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Encoding Phases Using Commutativity and Non-commutativity in a Logical Framework

  • Maxime Amblard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6736)

Abstract

This article presents an extension of Minimalist Categorial Grammars (MCG) to encode Chomsky’s phases. These grammars are based on Partially Commutative Logic (PCL) and encode properties of Minimalist Grammars (MG) of Stabler [22]. The first implementation of MCG were using both non-commutative properties (to respect the linear word order in an utterance) and commutative ones (to model features of different constituents). Here, we propose to augment Chomsky’s phases with the non-commutative tensor product of the logic. Then we can give account of the PIC [7] just with logical properties of the framework instead of defining a specific rule.

Keywords

Type theory syntax linguistic modeling generative theory phase Partially Commutative Logic 

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References

  1. 1.
    Amblard, M.: Calcul de représentations sémantiques et syntaxe générative: les grammaires minimalistes catégorielles. Ph.D. thesis, université de Bordeaux 1 (2007)Google Scholar
  2. 2.
    Amblard, M., Lecomte, A., Retore, C.: Categorial minimalist grammars: from generative syntax to logical forms. Linguistic Analysis 6(1-4), 273–308 (2010)Google Scholar
  3. 3.
    Amblard, M., Retore, C.: Natural deduction and normalisation for partially commutative linear logic and lambek calculus with product. In: Computation and Logic in the Real World, CiE 2007 (2007)Google Scholar
  4. 4.
    Baker, M.: Thematic Roles and Syntactic Structure. In: Haegeman, L. (ed.) Elements of Grammar, Handbook of Generative Syntax, pp. 73–137. Kluwer, Dordrecht (1997)Google Scholar
  5. 5.
    Chomsky, N.: Syntactic Structures. Mouton, The Hague (1957)zbMATHGoogle Scholar
  6. 6.
    Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  7. 7.
    Chomsky, N.: Derivation by phase. ms. MIT, Cambridge (1999)Google Scholar
  8. 8.
    de Groote, P.: Partially commutative linear logic: sequent calculus and phase semantics. In: Abrusci, V.M., Casadio, C. (eds.) Third Roma Workshop: Proofs and Linguistics Categories – Applications of Logic to the analysis and implementation of Natural Language, pp. 199–208. CLUEB, Bologna (1996)Google Scholar
  9. 9.
    de Groote, P.: Towards abstract categorial grammars. In: ACL 2001 (2001)Google Scholar
  10. 10.
    Hale, K.: On argument structure and the lexical expression of syntactic relations. The View from Building, vol. 20. MIT Press, Ithaca (1993)Google Scholar
  11. 11.
    Kratzer, A.: External arguments. In: Benedicto, E., Runner, J. (eds.) Functional Projections. University of Massachussets, Amherst (1994)Google Scholar
  12. 12.
    Lambek, J.: The mathematics of sentence structures. American mathematical monthly (1958)Google Scholar
  13. 13.
    Lecomte, A.: Categorial grammar for minimalism. Language and Grammar: Studies in Mathematical Linguistics and Natural Language CSLI Lecture Notes, vol. 168, pp. 163–188 (2005)Google Scholar
  14. 14.
    Lecomte, A.: Semantics in minimalist-categorial grammars. Formal Grammar (2008)Google Scholar
  15. 15.
    Lecomte, A., Retoré, C.: Extending Lambek grammars: a logical account of minimalist grammars. In: Proceedings of the 39th Annual Meeting of the Association for Computational Linguistics, ACL 2001, pp. 354–361. ACL, Toulouse (2001)Google Scholar
  16. 16.
    Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, ch. 2, pp. 93–178. Elsevier, Amsterdam (1997)CrossRefGoogle Scholar
  17. 17.
    Morrill, G.: Type logical grammar. Categorial Logic of Signs (1994)Google Scholar
  18. 18.
    Muskens, R.: Languages, lambdas and logic. Resource Sensitivity in Binding and Anaphora (2003)Google Scholar
  19. 19.
    Pollard, C.: Convergent grammars. Tech. rep., The Ohio State University (2007)Google Scholar
  20. 20.
    Retoré, C.: Pomset logic: a non-commutative extension of classical linear logic. In: de Groote, P., Hindley, J.R. (eds.) TLCA 1997. LNCS, vol. 1210, pp. 300–318. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    Retoré, C.: A description of the non-sequential execution of petri nets in partially commutative linear logic. Logic Colloquium 99 Lecture Notes in Logic, pp. 152–181 (2004)Google Scholar
  22. 22.
    Stabler, E.: Derivational minimalism. LACL 1328 (1997)Google Scholar
  23. 23.
    Stabler, E.: Recognizing head movement. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, p. 245. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  24. 24.
    Steedman, M.: Combinatory grammars and parasitic gaps. In: Natural Language and Linguistic Theory, vol. 5 (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Maxime Amblard
    • 1
    • 2
    • 3
  1. 1.LORIA - INRIA Nancy Grand EstVandoeuvre-lès-Nancy CedexFrance
  2. 2.Université Nancy 2Nancy cedexFrance
  3. 3.INPLVandoeuvreFrance

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