Advertisement

Relating Intensional Semantic Theories: Established Methods and Surprising Results

  • Kristina Liefke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10838)

Abstract

Formal semantics comprises a plethora of theories which interpret natural language through the use of different ontological primitives (e.g. individuals, possible worlds, situations, propositions, individual concepts). The ontological relations between these theories are, today, still largely unexplored. In particular, it remains an open question whether the primitives from some of these theories can be coded in terms of objects from other theories, or whether the ontologies of some theories can even be reduced to the ontologies of other, ontologically poorer, theories. This paper answers the above questions for a proper subset of formal semantic theories which are designed for the interpretation of doxastic attitude reports. The paper formalizes some ontological relations between these theories that are only suggested (but are not made explicit) in the literature, and identifies several new relations. The paper uses these relations to show that ‘the’ unifying theory for attitude reports is, in fact, a class of theories whose members are equivalent up to coding.

Keywords

Interpretation of doxastic attitude reports (Hyper-)Intensional semantics Ontological relations Unification Reduction 

References

  1. 1.
    Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logics, vol. 2. Springer, Dordrecht (1977).  https://doi.org/10.1007/978-94-010-1161-7_2CrossRefGoogle Scholar
  2. 2.
    Blamey, S.: Partial logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 5. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  3. 3.
    Carnap, R.: Meaning and Necessity: A Study in Semantics and Modal Logic. University of Chicago Press, Chicago (1988)zbMATHGoogle Scholar
  4. 4.
    Chierchia, G., Turner, R.: Semantics and property theory. Linguist. Philos. 11(3), 261–302 (1988)CrossRefGoogle Scholar
  5. 5.
    Church, A.: A formulation of the simple theory of types. J. Symb. Log. 5(2), 56–68 (1940)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cresswell, M.J.: Logics and Languages. Methuen Young Books, London (1973)Google Scholar
  7. 7.
    Cresswell, M.J.: Hyperintensional logic. Stud. Logica 34(1), 25–38 (1975)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cresswell, M.J.: Structured Meanings. MIT Press, Cambridge (1985)Google Scholar
  9. 9.
    Cresswell, M.J.: Entities and Indices. Kluwer Academic Publishers, Dordrecht (1990)CrossRefGoogle Scholar
  10. 10.
    Fox, C., Lappin, S., Pollard, C.: A higher-order fine-grained logic for intensional semantics. In: Proceedings of the 7th International Symposium on Logic and Language, pp. 37–46 (2002)Google Scholar
  11. 11.
    Friedman, J., Warren, D.: Lambda normal forms in an intensional logic for English. Stud. Logica 39, 311–324 (1980)CrossRefGoogle Scholar
  12. 12.
    Gallin, D.: Intensional and Higher-Order Modal Logic with Applications to Montague Semantics. North Holland, Elsevier (1975)CrossRefGoogle Scholar
  13. 13.
    Henkin, L.: Completeness in the theory of types. J. Symb. Log. 15, 81–91 (1950)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hintikka, J.: Impossible possible worlds vindicated. J. Philos. Log. 4(4), 475–484 (1975)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kaplan, D.: How to Russell a Frege-Church. J. Philos. 72, 716–29 (1975)CrossRefGoogle Scholar
  16. 16.
    Kleene, S.C.: Countable functionals. In: Heyting, A. (ed.) Constructivity in Mathematics, North-Holland, pp. 81–100 (1959)Google Scholar
  17. 17.
    Kreisel, G.: Interpretation of analysis by means of constructive functionals of finite types. In: Constructivity in Mathematics, pp. 101–128 (1959)Google Scholar
