*The Deductibility of the Aristotelian Modal Syllogism E⼞I◇O-4 from the Perspective of Mathematical Structuralism*

**DOI:**10.54647/philosophy720089 26 Downloads 4261 Views

**Author(s)**

**Abstract**

This paper firstly provides knowledge representations of Aristotelian modal syllogisms from the perspective of mathematical structuralism, and proves the validity of Aristotelian modal syllogism E⼞I◇O-4, and then by making full use of relevant definitions, facts, and some inference rules, formally derive other 30 valid modal syllogisms on the basis of one modal syllogism (i.e. E⼞I◇O-4) as a basic axiom. The reason why modal syllogisms are deducible is that the four Aristotelian quantifiers (i.e. all, no, some, and not all) can be mutually defined, and that so can the two modalities (i.e. ⼞ and ◇). Thus, one can establish a minimalist formal axiomatic system for modal syllogistic logic. This formal method is not only beneficial for the study of other types of syllogisms, but also for the development of a more intelligent inference engine for expert systems.

**Keywords**

Aristotelian modal syllogism; Aristotelian quantifier; symmetry; deducible relation

**Cite this paper**

Feifei Yang, Xiaojun Zhang,
The Deductibility of the Aristotelian Modal Syllogism E⼞I◇O-4 from the Perspective of Mathematical Structuralism
, *SCIREA Journal of Philosophy*.
Volume 4, Issue 1, February 2024 | PP. 23-33.
10.54647/philosophy720089

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