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Fully Lexicalized Pregroup Grammars

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

Abstract

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.

Keywords

Pregroups Lambek Categorial Grammars Simulation 

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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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