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.
Highlights
The paper presents a proof-theoretic semantics account of contextual domain restriction for quantified sentences in a fragment of English
The paper argues for the following principle: 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′
The purpose of this paper is to provide a proof-theoretic semantics (PTS)1 for a special case of the general context dependence problem, namely quantifier domain restriction (QDR)
Summary
222), for example, admit that they avoid giving a formal characterization of the notion of a context They just stipulate (for the QDR-problem) a certain marking in the syntactic tree (the logical form) that interfaces in a certain way with a context, and provide a description of the way this marking participates in meaning derivations (by intersecting the extension of the head noun with a set “pointed to” by the above mentioned marking). It is important to realise what is not the semantic problem discussed here, namely the determination of which is the right context for any given token of a contextually dependent meaning of a sentence The latter issue is always determined by extra-linguistic means, independently of whether MTS or PTS are employed as the theory of meaning. I do not take this interpretation of (1.8) as a meaning of (1.8) in any sense of ‘meaning’ that semantics is concerned with
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