How to Deduce 17 valid Non-trivial Generalized Modal Syllogisms from the Syllogism 口EA◇H-2

Volume 10, Issue 2, April 2025     |     PP. 27-36      |     PDF (210 K)    |     Pub. Date: June 17, 2025
DOI: 10.54647/computer520447    20 Downloads     221 Views  

Author(s)

Haowei Shi, Institute of Logic and Information Technology, Sichuan Normal University, Chengdu, China

Abstract
A modern Square{Q}={Q, Q, Q, Q} is composed of the quantifier Q, its inner negation Q, outer negation Q and dual negation Q. This paper focuses on studying the generalized modal syllogisms formed by modalities and the 8 quantifiers in Square{no} and Square{at most half of the}. More specifically, this paper firstly presents a knowledge representation of the syllogism 口EA◇H-2, then proves its validity according to the truth value definitions of some categorical propositions. Finally, with the help of some reducible operations, the other 17 valid non-trivial generalized modal syllogisms can be obtained from the syllogism 口EA◇H-2. This formal study is beneficial for knowledge mining in artificial intelligence.

Keywords
generalized modal syllogisms; validity; knowledge reasoning; knowledge mining

Cite this paper
Haowei Shi, How to Deduce 17 valid Non-trivial Generalized Modal Syllogisms from the Syllogism 口EA◇H-2 , SCIREA Journal of Computer. Volume 10, Issue 2, April 2025 | PP. 27-36. 10.54647/computer520447

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