Journal of Logic, Language and Information

, Volume 7, Issue 4, pp 399–411 | Cite as

Categorial Inference and Modal Logic

  • Natasha Kurtonina
Article

Abstract

This paper establishes a connection between structure sensitive categorial inference and classical modal logic. The embedding theorems for non-associative Lambek Calculus and the whole class of its weak Sahlqvist extensions demonstrate that various resource sensitive regimes can be modelled within the framework of unimodal temporal logic. On the semantic side, this requires decomposition of the ternary accessibility relation to provide its correlation with standard binary Kripke frames and models.

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References

  1. Buszkowski, W., 1997, “Mathematical linguistics and proof theory,” pp. 683–736 in Handbook of Logic and Language, J. van Benthem and A. ter Meulen, eds., Amsterdam: North-Holland/Elsevier.Google Scholar
  2. Kandulski, M., 1988, “The non-associative Lambek calculus,” pp. 141–151 in Categorial Grammar, Linguistic and Literary Studies in Eastern Europe, Vol. 25, W. Buszkowski, W. Marciszewski, and J. van Benthem, eds., Amsterdam: John Benjamins.Google Scholar
  3. Kurtonina, N., 1995, “Frames and labels,” ILLC and OTS Dissertation Seiws, University of Amsterdam and Utrecht University.Google Scholar
  4. Kurtonina, N. and Moortgat, M., 1997, “Structural control,” pp. 75–115 in Specifying Syntactic Structures, P. Blackburn and M. de Rijke, eds., Stanford, CA: CSLI.Google Scholar
  5. Lambek, J., 1958, “The mathematics of sentence structure,” American Mathematical Monthly 65, 154–170.Google Scholar
  6. Moortgat, M., 1997, Categorial Type Logics. Handbook of Logic and Language, Amsterdam: Elsevier.Google Scholar
  7. Morrill, G., 1994, Type Logical Grammar. Categorial Logic of Signs, Dordrecht: Kluwer Academic Publishers.Google Scholar
  8. van Benthem, J., 1985, Modal Logic and Classical Logic, Naples: Bibliopolis.Google Scholar
  9. van Benthem, J., 1991, Language in Action. Categories, Lambdas, and Dynamic Logic, Studies in Logic, Amsterdam: North-Holland.Google Scholar
  10. van Benthem, J. and ter Meulen, A., eds., 1997, Handbook of Logic and Language, Amsterdam: North-Holland/Elsevier.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Natasha Kurtonina
    • 1
  1. 1.Institute for Research in Cognitive ScienceUniversity of PennsylvaniaPhiladelphiaU.S.A.

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