Reducible Relationships between Generalized Syllogisms with the Quantifiers in Square{at least half of the}

Abstract

The main conclusions of this paper are as follows: Theorem 1 proves the validity of the generalized syllogism SAI-3. Theorem 2 takes the syllogism SAI-3 as the fundamental axiom, and then deduces the other 14 non-trivial valid generalized syllogisms with the quantifiers in Square{at least half of the}. It means that there are reducible relationships between these 15 syllogisms, and that the above knowledge mining processes are consistent. This innovative achievement can promote in-depth research on generalized syllogistic and provide methodological inspiration for knowledge mining in artificial intelligence.