Advertisement

Pregroup Calculus as a Logic Functor

  • Annie Foret
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4576)

Abstract

The concept of pregroup was introduced by Lambek for natural language analysis, with a close link to non-commutative linear logic. We reformulate the pregroup calculus so as to extend it by composition with other logics and calculii.The cut elimination property and the decidabilityproperty of the sequent calculus proposed in the article are shown.Properties of composed calculii are also discussed.

Keywords

Pregroups Lambek Categorial Grammars Logic Functor  Cut Elimination 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bargelli, D., Lambek, J.: An Algebraic Approach to French Sentence Structure. In: de Groote, P., Morill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)Google Scholar
  2. 2.
    Buszkowski, W.: Mathematical linguistics and proof theory. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 683–736. Elsevier, North-Holland (1997)Google Scholar
  3. 3.
    Buszkowski, W.: Lambek grammars based on pregroups. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)Google Scholar
  4. 4.
    Buszkowski, W.: Cut elimination for the Lambek calculus of adjoints. In: New Perspectives in Logic and Formal Linguisitics, Proceedings Vth ROMA Workshop, Bulzoni EditoreGoogle Scholar
  5. 5.
    Buszkowski, W.: Sequent systems for compact bilinear logic. Mathematical Logic Quarterly 49(5), 467–474 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Casadio, C., Lambek, J.: An Algebraic Analysis of Clitic Pronouns in Italian. In: de Groote, P., Morill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)Google Scholar
  7. 7.
    Fadda, Mario,: Towards flexible pregroup grammars. In: New Perspectives in Logic and Formal Linguistics, pp. 95–112. Bulzoni Editore, Roma (2002)Google Scholar
  8. 8.
    Ferré, S., Ridoux, O.: A Framework for Developing Embeddable Customized Logic. In: Pettorossi, A. (ed.) LOPSTR 2001. LNCS, vol. 2372, pp. 191–215. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Ferré, S., Ridoux, O.: Logic Functors : a Toolbox of Components for Building Customized and Embeddable Logics. Research report, no RR-5871, Inria (March 2006) http://www.inria.fr/rrrt/rr-5871.html
  10. 10.
    Kislak-Malinowska, Aleksandra, Pregroups with modalities, FG2006: the 11th conference on Formal Grammar, Malaga, Spain (July 2006)Google Scholar
  11. 11.
    Lambek, J.: Type grammars revisited. In: Lecomte, A., Perrier, G., Lamarche, F. (eds.) LACL 1997. LNCS (LNAI), vol. 1582, pp. 22–24. Springer, Heidelberg (1999)Google Scholar
  12. 12.
    Preller, A.: Category Theoretical Semantics for Pregroup Grammars. In: Blache, P., Stabler, E., Busquets, J.V., Moot, R. (eds.) LACL 2005. LNCS (LNAI), vol. 3492, Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Preller, A., Lambek, J.: Free compact 2-categories. Mathematical Structures for Computer Sciences (January 2007)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Annie Foret
    • 1
  1. 1.IRISA –Rennes 1, Avenue du Général Leclerc, 35042 Rennes CedexFrance

Personalised recommendations