The Reductions between/among Aristotelian Syllogisms Based on the Syllogism AII-3

Author(s)

Abstract
With the help of the definitions of the inner and outer negative Aristotelian quantifiers, the symmetry of Aristotelian quantifiers no and some, the anti-syllogism rules and the subsequent weakening rule, this paper illustrates the reducible relations between valid Aristotelian syllogisms of different figures and different forms. More specifically, this paper deduces the remaining 23 valid Aristotelian syllogisms only from the valid syllogism AII-3, and establishes a simple and clear formal axiom system for Aristotelian syllogistic. This formal and innovative research is not only beneficial to the study of reducible relations between other types of syllogisms, such as generalized syllogisms and modal syllogisms, but also to the knowledge representation, knowledge reasoning and natural language information processing in artificial intelligence.

Keywords
Aristotelian syllogisms; axioms; Aristotelian quantifiers; reductions

Cite this paper
Yijiang Hao, The Reductions between/among Aristotelian Syllogisms Based on the Syllogism AII-3 , SCIREA Journal of Philosophy. Volume 3, Issue 1, February 2023 | PP. 12-22. 10.54647/philosophy720083

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