Knowledge Reasoning Based on the Generalized Syllogism FMO-3

Abstract
This paper focuses on the validity and reducibility of the non-trivial generalized syllogisms with the quantifiers in Square{some} and Square{fewer than half of the}. To this end, this paper firstly presents knowledge representations of generalized syllogisms, and then proves the validity of the syllogism FMO-3, and subsequently deduces the other 21 valid non-trivial generalized syllogisms from the validity of the syllogism FMO-3. That is to say that there are reducible relations between/among these 22 valid non-trivial generalized syllogisms. This is so because the deduced syllogisms in this paper only involve the following 8 quantifiers: no, all, not all, some, fewer than half of the, most, at most half of the, and at least half of the, and because any of the first four quantifiers can define the other three quantifiers, as well as because the same goes for the last four quantifiers. This formal deductive reasoning not only provides a theoretical basis for English language information processing, but also inspiration for studying other kinds of syllogisms.

Keywords
generalized quantifiers; generalized syllogisms; validity; reducibility; knowledge reasoning

Cite this paper
Yijiang Hao, Knowledge Reasoning Based on the Generalized Syllogism FMO-3 , SCIREA Journal of Mathematics. Volume 9, Issue 4, August 2024 | PP. 93-101. 10.54647/mathematics110485

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