Fuzzy natural logic, generalized quantifiers, intermediate quantifiers, fuzzy type theory

This paper is a contribution to the formal theory of intermediate quantifiers (linguistic expressions such as most, few, most all, a lot of, many, a great deal of, a large part of, a smallpart of ). This concept informally introduced by Peterson was formalized in the frame of higher-order fuzzy logic by Nov´ak. We address the concept of measure, namely we introduce modifieddefinition providing its additivity and apply the theory to the intermediate quantifier ?Many?. We show that the ambiguous behavior of it can be also formally substantiated.