Knowledge Reasoning about the Aristotelian Syllogism IAI-4
DOI: 10.54647/mathematics110479 29 Downloads 36018 Views
Author(s)
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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