Knowledge Representation Based on the Aristotelian Modal Syllogism □AE◇E-2

Volume 8, Issue 5, October 2024     |     PP. 233-240      |     PDF (240 K)    |     Pub. Date: October 7, 2024
DOI: 10.54647/sociology841311    21 Downloads     1779 Views  

Author(s)

Haiping Wang, School of Philosophy, Anhui University, Hefei, China
Xiaojun Zhang, School of Philosophy, Anhui University, Hefei, China

Abstract
This paper firstly presents knowledge representations of Aristotelian modal syllogisms based on the structure of modal categorical propositions, and proves the validity of the syllogism □AE◇E-2 by using set theory, modal logic, Aristotelian quantifiers theory and so on, and then illustrates that the other 30 valid syllogisms are derived from □AE◇E-2. In other words, it shows that there are reducible relationships between/among them. Owing to Aristotelian quantifiers (that is, all, some, no, not all) can be mutually defined, as well as so can the possible modality (◇) and necessary modality (□), there are reducible relationships between/among valid Aristotelian modal syllogisms. This formal study not only provides new insights for knowledge mining in artificial intelligence, but also provides ideas for studying modern logic.

Keywords
Aristotelian modal syllogisms, Aristotelian quantifiers, reducible relationship, possible worlds

Cite this paper
Haiping Wang, Xiaojun Zhang, Knowledge Representation Based on the Aristotelian Modal Syllogism □AE◇E-2 , SCIREA Journal of Sociology. Volume 8, Issue 5, October 2024 | PP. 233-240. 10.54647/sociology841311

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