Formal theory of quantifiers in natural language and their syllogisms

Quantifiers occur in natural language as expressions using which we quantify a number of some objects in a given universe. A special class of them are intermediate quantifiers, for example, many, most, almost all, a few, a little and others. A detailed elaboration of the latter is provided in Peterson (2000). Their formal theory was established in (Novák, 2008). According to it, intermediate quantifiers form a special theory TIQ of higher-order fuzzy logic (fuzzy type theory) (FTT) with models based on the standard Łukasiewicz MVΔ-algebra.