Journal of Logic, Language and Information

, Volume 16, Issue 2, pp 173–194

Toward discourse representation via pregroup grammars

Origianl Article

Abstract

Every pregroup grammar is shown to be strongly equivalent to one which uses basic types and left and right adjoints of basic types only. Therefore, a semantical interpretation is independent of the order of the associated logic. Lexical entries are read as expressions in a two sorted predicate logic with ∈ and functional symbols. The parsing of a sentence defines a substitution that combines the expressions associated to the individual words. The resulting variable free formula is the translation of the sentence. It can be computed in time proportional to the parsing structure. Non-logical axioms are associated to certain words (relative pronouns, indefinite article, comparative determiners). Sample sentences are used to derive the characterizing formula of the DRS corresponding to the translation.

Keywords

Categorial grammars Pregroup grammars Discourse representation Semantic interpretation 

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References

  1. Béchet, D., Forêt, A., & Tellier, I. (2004). Learnability of pregroup grammars. In proc. international conference on grammatical inference (pp. 65–76). Berlin Heidelberg New York: Springer, LNAI 3262.Google Scholar
  2. Buszkowski, W. (2001). L. grammars based on pregroups. In P. de Groote et al. (Eds.), Logical aspects of computational linguistics. Berlin Heidelberg New York: Springer, LNAI 2099.Google Scholar
  3. Degeilh S., Preller A. (2005). Efficiency of pregroups and the French noun phrase. Journal of Language, Logic and Information 14(4): 423–444CrossRefGoogle Scholar
  4. Earley, J. (1970). An efficient context-free parsing algorithm. Communications of the AMC, 13(2), 94–102.Google Scholar
  5. Fenstad, J. E., Halvorsen, P.-K., Langholm, T., & van Benthem, J. (1978). Situations, language and logic, studies in linguistics and philisophy. Dordrecht: Reidel.Google Scholar
  6. Kamp, H., & Reyle U. (1993). From discourse to logic, introduction to modeltheoretic semantics of natural language. Dordrecht: Kluwer Academic Publishers.Google Scholar
  7. Lambek J. (1958). The mathematics of sentence structure. American Mathematical Monthly 65: 154–170CrossRefGoogle Scholar
  8. Lambek J., Scott P. (1986). Introduction to higher order categorical logic. Cambridge, Cambridge University PressGoogle Scholar
  9. Lambek, J. (1999). Type grammar revisited. In A. Lecomte et al. (Eds.), Logical aspects of computational linguistics(pp. 1–27.) Berlin Heidelberg New York: Springer, LNAI 1582.Google Scholar
  10. Lambek J. (2004). A computational algebraic approach to English grammar. Syntax 7(2): 128–147CrossRefGoogle Scholar
  11. Moortgat, M., & Oehrle, R. (2004). Pregroups and type-logical grammar: Searching for convergence. In P. Scott, C. Casadio, & R. A. Seeley (Eds.), Language and grammar studies in mathematical linguistics and natural language. Stanford: CSLI Publications.Google Scholar
  12. Pollard, C. (2004). Higher-Order categorical grammars. In Proc. of categorial grammars 04, Montpellier, France.Google Scholar
  13. Preller, A., & Lambek, J. (2005). Free compact 2-categories, mathematical structures for computer sciences. Cambridge: Cambridge University Press.Google Scholar
  14. Preller, A. (2005). Category theoretical semantics for pregroup grammars. In Blache, & Stabler (Eds.), LACL 2005, LNAI 3492 (pp. 254–270).Google Scholar
  15. van Benthem J. (2005). Guards, bounds and generalized semantics. journal of Language, Logic and Information 14: 263–279CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media 2007

Authors and Affiliations

  1. 1.LIRMMMonpellierFrance

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