A proof-theoretic semantics for contextual domain restriction

Abstract

The paper presents a proof-theoretic semantics account of contextual domain restriction for quantified sentences in a fragment of English. First, the technique is exemplified in the more familiar first-order logic, and in its restricted quantification variant. Then, a proof-theoretic semantics for the NL fragment is reviewed, and extended to handling contextual domain restriction. The paper addresses both the descriptive facet of the problem, deriving meaning relative to a context, as well as the fundamental aspect, defining explicitly a context (suitable for quantifier domain restriction), and specifying what it is about such a context that brings about the variation of meaning due to it.

The paper argues for the following principle: The context incorporation principle (CIP): For every quantified sentence S depending on a context c, there exists a sentence S', the meaning of which is independent of c, s.t. the contextually restricted meaning of S is equal to the  meaning of S'. Thus, the effect of a context can always be *internalized*. The current model-theoretic accounts of contextual domain restriction do not satisfy CIP, in that they imply intersection of some extension with an *arbitrary* subset of the domain, that need not be the denotation of any NL-expression.