The Reducibility of the Generalized Syllogism MMI-4 with the Quantifiers in Square{most} and Square{some}

Volume 9, Issue 4, August 2024     |     PP. 84-92      |     PDF (260 K)    |     Pub. Date: August 16, 2024
DOI: 10.54647/mathematics110491    36 Downloads     2751 Views  

Author(s)

Haiping Wang, School of Philosophy, Anhui University, China
Jiaojiao Yuan, Party School of Zigong Municipal Committee of the Communist Party of China

Abstract
This paper firstly proves the validity of the generalized syllogism MMI-4 with the quantifiers in Square{most} and Square{some}, and then making full use of the relevant definitions, facts, and reasoning rules to infer the other 20 valid generalized ones from the syllogism MMI-4. In other words, there are reducible relationships between/among these valid generalized syllogisms. The reason for this is because any quantifier in Square{some} can define the other three quantifiers, and so can any quantifier in Square{most}. This study has important theoretical value for natural language information processing.

Keywords
generalized quantifiers; generalized syllogisms; reducibility; validity

Cite this paper
Haiping Wang, Jiaojiao Yuan, The Reducibility of the Generalized Syllogism MMI-4 with the Quantifiers in Square{most} and Square{some} , SCIREA Journal of Mathematics. Volume 9, Issue 4, August 2024 | PP. 84-92. 10.54647/mathematics110491

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