Reduction between Categorical Syllogisms Based on the Syllogism EIO-2

Syllogism reasoning is a common and important form of in human thinking from Aristotle onwards. To overcome the shortcomings previous studies, this article makes full use set theory classical propositional logic, deduces remaining 23 valid syllogisms only on basis syllogism EIO-2 perspective mathematical structuralism, then successfully establishes concise formal axiom system for categorical syllogistic logic. More specifically, takes advantage trisection structure propositions such as Q(a, b), transformation relations between an Aristotelian quantifier its inner outer negation, symmetry two (that is, no some), some inference rules derives EIO-2, so to realize reduction different syllogisms.