM
asir-56165	101	5	halmos	halmo	NOUN
asir-56165	101	6	,	,	PUNCT
asir-56165	101	7	p.	p.	PROPN
asir-56165	101	8	r.	r.	PROPN
asir-56165	101	9	(	(	PUNCT
asir-56165	101	10	1974	1974	NUM
asir-56165	101	11	)	)	PUNCT
asir-56165	101	12	.	.	PUNCT
asir-56165	102	1	naive	naive	ADJ
asir-56165	102	2	set	set	NOUN
asir-56165	102	3	theory	theory	NOUN
asir-56165	102	4	.	.	PUNCT
asir-56165	103	1	new	new	PROPN
asir-56165	103	2	york	york	PROPN
asir-56165	103	3	:	:	PUNCT
asir-56165	103	4	springer	springer	NOUN
asir-56165	103	5	-	-	PUNCT
asir-56165	103	6	verlag	verlag	PROPN
asir-56165	103	7	.	.	PUNCT
asir-56165	104	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
asir-56165	104	2	978	978	NUM
asir-56165	104	3	-	-	SYM
asir-56165	104	4	14757	14757	NUM
asir-56165	104	5	-	-	PUNCT
asir-56165	104	6	1645	1645	NUM
asir-56165	104	7	-	-	SYM
asir-56165	104	8	0	0	NUM
asir-56165	104	9	hao	hao	PROPN
asir-56165	104	10	,	,	PUNCT
asir-56165	104	11	l.	l.	PROPN
asir-56165	104	12	h.	h.	PROPN
asir-56165	104	13	(	(	PUNCT
asir-56165	104	14	2024a	2024a	NUM
asir-56165	104	15	)	)	PUNCT
asir-56165	104	16	.	.	PUNCT
asir-56165	105	1	knowledge	knowledge	NOUN
asir-56165	105	2	reasoning	reasoning	NOUN
asir-56165	105	3	based	base	VERB
asir-56165	105	4	on	on	ADP
asir-56165	105	5	the	the	DET
asir-56165	105	6	generalized	generalized	ADJ
asir-56165	105	7	syllogism	syllogism	NOUN
asir-56165	105	8	ahh-2	ahh-2	PRON
asir-56165	105	9	.	.	PUNCT
asir-56165	105	10	scirea	scirea	PROPN
asir-56165	105	11	journal	journal	PROPN
asir-56165	105	12	of	of	ADP
asir-56165	105	13	computer	computer	NOUN
asir-56165	105	14	,	,	PUNCT
asir-56165	105	15	9(1	9(1	NUM
asir-56165	105	16	)	)	PUNCT
asir-56165	105	17	,	,	PUNCT
asir-56165	105	18	1	1	NUM
asir-56165	105	19	-	-	SYM
asir-56165	105	20	8	8	NUM
asir-56165	105	21	.	.	PUNCT
asir-56165	106	1	https://doi.org/10.54647/computer520396	https://doi.org/10.54647/computer520396	PROPN
asir-56165	106	2	hao	hao	PROPN
asir-56165	106	3	,	,	PUNCT
asir-56165	106	4	l.	l.	PROPN
asir-56165	106	5	h.	h.	PROPN
asir-56165	106	6	(	(	PUNCT
asir-56165	106	7	2024b	2024b	NUM
asir-56165	106	8	)	)	PUNCT
asir-56165	106	9	.	.	PUNCT
asir-56165	107	1	generalized	generalized	ADJ
asir-56165	107	2	syllogism	syllogism	NOUN
asir-56165	107	3	reasoning	reason	VERB
asir-56165	107	4	with	with	ADP
asir-56165	107	5	the	the	DET
asir-56165	107	6	quantifiers	quantifier	NOUN
asir-56165	107	7	in	in	ADP
asir-56165	107	8	modern	modern	ADJ
asir-56165	107	9	square{no	square{no	PROPN
asir-56165	107	10	}	}	PUNCT
asir-56165	107	11	and	and	CCONJ
asir-56165	107	12	square{most	square{most	ADJ
asir-56165	107	13	}	}	PUNCT
asir-56165	107	14	.	.	PUNCT
asir-56165	108	1	applied	apply	VERB
asir-56165	108	2	science	science	NOUN
asir-56165	108	3	and	and	CCONJ
asir-56165	108	4	innovative	innovative	ADJ
asir-56165	108	5	research	research	NOUN
asir-56165	108	6	,	,	PUNCT
asir-56165	108	7	8(1	8(1	NOUN
asir-56165	108	8	)	)	PUNCT
