Knowledge Reasoning about the Aristotelian Syllogism IAI-4

Volume 9, Issue 2, April 2024     |     PP. 23-30      |     PDF (234 K)    |     Pub. Date: April 1, 2024
DOI: 10.54647/mathematics110479    40 Downloads     37932 Views  

Author(s)

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

Abstract
On the basis of set theory, propositional logic and generalized quantifier theory, this paper indicates that the other 23 valid syllogisms can be only derived from the syllogism IAI-4. These derivations use the symmetry of quantifiers no and some, the definitions of inner and outer negation of Aristotelian quantifiers, deductive rules of propositional logic, and some relevant facts, and so on. Moreover, this paper establishes a concise formalized axiomatic system for Aristotelian syllogistic logic and puts forward a research paradigm for the study of other syllogistic. This formal method aligns with the idea of knowledge reasoning and knowledge mining in artificial intelligence.

Keywords
Aristotelian syllogisms; Aristotelian quantifiers; symmetry; reducibility

Cite this paper
Siyi Yu, Xiaojun Zhang, Knowledge Reasoning about the Aristotelian Syllogism IAI-4 , SCIREA Journal of Mathematics. Volume 9, Issue 2, April 2024 | PP. 23-30. 10.54647/mathematics110479

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