Formal System of Categorical Syllogistic Logic Based on the Syllogism <i>AEE-4</i>

Adopting a different method from the previous scholars, this article deduces remaining 23 valid syllogisms just taking syllogism AEE-4 as basic axiom. The idea of study is follows: firstly, make full use trichotomy structure categorical propositions to formalize syllogisms. Then, advantage deductive rules in classical propositional logic and facts generalized quantifier theory, we deduce by one (that is, AEE-4) This not only reveals reducible relations between other syllogisms, but also establishes concise formal axiomatic system for syllogistic logic. We hope that results methods will provide good mathematical paradigm studying kinds logics, project appeal specialists logic, linguistic semantics, computational cognitive science artificial intelligence.