The Remaining 23 Valid Aristotelian Syllogisms can be Deduced only from the Syllogism IAI-3

Volume 7, Issue 5, October 2022     |     PP. 85-95      |     PDF (230 K)    |     Pub. Date: December 11, 2022
DOI: 10.54647/computer52326    85 Downloads     160256 Views  

Author(s)

Cheng Zhang, School of Philosophy, Anhui University, Hefei, China

Abstract
Syllogism reasoning is a common and important form of reasoning in natural language and logic. This paper shows that the remaining 23 valid syllogisms can be deduced merely from the syllogism IAI-3 by making the best of propositional logic and generalized quantifier theory, so as to achieve the goal of deeply discussing the reducible relations between the syllogism IAI-3 and the other syllogisms. More specifically, on the basis of formalizing syllogisms, this paper makes full of rules of deduction in classical propositional logic, the definitions of outer and inner negative quantifiers of Aristotelian quantifiers, and the symmetry of Aristotelian quantifiers no and some in generalized quantifier theory, and then establishes a concise formalized axiom system for Aristotelian syllogistic logic. This innovative research not only shows that formalized logic has the characteristics of structuralism, but also provides a concise and general mathematical paradigm for studying other syllogistic logics, and also provides theoretical support for knowledge and information processing in artificial intelligence and computer science.

Keywords
Aristotelian syllogisms; Aristotelian quantifiers; reducible relations; negative quantifiers; symmetry of quantifiers

Cite this paper
Cheng Zhang, The Remaining 23 Valid Aristotelian Syllogisms can be Deduced only from the Syllogism IAI-3 , SCIREA Journal of Computer. Volume 7, Issue 5, October 2022 | PP. 85-95. 10.54647/computer52326

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