asir-56165	108	9	,	,	PUNCT
asir-56165	108	10	31	31	NUM
asir-56165	108	11	-	-	SYM
asir-56165	108	12	38	38	NUM
asir-56165	108	13	.	.	PUNCT
asir-56165	109	1	https://doi.org/10.22158/	https://doi.org/10.22158/	PROPN
asir-56165	109	2	asir.v8n1p31	asir.v8n1p31	PROPN
asir-56165	109	3	łukasiewicz	łukasiewicz	PROPN
asir-56165	109	4	,	,	PUNCT
asir-56165	109	5	j.	j.	PROPN
asir-56165	109	6	(	(	PUNCT
asir-56165	109	7	1957	1957	NUM
asir-56165	109	8	)	)	PUNCT
asir-56165	109	9	.	.	PUNCT
asir-56165	110	1	aristotle	aristotle	PROPN
asir-56165	110	2	’s	’s	PROPN
asir-56165	110	3	syllogistic	syllogistic	NOUN
asir-56165	110	4	:	:	PUNCT
asir-56165	110	5	from	from	ADP
asir-56165	110	6	the	the	DET
asir-56165	110	7	standpoint	standpoint	NOUN
asir-56165	110	8	of	of	ADP
asir-56165	110	9	modern	modern	ADJ
asir-56165	110	10	formal	formal	ADJ
asir-56165	110	11	logic	logic	NOUN
asir-56165	110	12	(	(	PUNCT
asir-56165	110	13	2nd	2nd	NOUN
asir-56165	110	14	edition	edition	NOUN
asir-56165	110	15	)	)	PUNCT
asir-56165	110	16	.	.	PUNCT
asir-56165	111	1	oxford	oxford	NOUN
asir-56165	111	2	:	:	PUNCT
asir-56165	111	3	clerndon	clerndon	PROPN
asir-56165	111	4	press	press	PROPN
asir-56165	111	5	.	.	PUNCT
asir-56165	112	1	ma	ma	PROPN
asir-56165	112	2	,	,	PUNCT
asir-56165	112	3	m.	m.	NOUN
asir-56165	112	4	w	w	PROPN
asir-56165	112	5	,	,	PUNCT
asir-56165	112	6	&	&	CCONJ
asir-56165	112	7	cao	cao	PROPN
asir-56165	112	8	,	,	PUNCT
asir-56165	112	9	q.	q.	PROPN
asir-56165	112	10	(	(	PUNCT
asir-56165	112	11	2024	2024	NUM
asir-56165	112	12	)	)	PUNCT
asir-56165	112	13	.	.	PUNCT
asir-56165	113	1	knowledge	knowledge	NOUN
asir-56165	113	2	mining	mining	NOUN
asir-56165	113	3	about	about	ADP
asir-56165	113	4	the	the	DET
asir-56165	113	5	generalized	generalize	VERB
asir-56165	113	6	modal	modal	NOUN
asir-56165	113	7	syllogism	syllogism	NOUN
asir-56165	113	8	em	em	VERB
asir-56165	113	9	◇	◇	NOUN
asir-56165	113	10	f-2	f-2	NOUN
asir-56165	113	11	with	with	ADP
asir-56165	113	12	the	the	DET
asir-56165	113	13	quantifiers	quantifier	NOUN
asir-56165	113	14	in	in	ADP
asir-56165	113	15	square{fewer	square{fewer	NOUN
asir-56165	113	16	than	than	ADP
asir-56165	113	17	half	half	NOUN
asir-56165	113	18	of	of	ADP
asir-56165	113	19	the	the	PRON
asir-56165	113	20	}	}	PUNCT
asir-56165	113	21	and	and	CCONJ
asir-56165	113	22	square{no	square{no	PROPN
asir-56165	113	23	}	}	PUNCT
asir-56165	113	24	.	.	PUNCT
asir-56165	114	1	scirea	scirea	PROPN
asir-56165	114	2	journal	journal	PROPN
asir-56165	114	3	of	of	ADP
asir-56165	114	4	computer	computer	NOUN
asir-56165	114	5	,	,	PUNCT
asir-56165	114	6	9(2	9(2	NUM
asir-56165	114	7	)	)	PUNCT
asir-56165	114	8	,	,	PUNCT
asir-56165	114	9	37	37	NUM
asir-56165	114	10	-	-	SYM
asir-56165	114	11	46	46	NUM
asir-56165	114	12	.	.	PUNCT
asir-56165	115	1	https://www.scirea.org/journal/paperinformation?paperid	https://www.scirea.org/journal/paperinformation?paperid	PROPN
