The Reducibility of Generalized Syllogisms with the Quantifiers in Square {not all} and Square {most}

To explore the reducibility of non-trivial generalized syllogisms with the quantifiers in Square {not all} and Square {most}, this paper first gives the formalization of generalized syllogisms on the basis of set theory, and then proves the validity of the generalized syllogism EMO-3 by first-order logic and generalized quantifier theory; Finally, with the help of some reductive operations, the other 20 valid generalized syllogisms are deduced from the syllogism EMO-3. In other words, there are the reducible relationships between/among the 21 valid syllogisms. The reason for this is that any quantifier in a square can define the other three quantifiers. This research method is applicable to the study of syllogisms with quantifiers in other squares.