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Reduction between the Syllogism OAO-3 and the Remaining 23 Valid Syllogisms

Volume 7, Issue 4, August 2022    |    PP. 75-84    |PDF (206 K)|    Pub. Date: November 13, 2022
DOI: 10.54647/computer52321    10 Downloads     265 Views  

Author(s)
Xiaojun Zhang, School of Philosophy, Anhui University, Hefei, China
Long Wei, School of Philosophy, Anhui University, Hefei, China
Yijiang Hao, Institute of Philosophy, Chinese Academy of Social Sciences, Beijing, China

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. Vol. 7 , No. 4 , 2022 , pp. 75 - 84 . https://doi.org/10.54647/computer52321

References

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