Generalized quantifiers; intermediate quantifiers; fuzzy type theory; evaluative linguistic expressions; generalized Aristotle's syllogisms.

In this paper, we continue development of the formal theory of \emph{intermediate quantifiers} (expressions such as \emph{most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of}). The theory is a fuzzy-logic formalization of the concept introduced by P. L. Peterson in his book. The main goal of this paper is to demonstrate how our theory works in a reasonable model. We will also show, how can we semantically verify validity of several examples of generalized intermediate syllogisms.

In this paper, we continue development of the formal theory of \emph{intermediate quantifiers} (expressions such as \emph{most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of}). The theory is a fuzzy-logic formalization of the concept introduced by P. L. Peterson in his book. The main goal of this paper is to demonstrate how our theory works in a reasonable model. We will also show, how can we semantically verify validity of several examples of generalized intermediate syllogisms.