An Analytic Tableau System for Natural Logic

  • Reinhard Muskens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6042)


In this paper we develop the beginnings of a tableau system for natural logic, the logic that is present in ordinary language and that us used in ordinary reasoning. The system is based on certain terms of the typed lambda calculus that can go proxy for linguistic forms and which we call Lambda Logical Forms. It is argued that proof-theoretic methods like the present one should complement the more traditional model-theoretic methods used in the computational study of natural language meaning.


Natural Logic Ordinary Language Generative Grammar Categorial Grammar Tableau System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aliseda-Llera, A.: Seeking Explanations: Abduction in Logic, Philosophy of Science and Artificial Intelligence. PhD thesis, ILLC (1997)Google Scholar
  2. 2.
    van Benthem, J.F.A.K.: Questions about Quantifiers. Journal of Symbolic Logic 49, 447–478 (1984)Google Scholar
  3. 3.
    van Benthem, J.F.A.K.: Essays in Logical Semantics. Reidel, Dordrecht (1986)Google Scholar
  4. 4.
    van Benthem, J.F.A.K.: Language in Action. North-Holland, Amsterdam (1991)zbMATHGoogle Scholar
  5. 5.
    Bernardi, R.: Reasoning with Polarity in Categorial Type Logic. PhD thesis, Utrecht University (2002)Google Scholar
  6. 6.
    Blackburn, P., Bos, J.: Representation and Inference for Natural Language. A First Course in Computational Semantics. CSLI (2005)Google Scholar
  7. 7.
    D’Agostino, M., Finger, M., Gabbay, D.: Cut-Based Abduction. Logic Journal of the IGPL 16(6), 537–560 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    van der Does, J.: Applied Quantifier Logics. PhD thesis, University of Amsterdam (1992)Google Scholar
  9. 9.
    Dowty, D.: The Role of Negative Polarity and Concord Marking in Natural Language Reasoning. In: Harvey, M., Santelmann, L. (eds.) Proceedings from SALT, vol. IV, pp. 114–144. Cornell University, Ithaca (1994)Google Scholar
  10. 10.
    van Eijck, J.: Generalized Quantifiers and Traditional Logic. In: van Benthem, J., ter Meulen, A. (eds.) Generalized Quantifiers in Natural Language. Foris, Dordrecht (1985)Google Scholar
  11. 11.
    van Eijck, J.: Natural Logic for Natural Language. In: ten Cate, B., Zeevat, H. (eds.) TbiLLC 2005. LNCS (LNAI), vol. 4363, pp. 216–230. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Fyodorov, F., Winter, Y., Francez, N.: Order-Based Inference in Natural Logic. Logic Journal of the IGPL 11(4), 385–416 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Heim, I., Kratzer, A.: Semantics in Generative Grammar. Blackwell, Oxford (1998)Google Scholar
  14. 14.
    Johnson-Laird, P.N.: Mental Models: Towards a Cognitive Science of Language, Inference, and Conciousness. Harvard University Press, Cambridge (1983)Google Scholar
  15. 15.
    Johnson-Laird, P.N.: How We Reason. Oxford University Press, Oxford (2006)Google Scholar
  16. 16.
    Lakoff, G.: Linguistics and Natural Logic. In: Davidson, D., Harman, G. (eds.) Semantics of Natural Language, pp. 545–665. Reidel, Dordrecht (1972)Google Scholar
  17. 17.
    MacCartney, B., Manning, C.: Natural Logic for Textual Inference. In: ACL 2007 Workshop on Textual Entailment and Paraphrasing (2007)Google Scholar
  18. 18.
    MacCartney, B., Manning, C.: An Extended Model of Natural Logic. In: Bunt, H., Petukhova, V., Wubben, S. (eds.) Proceedings of the 8th IWCS, Tilburg, pp. 140–156 (2009)Google Scholar
  19. 19.
    Montague, R.: The Proper Treatment of Quantification in Ordinary English. In: Hintikka, J., Moravcsik, J., Suppes, P. (eds.) Approaches to Natural Language, pp. 221–242. Reidel, Dordrecht (1973); Reprinted in[23]Google Scholar
  20. 20.
    Muskens, R.A.: Meaning and Partiality. CSLI, Stanford (1995)Google Scholar
  21. 21.
    Sánchez, V.: Studies on Natural Logic and Categorial Grammar. PhD thesis, University of Amsterdam (1991)Google Scholar
  22. 22.
    Sommers, F.: The Logic of Natural Language. The Clarendon Press, Oxford (1982)Google Scholar
  23. 23.
    Thomason, R. (ed.): Formal Philosophy, Selected Papers of Richard Montague. Yale University Press, New Haven (1974)Google Scholar
  24. 24.
    Zamansky, A., Francez, N., Winter, Y.: A ‘Natural Logic’ Inference System Using the Lambek Calculus. Journal of Logic, Language and Information 15, 273–295 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Zwarts, F.: Negatief-polaire Uitdrukkingen I. Glot 6, 35–132 (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Reinhard Muskens
    • 1
  1. 1.Tilburg Center for Logic and Philosophy of Science 

Personalised recommendations