Reduction between the Syllogism OAO-3 and the Remaining 23 Valid Syllogisms
DOI: 10.54647/computer52321 77 Downloads 160698 Views
Author(s)
Abstract
With the help of the definitions of three negative quantifiers of Aristotelian quantifiers (i.e. all, no, some and not all), the symmetry of no and some, and some basic inference rules in propositional logic, one can deduce the remaining 23 valid syllogisms only from the syllogism OAO-3. In other words, there is reducible relations between/among different forms and different figures of valid traditional syllogisms. And these reducible relations actually reflect the transformation relations between the monotonicity of the four Aristotelian quantifiers. This paper provides a computational level of reasoning for syllogistic logic and an important theoretical basis for knowledge representation and knowledge reasoning in computers.
Keywords
Aristotelian quantifiers; symmetry; reducible relations; generalized quantifier theory
Cite this paper
Xiaojun Zhang, Long Wei, Yijiang Hao,
Reduction between the Syllogism OAO-3 and the Remaining 23 Valid Syllogisms
, SCIREA Journal of Computer.
Volume 7, Issue 4, August 2022 | PP. 75-84.
10.54647/computer52321
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