The structure of generalized intermediate 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 introduce the generalization of all the figures and we show that for the proof of validity of all the generalized syllogisms, we need to prove the validity of only few of them so that the validity of the other ones immediately follows.