asir-56165	115	2	=	=	SYM
asir-56165	115	3	10947	10947	NUM
asir-56165	115	4	moss	moss	NOUN
asir-56165	115	5	,	,	PUNCT
asir-56165	115	6	l.	l.	PROPN
asir-56165	115	7	s.	s.	PROPN
asir-56165	115	8	(	(	PUNCT
asir-56165	115	9	2010	2010	NUM
asir-56165	115	10	)	)	PUNCT
asir-56165	115	11	.	.	PUNCT
asir-56165	116	1	syllogistic	syllogistic	ADJ
asir-56165	116	2	logics	logic	NOUN
asir-56165	116	3	with	with	ADP
asir-56165	116	4	verbs	verbs	PROPN
asir-56165	116	5	.	.	PROPN
asir-56165	116	6	journal	journal	PROPN
asir-56165	116	7	of	of	ADP
asir-56165	116	8	logic	logic	NOUN
asir-56165	116	9	and	and	CCONJ
asir-56165	116	10	computation	computation	NOUN
asir-56165	116	11	,	,	PUNCT
asir-56165	116	12	20(4	20(4	NOUN
asir-56165	116	13	)	)	PUNCT
asir-56165	116	14	,	,	PUNCT
asir-56165	116	15	947	947	NUM
asir-56165	116	16	-	-	SYM
asir-56165	116	17	967	967	NUM
asir-56165	116	18	.	.	PUNCT
asir-56165	117	1	https://doi.org/10.1093/logcom/exn086	https://doi.org/10.1093/logcom/exn086	PROPN
asir-56165	117	2	peters	peters	PROPN
asir-56165	117	3	,	,	PUNCT
asir-56165	117	4	s.	s.	PROPN
asir-56165	117	5	,	,	PUNCT
asir-56165	117	6	&	&	CCONJ
asir-56165	117	7	westerståhl	westerståhl	PROPN
asir-56165	117	8	,	,	PUNCT
asir-56165	117	9	d.	d.	PROPN
asir-56165	117	10	(	(	PUNCT
asir-56165	117	11	2006	2006	NUM
asir-56165	117	12	)	)	PUNCT
asir-56165	117	13	.	.	PUNCT
asir-56165	118	1	quantifiers	quantifier	NOUN
asir-56165	118	2	in	in	ADP
asir-56165	118	3	language	language	NOUN
asir-56165	118	4	and	and	CCONJ
asir-56165	118	5	logic	logic	NOUN
asir-56165	118	6	.	.	PUNCT
asir-56165	119	1	oxford	oxford	NOUN
asir-56165	119	2	:	:	PUNCT
asir-56165	119	3	claredon	claredon	PROPN
asir-56165	119	4	press	press	PROPN
asir-56165	119	5	.	.	PUNCT
asir-56165	120	1	wang	wang	PROPN
asir-56165	120	2	,	,	PUNCT
asir-56165	120	3	h.	h.	PROPN
asir-56165	120	4	p.	p.	PROPN
asir-56165	120	5	,	,	PUNCT
asir-56165	120	6	&	&	CCONJ
asir-56165	120	7	yuan	yuan	PROPN
asir-56165	120	8	,	,	PUNCT
asir-56165	120	9	j.	j.	PROPN
asir-56165	120	10	j.	j.	PROPN
asir-56165	120	11	(	(	PUNCT
asir-56165	120	12	2024	2024	NUM
asir-56165	120	13	)	)	PUNCT
asir-56165	120	14	.	.	PUNCT
asir-56165	121	1	the	the	DET
asir-56165	121	2	reducibility	reducibility	NOUN
asir-56165	121	3	of	of	ADP
asir-56165	121	4	the	the	DET
asir-56165	121	5	generalized	generalized	ADJ
asir-56165	121	6	syllogism	syllogism	NOUN
asir-56165	121	7	mmi-4	mmi-4	PUNCT
asir-56165	121	8	with	with	ADP
asir-56165	121	9	the	the	DET
asir-56165	121	10	quantifiers	quantifier	NOUN
asir-56165	121	11	in	in	ADP
asir-56165	121	12	square{most	square{most	ADJ
asir-56165	121	13	}	}	PUNCT
asir-56165	121	14	and	and	CCONJ
asir-56165	121	15	square{some	square{some	NUM
asir-56165	121	16	}	}	PUNCT
asir-56165	121	17	.	.	PUNCT
asir-56165	122	1	scirea	scirea	PROPN
asir-56165	122	2	journal	journal	PROPN
asir-56165	122	3	of	of	ADP
asir-56165	122	4	mathematics	mathematics	PROPN
