A formal theory of generalized intermediate syllogisms, Fuzzy Sets and Systems 186

This paper is a continuation of the formal theory of intermediate quantifiers (expressions such as most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of) introduced by Novák in [12]. The theory is a fuzzy-logic formalization of the concept introduced by Peterson in his book [17]. In this paper, we syntactically prove that 105 generalized Aristotle’s syllogism introduced in Peterson’s book are in our theory valid. At the same time, we also proved that various syllogisms listed there as invalid are invalid also in our theory. Therefore, we believe that our theory provides a reasonable mathematical model of the generalized syllogistics. Key words: Generalized quantifiers; intermediate quantifiers; fuzzy type theory; evaluative linguistic expressions; Aristotle’s syllogisms. 1