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Grammar specification in categorial logics and theorem proving

  • Saturnino F Luz-Filho
Session 9A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1104)

Abstract

This paper presents an application of automated theorem proving techniques to natural language processing, particularly to Categorial Grammar (CG) parsing. It describes the system LLKE, a labelled analytic tableau system which supports a framework for specification and proof for several calculi, starting with the Lambek calculus L, covering its substructural extensions such as LP, LPE, LPE, NL etc, and allowing for the implementation of modalities. The tableau expansion algorithms are presented and heuristics to improve their performance based on domain-specific knowledge are discussed along with comparisons of our system with other systems that implement categorial deduction.

Keywords

Mechanisms (semantic tableaux) and Applications (computational liguistics) 

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References

  1. 1.
    H. Andreka and S. Mikulas. Lambek calculus and its relational semantics: completeness and incompleteness. Journal of Logic, Language and Information, 3(1):1–37, 1994.Google Scholar
  2. 2.
    J. Barwise, D. Gabbay, and C. Hartonas. On the logic of information flow. Journal of the Interest Group in Pure and Applied Logic (IGPL), 3(1):7–50, 1995.Google Scholar
  3. 3.
    Johan van Benthem. The semantics of variety. In Wojciech Buszkowski, Witold Marciszewski, and Johan van Benthem, editors, Categorial Grammar, volume 25, chapter 6, pages 141–151. John Benjamins Publishing Company, Amsterdam, 1988.Google Scholar
  4. 4.
    S. A. Cook and R Reckhow. The relative efficiency of propositional proof systems. Journal of Symbolic Logic, pages 36–50, 1979.Google Scholar
  5. 5.
    Marcello D'Agostino and Dov Gabbay. A generalization of analytic deduction via labelled deductive systems I: Basic substructural logics. Journal of Automated Reasoning, 1994.Google Scholar
  6. 6.
    Marcello D'Agostino and Marco Mondadori. The taming of the cut. Journal of Logic and Computation, 4:285–319, 1994.Google Scholar
  7. 7.
    Nachum Dershowitz and Jean-Pierre Jouannaud. Rewrite systems. In Handbook of theoretical computer science, volume Vol.B Formal models and semantics, chapter 6, pages 245–320. The MIT Press: Cambridge, MA, 1990.Google Scholar
  8. 8.
    Melvin Fitting. First-order Logic and Automatic Theorem Proving. Texts and Monographs in Computer Science. Springer-Verlag, New York, 1990.Google Scholar
  9. 9.
    Dov M. Gabbay. LDS — Labelled Deductive Systems, volume 1 — foundations. Technical Report MPI-I-94-223, Max-Planck-Institut für Informatik, 1994.Google Scholar
  10. 10.
    Joachim Lambek. The mathematics of sentence structure. American Mathematical Monthly, 65:154–170, 1958.Google Scholar
  11. 11.
    Joachim Lambek. Categorial and categorical grammars. In Richard Oehrle et al., editor, Categorical Grammars and Natural Language Structures, pages 297–317. D. Reidel Publishing Company: Dordrecht, The Netherlands, 1988.Google Scholar
  12. 12.
    Joachim Lambek. Bilinear logic. In Advances in Linear Logic, London Mathematical Society, Lecture Note Series, pages 43–59. Cambridge University Press, 1995.Google Scholar
  13. 13.
    Saturnino F. Luz Filho and Patrick Sturt. A labelled deductive theorem proving environment for categorial grammar. In Proceedings of the IV International Workshop on Parsing Technologies, Prague, Czech Republic, September 1995. ACL/SIGPARSE.Google Scholar
  14. 14.
    Michael Moortgat. Categorial Investigations. Foris Publications, Dordrecht, 1988.Google Scholar
  15. 15.
    Michael Moortgat. Labelled deductive systems for categorial theorem proving. Technical Report OTS-WP-CL-92-003, OTS, Utrecht, NL, 1992.Google Scholar
  16. 16.
    Glyn Morrill. Clausal proofs and discontinuity. Journal of the Interest Group in Pure and Applied Logic (IGPL), 3(2), 1995. Special Issue on Deduction and Language.Google Scholar
  17. 17.
    Raymond M Smullyan. First-Order Logic, volume 43 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin, 1968.Google Scholar
  18. 18.
    Wojciech Zielonka. Axiomatizability of ajdukiewicz-lambek calculus by means of cancellation schemes. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, pages 215–224, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Saturnino F Luz-Filho
    • 1
  1. 1.University of Edinburgh - CCSEdinburghScotland, UK

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