The Validity of Generalized Modal Syllogisms with the Generalized Quantifiers in Square{most}

Volume 4, Issue 1, February 2024     |     PP. 11-22      |     PDF (292 K)    |     Pub. Date: April 1, 2024
DOI: 10.54647/philosophy720087    28 Downloads     34705 Views  

Author(s)

Siyi Yu, School of Philosophy, Anhui University, Hefei, China
Xiaojun Zhang, School of Philosophy, Anhui University, Hefei, China

Abstract
Due to the large number of generalized quantifiers in the English language, this paper only studies the fragment of generalized modal syllogistic that contains the quantifiers in Square{all} and Square{most}. On the basis of generalized quantifier theory, possible-world semantics, and set theory, this paper shows that there are reducible relations between/among the generalized modal syllogism ⼞EM◇O-3 and at least the other 29 valid generalized modal syllogisms. This method can also be used to study syllogisms with other generalized quantifiers. The results obtained by means of formal deductive method have not only consistency, but also theoretical value for the development of inference theory in artificial intelligence.

Keywords
generalized modal syllogisms; reducibility; modality; validity

Cite this paper
Siyi Yu, Xiaojun Zhang, The Validity of Generalized Modal Syllogisms with the Generalized Quantifiers in Square{most} , SCIREA Journal of Philosophy. Volume 4, Issue 1, February 2024 | PP. 11-22. 10.54647/philosophy720087

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