The Reducibility of Modal Syllogisms Based on the Syllogism EI◇O-2

Abstract

Syllogistic reasoning plays a crucial part in natural language information processing For the purpose of providing a consistent interpretation for Aristotelian modal syllogistic this paper firstly proves the validity of the syllogism EI O-2 and then takes it as the basic axiom to derive the other 38 valid modal syllogisms by taking advantage of some reasoning rules in classical propositional logic the symmetry of two Aristotelian quantifiers i e some and no the transformation between any one of Aristotelian quantifiers and its three negative quantifiers as well as some facts in first order logic In other words there are reducible relations between the modal syllogism EI O-2 and the other 38 valid modal syllogisms There are infinitely many instances in natural language corresponding to any valid modal syllogism Therefore this study has theoretical value and practical significance for natural language information processing in computer science