The Deductibility of the Generalized Syllogism AAM-1

Volume 8, Issue 5, October 2024     |     PP. 186-193      |     PDF (258 K)    |     Pub. Date: October 7, 2024
DOI: 10.54647/isss120362    25 Downloads     1668 Views  

Author(s)

Jingyi Zhang, Institute of Logic and Information, Sichuan Normal University, Chengdu, China
Long Wei, Department of Philosophy(Zhuhai), Sun Yat-Sen University, Zhuhai, China

Abstract
Firstly, according to set theory, the validity of the generalized syllogism AAM-1 is proved in accordance with the truth-value definitions of quantified statements. Then, on the basis of generalized quantifier theory, this paper derives the other 14 valid generalized syllogisms from the validity of generalized syllogism AAM-1 by taking full advantage of the inner and outer negation of a generalized quantifier, the symmetry of the two Aristotelian quantifiers ‘some’ and ‘no’, the subsequent weakening rule, the anti-syllogism inference rules, and other reduction operations. This research method conforms to the demand of formal transformation for natural language information in the era of mega data.

Keywords
generalized syllogism; deductibility; truth-value definition; quantifier

Cite this paper
Jingyi Zhang, Long Wei, The Deductibility of the Generalized Syllogism AAM-1 , SCIREA Journal of Information Science and Systems Science. Volume 8, Issue 5, October 2024 | PP. 186-193. 10.54647/isss120362

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