Fuzzy type theory; Generalized quantifiers; Intermediate quantifiers; Logical syllogisms

In this paper, we continue development of the formal theory of intermediate quantifiers which are expressions of the natural language (''most``,''many``,''few``, etc.). In the previous paper, we demonstrated that 105 generalized syllogisms are valid in our theory. We continue here analysis of new intermediate genera-lized quantifier ''more than half`` and prove 19 new intermediate generalized syllogisms with this quantifier. We show that for the proof of validity of all the generalized syllogisms, we need to prove validity of only few of them so that validity of the other ones immediately follows. In the end of this paper, we introduce generalization of all the figures .

In this paper, we continue development of the formal theory of intermediate quantifiers which are expressions of the natural language (''most``,''many``,''few``, etc.). In the previous paper, we demonstrated that 105 generalized syllogisms are valid in our theory. We continue here analysis of new intermediate genera-lized quantifier ''more than half`` and prove 19 new intermediate generalized syllogisms with this quantifier. We show that for the proof of validity of all the generalized syllogisms, we need to prove validity of only few of them so that validity of the other ones immediately follows. In the end of this paper, we introduce generalization of all the figures .