Screening out All Valid Aristotelian Modal Syllogisms
Applied and Computational Mathematics
Volume 8, Issue 6, December 2019, Pages: 95-104
Received: Jan. 5, 2020; Accepted: Jan. 15, 2020; Published: Feb. 13, 2020
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Xiaojun Zhang, Institute of Logic and Information, Sichuan Normal University, Chengdu, China
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It is easy to understand that whether a classical syllogism is valid. That whether a modal syllogism is valid is not so transparent. The prevailing view on Aristotelian modal syllogistic is that the syllogistic is incomprehensible due to its many faults and inconsistencies. Although adequate semantic analysis or reconstruction of the syllogistic have be given by many authors, it is far from obvious how to extend these results so as to consistently cover the whole modal syllogistic developed. The major aim of this paper is to overcome these difficulties, and screen out 384 Aristotelian valid modal syllogisms from 6656 Aristotelian modal syllogisms in natural language. They can be formalized by means of set theory and generalized quantifier theory, and their validity can be proved by possible world semantics and the truth definition of Aristotelian quantifiers defined in generalized quantifier theory. The basic steps of screening out all valid Aristotelian modal syllogisms are as follows: firstly one can get all possible modal syllogisms obtained by adding modal operators to 24 valid classical syllogisms, and secondly eliminate invalid modal syllogisms by characteristic rules of modal syllogisms. It is hoped that these innovative achievements will make contributions to promote the development of Aristotelian and generalized modal syllogistic, natural language information processing, and further research on knowledge representation and knowledge reasoning in computer science.
Generalized Quantifier Theory, Aristotelian Modal Syllogisms, Formalization, Validity, Possible Worlds
To cite this article
Xiaojun Zhang, Screening out All Valid Aristotelian Modal Syllogisms, Applied and Computational Mathematics. Vol. 8, No. 6, 2019, pp. 95-104. doi: 10.11648/j.acm.20190806.12
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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