The analysis of the generalized square of opposition
نویسندگان
چکیده
In this paper, we continue the development of a formal theory of intermediate quantifiers (linguistic expressions such as “most”, “many”, “few”, “almost all”, etc.). In previous work, we demonstrated that 105 generalized syllogisms are valid in our theory. We turn our attention to another problem which is the analysis of the generalized Aristotelian square of opposition which, besides the classical quantifiers, is extended also by several selected intermediate quantifiers. We show that the expected relations can be well modeled in our theory. The formal theory of intermediate quantifiers is developed within a special higher-order fuzzy logic — Łukasiewicz fuzzy type theory.
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