Knowledge Mining about the Generalized Modal Syllogism E▯M◇F-2 with the Quantifiers in Square{fewer than half of the} and Square{no}

Volume 9, Issue 2, April 2024     |     PP. 37-46      |     PDF (270 K)    |     Pub. Date: May 7, 2024
DOI: 10.54647/computer520416    32 Downloads     3005 Views  

Author(s)

Mingwei Ma, School of Statistics, Capital University of Economics and Business, Beijing, China
Qing Cao, School of Philosophy, Anhui University, Hefei, China

Abstract
On the basis of set theory, generalized quantifier theory, and modal logic, this paper mainly focuses on the knowledge mining about generalized modal syllogism with the quantifiers in Square{fewer than half of the} and Square{no}. To this end, this paper firstly proves the validity of the non-trivial syllogism E▯M◇F-2, and deduces other 22 valid non-trivial generalized modal syllogisms based on relative reduction operations. The reason why syllogisms with different figures and forms can be mutually reduced is that any quantifier in Square{fewer than half of the} and Square{no} can define the other three quantifiers, and the necessary and possible modality are mutually dual. Since all the proofs in this article are deductive reasoning, their conclusions are consistent.

Keywords
knowledge mining; Square{fewer than half of the}; Square{no}; generalized modal syllogisms

Cite this paper
Mingwei Ma, Qing Cao, Knowledge Mining about the Generalized Modal Syllogism E▯M◇F-2 with the Quantifiers in Square{fewer than half of the} and Square{no} , SCIREA Journal of Computer. Volume 9, Issue 2, April 2024 | PP. 37-46. 10.54647/computer520416

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