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An Analytic Tableau System for Natural Logic

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Logic, Language and Meaning

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6042))

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Abstract

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.

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References

  1. Aliseda-Llera, A.: Seeking Explanations: Abduction in Logic, Philosophy of Science and Artificial Intelligence. PhD thesis, ILLC (1997)

    Google Scholar 

  2. van Benthem, J.F.A.K.: Questions about Quantifiers. Journal of Symbolic Logic 49, 447–478 (1984)

    Google Scholar 

  3. van Benthem, J.F.A.K.: Essays in Logical Semantics. Reidel, Dordrecht (1986)

    Google Scholar 

  4. van Benthem, J.F.A.K.: Language in Action. North-Holland, Amsterdam (1991)

    MATH  Google Scholar 

  5. Bernardi, R.: Reasoning with Polarity in Categorial Type Logic. PhD thesis, Utrecht University (2002)

    Google Scholar 

  6. Blackburn, P., Bos, J.: Representation and Inference for Natural Language. A First Course in Computational Semantics. CSLI (2005)

    Google Scholar 

  7. D’Agostino, M., Finger, M., Gabbay, D.: Cut-Based Abduction. Logic Journal of the IGPL 16(6), 537–560 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. van der Does, J.: Applied Quantifier Logics. PhD thesis, University of Amsterdam (1992)

    Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  12. Fyodorov, F., Winter, Y., Francez, N.: Order-Based Inference in Natural Logic. Logic Journal of the IGPL 11(4), 385–416 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Heim, I., Kratzer, A.: Semantics in Generative Grammar. Blackwell, Oxford (1998)

    Google Scholar 

  14. Johnson-Laird, P.N.: Mental Models: Towards a Cognitive Science of Language, Inference, and Conciousness. Harvard University Press, Cambridge (1983)

    Google Scholar 

  15. Johnson-Laird, P.N.: How We Reason. Oxford University Press, Oxford (2006)

    Google Scholar 

  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. MacCartney, B., Manning, C.: Natural Logic for Textual Inference. In: ACL 2007 Workshop on Textual Entailment and Paraphrasing (2007)

    Google Scholar 

  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. 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. Muskens, R.A.: Meaning and Partiality. CSLI, Stanford (1995)

    Google Scholar 

  21. Sánchez, V.: Studies on Natural Logic and Categorial Grammar. PhD thesis, University of Amsterdam (1991)

    Google Scholar 

  22. Sommers, F.: The Logic of Natural Language. The Clarendon Press, Oxford (1982)

    Google Scholar 

  23. Thomason, R. (ed.): Formal Philosophy, Selected Papers of Richard Montague. Yale University Press, New Haven (1974)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  25. Zwarts, F.: Negatief-polaire Uitdrukkingen I. Glot 6, 35–132 (1981)

    Google Scholar 

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Muskens, R. (2010). An Analytic Tableau System for Natural Logic. In: Aloni, M., Bastiaanse, H., de Jager, T., Schulz, K. (eds) Logic, Language and Meaning. Lecture Notes in Computer Science(), vol 6042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14287-1_11

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  • DOI: https://doi.org/10.1007/978-3-642-14287-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14286-4

  • Online ISBN: 978-3-642-14287-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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