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Generation as deduction on labelled proof nets

  • Josep M. Merenciano
  • Glyn Morrill
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1328)

Abstract

In the framework of labelled proof nets the task of parsing in categorial grammar can be reduced to the problem of first-order matching under theory. Here we shall show how to use the same method of labelled proof nets to reduce the task of generating to the problem of higher-order matching.

Keywords

Deductive System Lexical Entry Sequent Calculus Unit Clause Categorial Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    V. Danos and L. Regnier. The structure of multiplicatives. Archive for mathematical logic, (28):181–203, 1989.CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Gilles Dowek. Third order matching is decidable. In 7th Annual IEEE Symposium of Logic in Computer Science, pages 2–10, 1992.Google Scholar
  3. 3.
    Dov Gabbay. Labelled Deductive Systems. Oxford University Press, 1996.Google Scholar
  4. 4.
    Jean Gallier and Wayne Snyder. Designing unification procedures using transformations: a survey. In Workshop Logic For Computer Science. MSRI Berkeley, 1989.Google Scholar
  5. 5.
    Jean-Yves Girard. Linear logic. Theoretical Computer Science, 50(1):1–102, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    W. Goldfard. The undecibility of the second-order unification problem. Theoretical Computer Science, 13(2):225–230, 1981.CrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Huet. Constrained Resolution: A Complete Method for Higher-Order Logic. PhD thesis, Case Western Reserve University, 1972.Google Scholar
  8. 8.
    G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1(1):27–57, 1975.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Lambek. The mathematics of sentence structure. American Mathematical Monthly, (65): 154–170, 1958.CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Jordi Levy. Linear second-order unification. Rewriting Techniques and Applications, 1996.Google Scholar
  11. 11.
    Xavier Lloré and Glyn Morrill. Difference lists and difference bags for logic programming of categorial deduction. In Proceedings of the Sociedad Espanola para el Procesamiento del Lenguaje Natural, pages 115–129, 1995.Google Scholar
  12. 12.
    Michael Moortgat. Labelled deductive systems for categorial theorem proving. In Proceedings Eight Amsterdam Colloquium, pages 403–424, Amsterdam, 1992. Institute of Language, Logic and Information, Universiteit van Amsterdam.Google Scholar
  13. 13.
    Glyn Morrill. Type Logical Grammar: Categorial Logic of Signs. Kluwer Academic Publishers, 1994.Google Scholar
  14. 14.
    Glyn Morrill. Clausal proofs and discontinuity. Bulletin of the Interest Group in Pure and Applied Logics, 3(2–3):403–427, 1995.zbMATHMathSciNetGoogle Scholar
  15. 15.
    Glyn Morrill. Higher-order linear logic programming of categorial deduction. In Proceedings ACL, pages 133–140, 1995.Google Scholar
  16. 16.
    Glyn Morrill. Memoisation of categorial proof nets: parallelism in categorial processing. In Michele Abrusci and Claudia Casadio, editors, Proof and Linguistic Categories: Proceedings 1996 Roma Workshop, pages 157–169. Università di Bologna, 1996. To appear in S. Manandhar, W. Nutt and G. Lopez (eds.), Springer-Verlag.Google Scholar
  17. 17.
    F. Pereira and D. Warren. Parsing as deduction. In Proceedings ACL, pages 132–144, 1983.Google Scholar
  18. 18.
    Dirk Roorda. Resource Logics: Proof-theoretical Investigations. PhD thesis, Universiteit van Amsterdam, 1991.Google Scholar
  19. 19.
    Wayne Snyder and Jean Gallier. Higher-order unification revisited: Complete sets of transformations. Journal of Symbolic Computation, (8): 101–140, 1989.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Josep M. Merenciano
    • 1
  • Glyn Morrill
    • 1
  1. 1.Departement de Llenguatges i Sistemes InformáticsUniversität Politècnica de CatalunyaBarcelona

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