Knowledge Mining Based on the Valid Aristotelian Modal Syllogism ⼞AA◇A-1

Abstract
This paper firstly presents knowledge representations of Aristotelian modal syllogisms based on the structure of modal categorical propositions; Then, the validity of syllogism ⼞AA◇A-1 was proved by using the truth value definitions of these propositions. And then this syllogism was used for knowledge reasoning with the help of some reduction operations. More specifically, the validity of the other 30 syllogisms can be inferred from that of ⼞AA◇A-1 with the help of possible world semantics and generalized quantifier theory. Owing to the possible modality (◇) and necessary modality (⼞) can be defined mutually, and any one Aristotelian quantifier can define the other three, so there are reducible relations between/among 31 valid Aristotelian modal syllogisms. Due to the other 30 valid syllogisms obtained by deductive methods, these results are consistent. That is superior to previous works. This formal method is consistent with the ideas of knowledge mining in artificial intelligence.

Keywords
Aristotelian modal syllogisms; reducible relations; knowledge reasoning; knowledge mining

Cite this paper
Qing Cao, Long Wei, Knowledge Mining Based on the Valid Aristotelian Modal Syllogism ⼞AA◇A-1 , SCIREA Journal of Philosophy. Volume 4, Issue 1, February 2024 | PP. 1-10. 10.54647/philosophy720086

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