Skip to main content

Agnostic Possible Worlds Semantics

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7351)

Abstract

Working within standard classical higher-order logic, we propose a possible worlds semantics (PWS) which combines the simplicity of the familiar Montague semantics (MS), in which propositions are sets of worlds, with the fine-grainedness of the older but less well-known tractarian semantics (TS) of Wittgenstein and C.I. Lewis, wherein worlds are maximal consistent sets of propositions. The proposed agnostic PWS makes neither montagovian nor tractarian ontological commitments, but is consistent with (and easily extensible to) either alternative (among many others). It is technically straightforward and, we believe, capable of everything linguists need PWS to do, such as interfacing with a logical grammar and serving as a basis for dynamic semantics.

Keywords

  • propositions
  • possible worlds
  • maximal consistent sets
  • Montague semantics
  • tractarian semantics

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, R.: Theories of actuality. Noûs 8, 211–231 (1974)

    CrossRef  Google Scholar 

  2. Bolzano, B.: Theory of Science. Translation of Wissenschaftslehre, 1837, edited and translated by R. George. University of California Press, Berkeley (1972)

    Google Scholar 

  3. Bolzano, B.: Theory of Science. Translation of Wissenschaftslehre, 1837, edited by J. Berg and translated by B. Terrell. D. Reidel Publishing Company, Berkeley and Los Angeles, Dordrecht (1973)

    Google Scholar 

  4. Carnap, R.: Meaning and Necessity. University of Chicago Press, Chicago (1947)

    MATH  Google Scholar 

  5. Church, A.: A formulation of the simple theory of types. Journal of Symbolic Logic 5, 56–68 (1940)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Cresswell, M.: Structured Meanings. MIT Press (1985)

    Google Scholar 

  7. Dowty, D., Wall, R., Peters, S.: Introduction to Montague Semantics. D. Reidel Publishing Company, Dordreht (1981)

    Google Scholar 

  8. Frege, G.: On sense and reference. Translation of Über Sinn und Bedeutung, 1892. In: Geach, P., Black, M. (eds.) Translations from the Philosophical Writings of Gottlob Frege, 3rd edn. Blackwell, Oxford (1980)

    Google Scholar 

  9. Gallin, D.: Intensional and Higher Order Modal Logic. North-Holland, Amsterdam (1975)

    MATH  Google Scholar 

  10. Henkin, L.: Completeness in the theory of types. Journal of Symbolic Logic 15, 81–91 (1950)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Jónsson, B., Tarski, A.: Boolean algebras with operators, part 1. American Journal of Mathematics 73(4), 891–939 (1951)

    CrossRef  MathSciNet  Google Scholar 

  12. King, J.: Structured propositions and sentence structure. Journal of Philosophical Logic 25, 495–521 (1996)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. King, J.: The Nature and Structure of Content. Oxford University Press, Oxford (2007)

    CrossRef  Google Scholar 

  14. Kripke, S.: A completeness theorem in modal logic. Journal of Symbolic Logic 24, 1–14 (1959)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Kripke, S.: Semantic analysis of modal logic I: normal modal propositional calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9, 67–96 (1963)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Lambek, J., Scott, P.: Introduction to Higher-Order Categorical Logic. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  17. Lewis, C.I.: Facts, systems, and the unity of the world. Journal of Philosophy 20, 141–151 (1923)

    CrossRef  MATH  Google Scholar 

  18. Lewis, C.I.: The modes of meaning. Philosophy and Phenomenological Reseach 4(2), 236–250 (1943)

    CrossRef  Google Scholar 

  19. Lewis, D.: General semantics. Synthese 22, 18–67 (1970)

    CrossRef  MATH  Google Scholar 

  20. Lycan, W.: The trouble with possible worlds. In: Loux, M. (ed.) The Possible and the Actual, pp. 274–316. Cornell University Press, Ithaca (1979)

    Google Scholar 

  21. Montague, R.: The proper treatment of quantification in ordinary English. In: Thomason, R. (ed.) Formal Philosophy: Selected Papers of Richard Montague, pp. 247–270. Yale University Press, New Haven (1974)

    Google Scholar 

  22. Muskens, R.: Sense and the computation of reference. Linguistics and Philosophy 28(4), 473–504 (2005)

    CrossRef  Google Scholar 

  23. Plantinga, A.: The Nature of Necesiity. Clarendon, Oxford (1974)

    Google Scholar 

  24. Plummer, A., Pollard, C.: A flexible higher order framework for possible-worlds semantics (in preparation)

    Google Scholar 

  25. Pollard, C.: Hyperintensions. Journal of Logic and Computation 18(2), 257–282 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. Pollard, C.: Are (Linguists’) Propositions (Topos) Propositions? In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS (LNAI), vol. 6736, pp. 205–218. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  27. Soames, S.: Direct reference, propositional attitudes, and semantic content. Philosophical Topics 15, 47–87 (1987)

    Google Scholar 

  28. Stalnaker, R.: Propositions. In: MacKay, A.F., Merril, D.D. (eds.) Issues in the Philosophy of Language, pp. 79–91. Yale University Press, New Haven (1976)

    Google Scholar 

  29. Stalnaker, R.: Inquiry. Bradford Books/MIT Press, Cambridge (1984)

    Google Scholar 

  30. Stone, M.: The theory of representation for boolean algebras. Transactions of the American Mathematical Society 40, 37–111 (1936)

    MathSciNet  Google Scholar 

  31. Thomason, R.: A model theory for propositional attitudes. Linguistics and Philosophy 4, 47–70 (1980)

    CrossRef  Google Scholar 

  32. Wittgenstein, L.: Tractatus Logico-Philosophicus. Translation by D.F. Pears and B.F. McGuinness of Logisch-Philosophische Abhandlung in Annalen der Naturphilosophie, 1921. Routledge & Kegan Paul, London and Henley (1961)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Plummer, A., Pollard, C. (2012). Agnostic Possible Worlds Semantics. In: Béchet, D., Dikovsky, A. (eds) Logical Aspects of Computational Linguistics. LACL 2012. Lecture Notes in Computer Science, vol 7351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31262-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31262-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31261-8

  • Online ISBN: 978-3-642-31262-5

  • eBook Packages: Computer ScienceComputer Science (R0)