Agnostic Possible Worlds Semantics

  • Andrew Plummer
  • Carl Pollard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7351)


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.


propositions possible worlds maximal consistent sets Montague semantics tractarian semantics 


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  1. [1974]
    Adams, R.: Theories of actuality. Noûs 8, 211–231 (1974)CrossRefGoogle Scholar
  2. [1837]
    Bolzano, B.: Theory of Science. Translation of Wissenschaftslehre, 1837, edited and translated by R. George. University of California Press, Berkeley (1972)Google Scholar
  3. [1837]
    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. [1947]
    Carnap, R.: Meaning and Necessity. University of Chicago Press, Chicago (1947)zbMATHGoogle Scholar
  5. [1940]
    Church, A.: A formulation of the simple theory of types. Journal of Symbolic Logic 5, 56–68 (1940)MathSciNetzbMATHCrossRefGoogle Scholar
  6. [1985]
    Cresswell, M.: Structured Meanings. MIT Press (1985)Google Scholar
  7. [1981]
    Dowty, D., Wall, R., Peters, S.: Introduction to Montague Semantics. D. Reidel Publishing Company, Dordreht (1981)Google Scholar
  8. [1892]
    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. [1975]
    Gallin, D.: Intensional and Higher Order Modal Logic. North-Holland, Amsterdam (1975)zbMATHGoogle Scholar
  10. [1950]
    Henkin, L.: Completeness in the theory of types. Journal of Symbolic Logic 15, 81–91 (1950)MathSciNetzbMATHCrossRefGoogle Scholar
  11. [1951]
    Jónsson, B., Tarski, A.: Boolean algebras with operators, part 1. American Journal of Mathematics 73(4), 891–939 (1951)MathSciNetCrossRefGoogle Scholar
  12. [1996]
    King, J.: Structured propositions and sentence structure. Journal of Philosophical Logic 25, 495–521 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  13. [2007]
    King, J.: The Nature and Structure of Content. Oxford University Press, Oxford (2007)CrossRefGoogle Scholar
  14. [1959]
    Kripke, S.: A completeness theorem in modal logic. Journal of Symbolic Logic 24, 1–14 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  15. [1963]
    Kripke, S.: Semantic analysis of modal logic I: normal modal propositional calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9, 67–96 (1963)MathSciNetzbMATHCrossRefGoogle Scholar
  16. [1986]
    Lambek, J., Scott, P.: Introduction to Higher-Order Categorical Logic. Cambridge University Press, Cambridge (1986)zbMATHGoogle Scholar
  17. [1923]
    Lewis, C.I.: Facts, systems, and the unity of the world. Journal of Philosophy 20, 141–151 (1923)zbMATHCrossRefGoogle Scholar
  18. [1943]
    Lewis, C.I.: The modes of meaning. Philosophy and Phenomenological Reseach 4(2), 236–250 (1943)CrossRefGoogle Scholar
  19. [1970]
    Lewis, D.: General semantics. Synthese 22, 18–67 (1970)zbMATHCrossRefGoogle Scholar
  20. [1979]
    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. [1974]
    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. [2005]
    Muskens, R.: Sense and the computation of reference. Linguistics and Philosophy 28(4), 473–504 (2005)CrossRefGoogle Scholar
  23. [1974]
    Plantinga, A.: The Nature of Necesiity. Clarendon, Oxford (1974)Google Scholar
  24. [in prep.]
    Plummer, A., Pollard, C.: A flexible higher order framework for possible-worlds semantics (in preparation)Google Scholar
  25. [2008]
    Pollard, C.: Hyperintensions. Journal of Logic and Computation 18(2), 257–282 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  26. [2011]
    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)CrossRefGoogle Scholar
  27. [1987]
    Soames, S.: Direct reference, propositional attitudes, and semantic content. Philosophical Topics 15, 47–87 (1987)Google Scholar
  28. [1976]
    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. [1984]
    Stalnaker, R.: Inquiry. Bradford Books/MIT Press, Cambridge (1984)Google Scholar
  30. [1936]
    Stone, M.: The theory of representation for boolean algebras. Transactions of the American Mathematical Society 40, 37–111 (1936)MathSciNetGoogle Scholar
  31. [1980]
    Thomason, R.: A model theory for propositional attitudes. Linguistics and Philosophy 4, 47–70 (1980)CrossRefGoogle Scholar
  32. [1921]
    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

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew Plummer
    • 1
  • Carl Pollard
    • 1
  1. 1.The Ohio State UniversityColumbusUSA

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