asir-56165	122	5	,	,	PUNCT
asir-56165	122	6	9(4	9(4	NOUN
asir-56165	122	7	)	)	PUNCT
asir-56165	122	8	,	,	PUNCT
asir-56165	122	9	84	84	NUM
asir-56165	122	10	-	-	SYM
asir-56165	122	11	92	92	NUM
asir-56165	122	12	.	.	PUNCT
asir-56165	123	1	https://doi.org/10.54647/mathematics110491	https://doi.org/10.54647/mathematics110491	PROPN
asir-56165	123	2	xu	xu	PROPN
asir-56165	123	3	,	,	PUNCT
asir-56165	123	4	j.	j.	PROPN
asir-56165	123	5	,	,	PUNCT
asir-56165	123	6	&	&	CCONJ
asir-56165	123	7	yu	yu	PROPN
asir-56165	123	8	,	,	PUNCT
asir-56165	123	9	z.	z.	PROPN
asir-56165	123	10	p.	p.	PROPN
asir-56165	123	11	(	(	PUNCT
asir-56165	123	12	2024	2024	NUM
asir-56165	123	13	)	)	PUNCT
asir-56165	123	14	.	.	PUNCT
asir-56165	124	1	the	the	DET
asir-56165	124	2	reducibility	reducibility	NOUN
asir-56165	124	3	of	of	ADP
asir-56165	124	4	generalized	generalized	ADJ
asir-56165	124	5	syllogisms	syllogism	NOUN
asir-56165	124	6	with	with	ADP
asir-56165	124	7	the	the	DET
asir-56165	124	8	quantifiers	quantifier	NOUN
asir-56165	124	9	in	in	ADP
asir-56165	124	10	square{not	square{not	ADV
asir-56165	124	11	all	all	PRON
asir-56165	124	12	}	}	PUNCT
asir-56165	124	13	and	and	CCONJ
asir-56165	124	14	square{most	square{most	NUM
asir-56165	124	15	}	}	PUNCT
asir-56165	124	16	.	.	PUNCT
asir-56165	125	1	philosophy	philosophy	PROPN
asir-56165	125	2	international	international	ADJ
asir-56165	125	3	journal	journal	NOUN
asir-56165	125	4	,	,	PUNCT
asir-56165	125	5	7(3	7(3	NUM
asir-56165	125	6	)	)	PUNCT
asir-56165	125	7	,	,	PUNCT
asir-56165	125	8	000339	000339	NUM
asir-56165	125	9	.	.	PUNCT
asir-56165	126	1	https://medwinpublishers	https://medwinpublisher	NOUN
asir-56165	126	2	.	.	PUNCT
asir-56165	126	3	com	com	NOUN
asir-56165	126	4	/	/	SYM
asir-56165	126	5	article	article	NOUN
asir-56165	126	6	-	-	PUNCT
asir-56165	126	7	description.php?artid=13462	description.php?artid=13462	PROPN
asir-56165	126	8	https://www.scirea.org/journal/philosophy	https://www.scirea.org/journal/philosophy	NOUN
asir-56165	126	9	https://www.scirea.org/journal/philosophy	https://www.scirea.org/journal/philosophy	NOUN
asir-56165	126	10	http://link.springer.com/book/10.1007/978-3-662-47709-0	http://link.springer.com/book/10.1007/978-3-662-47709-0	ADV
asir-56165	126	11	http://link.springer.com/book/10.1007/978-3-662-47709-0	http://link.springer.com/book/10.1007/978-3-662-47709-0	ADV
asir-56165	126	12	https://doi.org/10.1007/978-3	https://doi.org/10.1007/978-3	PROPN
asir-56165	126	13	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
asir-56165	127	1	https://doi.org/10.22158/	https://doi.org/10.22158/	PROPN
asir-56165	127	2	https://medwinpublishers.com/article-description.php?artid=13462	https://medwinpublishers.com/article-description.php?artid=13462	INTJ
asir-56165	127	3	https://medwinpublishers.com/article-description.php?artid=13462	https://medwinpublishers.com/article-description.php?artid=13462	INTJ