The Validity of Generalized Modal SyllogismsBased on the SyllogismE□M◇O-1

Volume 9, Issue 1, February 2024     |     PP. 11-22      |     PDF (292 K)    |     Pub. Date: February 3, 2024
DOI: 10.54647/mathematics110451    31 Downloads     218748 Views  

Author(s)

Liheng Hao, School of Artificial Intelligence and Automation, Beijing University of Technology, Beijing, China

Abstract
The simple and feasible methods for screening valid generalized modal syllogisms are as follows: (1) First, prove the validity of a generalized syllogism, then add at least one necessary modality (□) or possible modality (◇) to this syllogism, (2) Secondly, according to the basic fact that the conclusion of a modal syllogism is determined by the weakest premise, 12 valid generalized modal syllogisms in the same figure can be obtained by deleting invalid syllogisms; (3) Finally, taking each of these 12 syllogisms as a basic axiom, one can derive generalized modal syllogisms with different figures and forms by means of some definitions, facts, and deductive rules. This paper takes the generalized syllogisms with the general quantifier ‘most’ as an example to illustrate the above methods. The results obtained by this deductive method are logically consistent. This study not only has important theoretical value for us to deeply reveal the connections between/among things, but also has important practical significance for knowledge reasoning in artificial intelligence.

Keywords
generalized quantifiers; generalized syllogisms; generalized modal syllogisms; validity

Cite this paper
Liheng Hao, The Validity of Generalized Modal SyllogismsBased on the SyllogismE□M◇O-1 , SCIREA Journal of Mathematics. Volume 9, Issue 1, February 2024 | PP. 11-22. 10.54647/mathematics110451

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