Intermediate Syllogisms in Fuzzy Natural Logic

Abstract

The goal of this paper is twofold: first, we give overview of the results of one part of the Fuzzy Natural Logic - the formal theory of intermediate quantifiers and syllogisms based on them. We present 105 valid basic syllogisms and show that for the proof of validity of all of them, we need to prove validity of only few of them so that validity of the other ones immediately follows. In the second part of the paper, we focused on conditions under which non-trivial intermediate syllogisms are valid. The latter are syllogisms which contain two or even three general intermediate quantifiers (not equal to any of $\forall$ or $\exists$).