Knowledge Reasoning Based on the Generalized Modal Syllogism ⧠AM◇M-1 with ‘Most’ - Hao, Liheng; Cao, Chongzi (Transactions on Engineering and Computing Sciences, 2024)
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.