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

TL;DR

This paper introduces a type-theoretic logical framework for interpreting generic noun phrases with 'most', modeling their meanings as specimens akin to stereotypes, and diverging from traditional untyped approaches.

Contribution

It proposes a novel type-theoretic approach incorporating Hilbert epsilon-calculus and medieval philosophy to analyze generic noun phrases, extending current lexical semantics models.

Findings

Model effectively interprets generic noun phrases with 'most'

Differentiates semantic and pragmatic components via typing

Aligns with ongoing lexical semantics research

Abstract

This paper proposes 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 significantly from the dominant Fregean view with a single untyped universe. Indeed, our proposal adopts type theory with some hints from Hilbert \epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined.