Continuations and the Nature of Quantification

Natural Language Semantics 10 (3):211-242 (2002)
This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement and scope ambiguity. To prove this claim, I exhibit a simple finite context-free grammar with a strictly compositional semantics in which quantificational NPs are interpreted in situ but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or similar mechanisms used in many recent HPSG, Categorial, or Type-logical treatments), and no need for type-shifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either type-shifting or type polymorphism. Compositionality issues are discussed in some detail
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DOI 10.1023/A:1022183511876
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Parasitic Scope.Chris Barker - 2007 - Linguistics and Philosophy 30 (4):407-444.
Indefinites and Intentional Identity.Samuel Cumming - 2014 - Philosophical Studies 168 (2):371-395.
Types as Graphs: Continuations in Type Logical Grammar. [REVIEW]Chris Barker & Chung-chieh Shan - 2006 - Journal of Logic, Language and Information 15 (4):331-370.

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