Knowledge Reasoning for the Generalized Modal Syllogism □AM◇I-3

Volume 8, Issue 4, August 2024     |     PP. 129-138      |     PDF (293 K)    |     Pub. Date: August 16, 2024
DOI: 10.54647/isss120354    21 Downloads     2327 Views  

Author(s)

Haiping Wang, School of Philosophy, Anhui University, China
Zhaolong Yuan, School of Philosophy and Social Development, South China Normal University, China

Abstract
This paper first proves the validity of the generalized modal syllogism □AM◇I-3 with the non-trivial generalized quantifier ‘most’ and the two trivial generalized quantifiers ‘all’ and ‘some’. And then making best of relevant facts and deductive rules, this paper deduces 20 other valid generalized modal syllogisms from the syllogism □AM◇I-3. In other words, there are reducible relationships between/among the 21 valid generalized modal syllogisms. The reasons for this conclusion are as follows: (1) any quantifier in Square{some} can define the other three quantifiers, and so can any quantifier in Square{most}. (2) necessary modality (□) and possible modality (◇) can be mutually defined. This results not only provide a common mathematical paradigm for studying the validity and reducibility of different kinds of syllogisms, but also a formal method for other types of knowledge reasoning in artificial intelligence that can be used as a reference.

Keywords
generalized modal syllogisms; generalized quantifiers; reducibility

Cite this paper
Haiping Wang, Zhaolong Yuan, Knowledge Reasoning for the Generalized Modal Syllogism □AM◇I-3 , SCIREA Journal of Information Science and Systems Science. Volume 8, Issue 4, August 2024 | PP. 129-138. 10.54647/isss120354

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