  18. 18.
    Kripke, S.A.: Naming and Necessity. Harvard University Press, Cambridge (1980)Google Scholar
  19. 19.
    Kusumoto, K.: On the quantification over times in natural language. Nat. Lang. Semant. 13(4), 317–357 (2005)CrossRefGoogle Scholar
  20. 20.
    Lappin, S.: Curry typing, polymorphism, and fine-grained intensionality. In: Lappin, S., Fox, C. (eds.) Handbook of Contemporary Semantic Theory, 2nd edn, pp. 408–428. Wiley-Blackwell (2015)CrossRefGoogle Scholar
  21. 21.
    Lewis, D.: General semantics. Synthese 22(1-2), 18–67 (1970)CrossRefGoogle Scholar
  22. 22.
    Liefke, K.: Codability and robustness in formal natural language semantics. In: Murata, T., Mineshima, K., Bekki, D. (eds.) JSAI-isAI 2014. LNCS (LNAI), vol. 9067, pp. 6–22. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48119-6_2CrossRefGoogle Scholar
  23. 23.
    Liefke, K.: A compositional pluralist semantics for extensional and attitude verbs. In: Löbner, S., et al. (eds.) Language, Cognition, and Mind. Selected Revised Papers from Cognitive Structures 16. Springer, Heidelberg (forthcoming)Google Scholar
  24. 24.
    Liefke, K., Sanders, S.: A computable solution to Partee’s temperature puzzle. In: Amblard, M., de Groote, P., Pogodalla, S., Retoré, C. (eds.) LACL 2016. LNCS, vol. 10054, pp. 175–190. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53826-5_11CrossRefGoogle Scholar
  25. 25.
    Montague, R.: English as a formal language. In: Thomason, R.H. (ed.) Formal Philosophy. Selected Papers of Richard Montague, Yale UP, pp. 188–221 (1976, 1970a)Google Scholar
  26. 26.
    Montague, R.: Universal grammar. In: Thomason, R.H. (ed.) Formal Philosophy. Selected Papers of Richard Montague, pp. 222–246 (1976, 1970b)Google Scholar
  27. 27.
    Montague, R.: The proper treatment of quantification in ordinary English. In: Thomason, R.H. (ed.) Formal Philosophy. Selected Papers of Richard Montague, pp. 247–270 (1976, 1973)Google Scholar
  28. 28.
    Moschovakis, Y.: A logical calculus of meaning and synonymy. Linguist. Philos. 29(1), 27–89 (2006)CrossRefGoogle Scholar
  29. 29.
    Muskens, R.: Meaning and Partiality. CSLI Publications, Stanford (1995)Google Scholar
  30. 30.
    Muskens, R.: Sense and the computation of reference. Linguist. Philos. 28(4), 473–504 (2005)CrossRefGoogle Scholar
  31. 31.
    Pollard, C.: Hyperintensions. J. Log. Comput. 18(2), 257–282 (2008)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Pollard, C.: Agnostic hyperintensional semantics. Synthese 192(3), 535–562 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Schlenker, P.: Ontological symmetry in language: a brief manifesto. Mind Lang. 21(4), 504–539 (2006)CrossRefGoogle Scholar
  34. 34.
    Stephenson, T.: Vivid attitudes: centered situations in the semantics of ‘remember’ and ‘imagine’. Semant. Linguist. Theor. 20, 147–160 (2010)CrossRefGoogle Scholar
  35. 35.
    Stone, M.H.: The theory of representation for Boolean algebras. Trans. Am. Math. Soc. 40(1), 37–111 (1936)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Thomason, R.H.: A model theory for the propositional attitudes. Linguist. Philos. 4(1), 47–70 (1980)CrossRefGoogle Scholar
  37. 37.
    Turner, R.: Types. In: Benthem, J.V., et al. (eds.) Handbook of Logic and Language. Elsevier (1997)CrossRefGoogle Scholar
  38. 38.
    Zalta, E.N.: A classically-based theory of impossible worlds. Notre Dame J. Formal Log. 38(4), 640–660 (1997)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Zimmermann, T.E.: Intensional logic and two-sorted type theory. J. Symb. Log. 54(1), 65–77 (1989)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for LinguisticsGoethe University FrankfurtFrankfurt am MainGermany

Personalised recommendations