The Validity of Generalized Modal Syllogisms with the Quantifiers in Square {most} and Square{no}

On the basis of the valid generalized modal syllogism £EM¯O-2 containing the quantifiers in Square{most} and Square{no}, this paper explores the validity of the other generalized modal syllogisms. The reasons of the reducibility between/among valid generalized modal syllogisms are: that there are transformational relationships between/among Aristotelian quantifiers in Square{no} or generalized ones in Square{most}, and that the necessary modality and the possible one are dual, and that the quantifiers some and no are symmetric. This method is universal, and helps to study the validity of other kinds of syllogisms. It is hoped that the above results can promote the development of related fields such as computational linguistics.