Natural Language Semantics

, Volume 10, Issue 3, pp 211–242 | Cite as

Continuations and the Nature of Quantification

  • Chris Barker

Abstract

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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REFERENCES

  1. Barker, C.: 2001, 'Integrity: A Syntactic Constraint on Quantificational Scoping', in K. Megerdoomian and L. A. Bar-el (eds.), Proceedings of WCCFL 20, pp. 101–114. Cascadilla Press, Somerville, Mass.Google Scholar
  2. Barwise, J. and R. Cooper: 1981, 'Generalized Quantifiers in Natural Language', Linguistics and Philosophy 4, 159–200.Google Scholar
  3. Chierchia, G.: 1995, Dynamics of Meaning, the University of Chicago Press, Chicago.Google Scholar
  4. Chierchia, G. and S. McConnell-Ginet: 1990, Introduction to Formal Semantics, MIT Press, Cambridge, Mass.Google Scholar
  5. Crouch, R.: 1999, 'Ellipsis and Glue Languages', in S. Lappin and E. Benmamoun (eds.), Fragments: Studies in Ellipsis and Gapping, pp. 32–67. Oxford University Press, Oxford.Google Scholar
  6. Dalrymple, M., J. Lamping, F. Pereira, and V. Saraswat: 1997, 'Quantifiers, Anaphora, and Intensionality', Journal of Logic, Language, and Information 6, 219–273.Google Scholar
  7. Danvy, O. and C. A. Talcott: 1998, 'Introduction (to a special issue on continuations)', Higher-Order and Symbolic Computation 11(2), 115–116.Google Scholar
  8. Dever, J.: 1999, 'Compositionality as Methodology', Linguistics and Philosophy 22, 311–326.Google Scholar
  9. Egli, U. and K. Heusinger (eds.): 1995, Choice Functions in Natural Language Semantics, Arbeitspapier Nr. 71, Fachgruppe Sprachwissenschaft, Universität Konstanz.Google Scholar
  10. de Groote, P.: 2001, 'Continuations, Type Raising, and Classical Logic', in R. van Rooy and M. Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium, pp. 97–101. Institute for Logic, Language and Computation, Universiteit van Amsterdam.Google Scholar
  11. Heim, I. and A. Kratzer: 1998, Semantics in Generative Grammar, Blackwell, Oxford.Google Scholar
  12. Hendriks, H.: 1988, 'Type Change in Semantics: The Scope of Quantification and Coordination', in E. Klein and J. van Benthem (eds.), Categories, Polymorphism and Unification, pp. 96–119. ITLI, Amsterdam.Google Scholar
  13. Hendriks, H.: 1993, Studied Flexibility, ILLC Dissertation Series, Amsterdam.Google Scholar
  14. Jacobson, P.: 1999, 'Towards a Variable Free Semantics', Linguistics and Philosophy 22, 117–184.Google Scholar
  15. Janssen, T.: 1986, Foundations and Applications of Montague Grammar, Part I: Philosophy, Framework, Computer Science (CWI Tract 19), Center of Mathematics and Computer Science, Amsterdam.Google Scholar
  16. Keenan, E.: 1987, 'Semantic Case Theory', in J. Groenendijk, M. Stokhof, and P. Veltmann (eds.), Proceedings of the 6th Amsterdam Colloquium, pp. 109–132. Institute for Logic, Language and Computation, Universiteit van Amsterdam.Google Scholar
  17. Kelsey, R., W. Clinger, and J. Rees (eds.): 1998, 'The Revised5 Report on the Algorithmic Language Scheme', Higher-Order and Symbolic Computation 11, 7–105.Google Scholar
  18. Kratzer, A.: 1998, 'Scope or Pseudoscope? Are There Wide-Scope Indefinites?', in S. Rothstein (ed.), Events and Grammar, pp. 163–196. Kluwer, Dordrecht.Google Scholar
  19. May, R.: 1985, Logical Form: Its Structure and Derivation, MIT Press, Cambridge, Mass.Google Scholar
  20. Meyer, A. R. and M. Wand: 1985, 'Continuation Semantics in Typed Lambda-Calculi (summary)', in R. Parikh (ed.), Logics of Programs-Proceedings, pp. 219–224. Springer-Verlag, New York.Google Scholar
  21. Montague, R.: 1973, 'The Proper Treatment of Quantification in English', in J. Hintikka, J. Moravcsik, and P. Suppes (eds.), Approaches to Natural Language: Proceedings of the 1970 Stanford Workshop on Grammar and Semantics, pp. 221–242. Reidel, Dordrecht. Also in R. Thomason (ed.), Formal Philosophy: Selected Papers of Richard Montague, pp. 247–270. Yale University Press, New Haven, Conn., 1974.Google Scholar
  22. Partee, B. H.: 1987, 'Noun Phrase Interpretation and Type-Shifting Principles', in J. Groenendijk, D. de Jongh, and M. Stokhof (eds.), Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers, pp. 115–143. Foris, Dordrecht.Google Scholar
  23. Partee, B. H. and M. Rooth: 1983, 'Generalized Conjunction and Type Ambiguity', in R. Bäuerle, C. Schwarze, and A. von Stechow (eds.), Meaning, Use, and Interpretation of Language, pp. 361–383. Walter de Gruyter, Berlin.Google Scholar
  24. Pelletier, F. J.: 1994, 'The Principle of Semantic Compositionality', Topoi 13, 11–24.Google Scholar
  25. Plotkin, G. D.: 1975, 'Call-by-Name, Call-by-Value and the Lambda-Calculus', Theoretical Computer Science 1, 125–159.Google Scholar
  26. Reinhart, T.: 1979, 'Syntactic Domains for Semantic Rules', in F. Guenthner and S. J. Schmidt (eds.), Formal Semantics and Pragmatics for Natural Language, pp. 107–130. Reidel, Dordrecht.Google Scholar
  27. Reynolds, J. C.: 1993, 'The Discoveries of Continuations', Lisp and Symbolic Computation 6, 233–247.Google Scholar
  28. Shan, C-C.: 2002, 'A Continuation Semantics of Interrogatives that Accounts for Baker's Ambiguity', in B. Jackson (ed.), Proceedings of SALT XII, Cornell University Press, Ithaca, N.Y.Google Scholar
  29. Steedman, M.: 2000, The Syntactic Process, MIT Press, Cambridge, Mass.Google Scholar
  30. Westerstå hl, D.: 1998, 'On Mathematical Proofs of the Vacuity of Compositionality', Linguistics and Philosophy 21, 635–643.Google Scholar
  31. Zadrozny, W.: 1994, 'From Compositional to Systematic Semantics', Linguistics and Philosophy 17, 329–342.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Chris Barker
    • 1
  1. 1.Department of LinguisticsUniversity of California, San DiegoLa JollaUSA

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