Linguistics and Philosophy

, Volume 28, Issue 4, pp 473–504 | Cite as

Sense and the Computation of Reference



The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization.


Artificial Intelligence Logic Program Computational Linguistic Liar Paradox Light Formalization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andrews, P. 1971‘Resolution in Type Theory’.Journal of Symbolic Logic36414432Google Scholar
  2. Apt, K. 1990‘Introduction to Logic Programming’Leeuwen, J. eds. Handbook of Theoretical Computer Science Vol. B.ElsevierAmsterdam495574Google Scholar
  3. Barwise, J. 1997‘Information and Impossibilities’.Notre Dame Journal of Formal Logic38488515CrossRefGoogle Scholar
  4. Barwise, J., Etchemendy, J. 1987The Liar: An Essay on Truth and CircularityOxford University PressNew YorkGoogle Scholar
  5. Benzmüller C., Brown C.E., Kohlhase M. (2004) ‘Higher Order Semantics and Extensionality’. Journal of Symbolic Logic 69, (to appear).Google Scholar
  6. Blackburn P., Bos J., Striegnitz K. (2001) Learn Prolog Now! Scholar
  7. Carnap, R. 1947Meaning and NecessityChicago UPChicagoGoogle Scholar
  8. Chierchia, G., Turner, R. 1988‘Semantics and Property Theory’Linguistics and Philosophy11261302CrossRefGoogle Scholar
  9. Church, A. 1940‘A Formulation of the Simple Theory of Types’Journal of Symbolic Logic55668Google Scholar
  10. Cresswell, M. 1972‘Intensional Logics and Logical Truth’Journal of Philosophical Logic1215CrossRefGoogle Scholar
  11. Cresswell, M. 1985Structured MeaningsMIT PressCambridge, MAGoogle Scholar
  12. Dowek, G. 2001‘Higher-Order Unification and Matching’Robinson, A.Voronkov, A. eds. Handbook of Automated Reasoning.ElsevierAmsterdam10091062Google Scholar
  13. Dummett, M. 1978Truth and Other EnigmasDuckworthLondonGoogle Scholar
  14. Fitting, M. 2002Types, Tableaus, and Gödels GodKluwer Academic PublishersDordrechtGoogle Scholar
  15. Fox, C., Lappin, S. 2001‘A Framework for the Hyperintensional Semantics of Natural Language with Two Implementations’De Groote, P.Morrill, G.Retoré, C. eds. Logical Aspects of Computational Linguistics.Springer-VerlagBerlin175192Google Scholar
  16. Fox, C., Lappin S., and C. Pollard: (2002), ‘A Higher-order Fine-grained Logic for Intensional Semantics’, in Alberti G., Balough K., and P. Dekker (eds.), Proceedings of the Seventh Symposium for Logic and Language, pp. 37–46, Pecs, Hungary.Google Scholar
  17. Goldfarb, W. 1981‘The Undecidability of the Second-order Unification Problem’Theoretical Computer Science13225230CrossRefGoogle Scholar
  18. Hintikka, J. 1975‘Impossible Possible Worlds Vindicated’Journal of Philosophical Logic4475484CrossRefGoogle Scholar
  19. Huet, G. 1973‘The Undecidability of Unification in Third-Order Logic’Information and Control22257267CrossRefGoogle Scholar
  20. Kripke, S. 1975‘Outline of a Theory of Truth’Journal of Philosophy72690716Google Scholar
  21. Lappin, S. and C. Pollard: (2000), ‘Strategies for Hyperintensional Semantics’. ms.Google Scholar
  22. Lewis, D. 1972‘General Semantics’Davidson, D.Harman, G. eds. Semantics of Natural Language.ReidelDordrecht169218Google Scholar
  23. Miller, D. 1991‘A Logic Programming Language with Lambda-abstraction, Function Variables, and Simple Unification’.Journal of Logic and Computation1497536Google Scholar
  24. Montague, R.: (1970), ‘Universal Grammar’, in Formal Philosophy, pp. 222–246, Yale University Press, New Haven.Google Scholar
  25. Montague R.: (1973), ‘The Proper Treatment of Quantification in Ordinary English’, in Formal Philosophy, pp. 247–270, Yale University Press, New Haven.Google Scholar
  26. Moschovakis, Y.: (1994), ‘Sense and Denotation as Algorithm and Value’, in Logic Colloquium ’90 (Helsinki 1990), Vol. 2 of Lecture Notes in Logic, pp. 210–249, Springer, Berlin.Google Scholar
  27. Moschovakis, Y.: (2003), ‘A Logical Calculus of Meaning and Synonymy’, Corrected and edited notes for a course in NASSLLI 2003.Google Scholar
  28. Muskens, R. 1991‘Hyperfine-Grained Meanings in Classical Logic’Logique et Analyse133/134159176Google Scholar
  29. Muskens, R. 2005‘Higher Order Modal Logic’Blackburn, P.Benthem, J.Wolter, F. eds. Handbook of Modal Logic, Studies in Logic and Practical Reasoning.ElsevierDordrecht(to appear)Google Scholar
  30. Prawitz, D. 1968‘Hauptsatz for Higher Order Logic’Journal of Symbolic Logic33452457Google Scholar
  31. Rantala, V. 1982‘Quantified Modal Logic: Non-normal Worlds and Propositional Attitudes’Studia Logica414165CrossRefGoogle Scholar
  32. Takahashi, M. 1967‘A Proof of Cut-elimination Theorem in Simple Type Theory’Journal of the Mathematical Society of Japan19399410Google Scholar
  33. Thomason, R. 1980‘A Model Theory for Propositional Attitudes’Linguistics and Philosophy44770CrossRefGoogle Scholar
  34. Tichý, P. 1988The Foundations of Frege’s LogicDe GruyterBerlinGoogle Scholar
  35. Turner, R. 1987‘A Theory of Properties’Journal of Symbolic Logic52455472Google Scholar
  36. van Lambalgen, M. and F. Hamm: (2003), ‘Moschovakis’ Notion of Meaning as Applied to Linguistics’, in M. Baaz and J. Krajicek (eds.), Logic Colloquium ’01, ASL Lecture Notes in Logic.Google Scholar
  37. Zalta, E. 1997‘A Classically-Based Theory of Impossible Worlds’Notre Dame Journal of Formal Logic38640660CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of LinguisticsTilburg UniversityThe Netherlands

Personalised recommendations