Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

We propose a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier “most”. We call these generics “specimens” and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can thereafter be interpreted in your favourite models. To do so, we depart from the Fregean view with a single untyped universe and we adopt a type theory with some hints from Hilbert ε-calculus and from medieval philosophy. Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics by Asher, Luo and us. Our model applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. Thus, in the minimalism-contextualism debate, our type theoretical view is that terms encode the purely semantic meaning while types are pragmatically determined.