Fully Lexicalized Pregroup Grammars

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


Pregroup grammars are a context-free grammar formalism introduced as a simplification of Lambek calculus. This formalism is interesting for several reasons: the syntactical properties of words are specified by a set of types like the other type-based grammar formalisms ; as a logical model, compositionality is easy ; a polytime parsing algorithm exists.

However, this formalism is not completely lexicalized because each pregroup grammar is based on the free pregroup built from a set of primitive types together with a partial order, and this order is not lexical information. In fact, only the pregroup grammars that are based on primitive types with an order that is equality can be seen as fully lexicalized.

We show here how we can transform, using a morphism on types, a particular pregroup grammar into another pregroup grammar that uses the equality as the order on primitive types. This transformation is at most quadratic in size (linear for a fixed set of primitive types), it preserves the parse structures of sentences and the number of types assigned to a word.


Pregroups Lambek Categorial Grammars Simulation 


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  1. 1.
    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
  2. 2.
    Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65, 154–170 (1958)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Casadio, C., Lambek, J.: An algebraic analysis of clitic pronouns in italian. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)Google Scholar
  4. 4.
    Bargelli, D., Lambek, J.: An algebraic approach to french sentence structure. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)Google Scholar
  5. 5.
    Lambek, J.: Type grammar meets german word order. Theoretical Linguistics 26, 19–30 (2000)CrossRefGoogle Scholar
  6. 6.
    Lambek, J., Preller, A.: An algebraic approach to the german noun phrase. Linguistic Analysis 31, 3–4 (2003)Google Scholar
  7. 7.
    Cardinal, K.: An algebraic study of Japanese grammar. McGill University, Montreal (2002)Google Scholar
  8. 8.
    Lambek, J.: Mathematics and the mind. In: Abrusci, V., Casadio, C. (eds.) New Perspectives in Logic and Formal Linguisitics. In: Proceedings Vth ROMA Workshop, Bulzoni Editore (2001)Google Scholar
  9. 9.
    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

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Denis Béchet
    • 1
  • Annie Foret
    • 2
  1. 1.LINA – Université de Nantes, 2, rue de la Houssiniére – BP 92208, 44322 Nantes Cedex 03France
  2. 2.IRISA – Université de Rennes 1, Avenue du Général Leclerc, 35042 Rennes CedexFrance

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