How to Deduce the Remaining 23 Valid Syllogisms from the Validity of the Syllogism EIO-1
Xiaojun Zhang,
Hui Li,
Yijiang Hao
Issue:
Volume 11, Issue 6, December 2022
Pages:
160-164
Received:
9 October 2022
Accepted:
1 November 2022
Published:
11 November 2022
DOI:
10.11648/j.acm.20221106.11
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Abstract: Syllogistic reasoning plays an important role in human reasoning, and has been widely studied from Aristotle onward. In previous studies, when deriving all the other valid syllogisms, at least two valid syllogisms were taken as the basic axioms. While this paper derives all other valid syllogisms only from one valid syllogism. On the basis of generalized quantifier theory and set theory, this paper shows that the remaining 23 valid syllogisms can be derived only from the syllogism EIO-1 by making the best of the definitions of three negative quantifiers of Aristotelian quantifiers, the symmetry of Aristotelian quantifiers no and some, and several propositional reasoning rules such as anti-syllogism rules and the subsequent weakening rule, and so on. This paper syntactically provides a simple and reasonable mathematical model for studying other kinds of syllogisms, such as generalized syllogistic, rational syllogistic, Aristotelian modal syllogistic and generalized modal syllogistic. And this research shows that formalized logic has the characteristics of structuralism, that is, it studies not only the forms and laws of thinking, but also the structure of thinking objects and the relationship between structures. It is hoped that this formal and innovative research is not only beneficial to the further development of various syllogistic logics, but also to natural language information processing in computer science, and also to knowledge representation and knowledge reasoning in Artificial Intelligence.
Abstract: Syllogistic reasoning plays an important role in human reasoning, and has been widely studied from Aristotle onward. In previous studies, when deriving all the other valid syllogisms, at least two valid syllogisms were taken as the basic axioms. While this paper derives all other valid syllogisms only from one valid syllogism. On the basis of gener...
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