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