Fuzzy type theory; Intermediate quantifiers; Generalized Aristotle's square of opposition; Generalized Peterson's square of opposition

In this contribution, we introduce formal theory on the basis of which we can analyze the generalized Aristotelian square of opposition, that, in addition to the classical quantifiers, can be extended by several selected intermediate quantifiers (for example, ``most'', ``many'', etc.). We show that the expected relations can be well modeled in our theory. Our analysis is motivated by Peterson's analysis as presented in his book, and our goal is to demonstrate that the proposed formal theory addresses well all of the problems that are encountered when considering intermediate quantifiers. It is also clear that the studied relations correspond to the proved generalized syllogisms.

Aristotelian square of opposition, that, in addition to the classical quantifiers, can be extended by several selected intermediate quantifiers (for example, ``most'', ``many'', etc.). We show that the expected relations can be well modeled in our theory. Our analysis is motivated by Peterson's analysis as presented in his book, and our goal is to demonstrate that the proposed formal theory addresses well all of the problems that are encountered when considering intermediate quantifiers. It is also clear that the studied relations correspond to the proved generalized syllogisms.