Knowledge Reasoning Based on the Generalized Modal Syllogism ⧠AM◇M-1 with ‘Most’

Abstract

This paper firstly illustrates knowledge representation of generalized modal syllogisms based on the structure of generalized quantification propositions, and proves the validity of the generalized modal syllogism ⧠ AM◇M-1 on the basis of set theory and modal logic. And then the paper shows that the other 37 valid generalized modal syllogisms can be deduced from ⧠ AM◇M-1. Similarly, more valid generalized modal syllogisms can be derived from it. The reason why these syllogisms are reducible is that the necessary modality ⧠ and possible one ◇ are able to define mutually, and that the two Aristotelian quantifiers some and no are symmetric.