Fuzzy type theory; Aristotle's square of opposition; Generalized complete square of opposition;

We continue development of the formal theory of intermediate quantifiers. The latter are expressions of natural language such as ``most'', ``many'', ``few'', etc. In the previous paper, we demonstrated that a generalized complete square of opposition with intermediate quantifiers can be modeled in a special theory of higher-order fuzzy logic. In this paper we extended the square by new intermediate quantifier ``more than half''. Furthermore, we introduced general principle for introduction new intermediate quantifiers and proved that the generalized the square of opposition works with them accordingly. Because our results are proved syntactically, they hold in arbitrary model and so, our theory has great potential for various kinds of applications.

We continue development of the formal theory of intermediate quantifiers. The latter are expressions of natural language such as ``most'', ``many'', ``few'', etc. In the previous paper, we demonstrated that a generalized complete square of opposition with intermediate quantifiers can be modeled in a special theory of higher-order fuzzy logic. In this paper we extended the square by new intermediate quantifier ``more than half''. Furthermore, we introduced general principle for introduction new intermediate quantifiers and proved that the generalized the square of opposition works with them accordingly. Because our results are proved syntactically, they hold in arbitrary model and so, our theory has great potential for various kinds of applications.