A proof-theoretic semantics for contextual domain restriction

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.