Journal of Logic, Language and Information

, Volume 19, Issue 2, pp 185–200 | Cite as

A Faithful Representation of Non-Associative Lambek Grammars in Abstract Categorial Grammars

  • Christian RetoréEmail author
  • Sylvain Salvati


This paper solves a natural but still open question: can abstract categorial grammars (ACGs) respresent usual categorial grammars? Despite their name and their claim to be a unifying framework, up to now there was no faithful representation of usual categorial grammars in ACGs. This paper shows that Non-Associative Lambek grammars as well as their derivations can be defined using ACGs of order two. To conclude, the outcome of such a representation are discussed.


Lambda calculus Formal language theory Categorial grammar 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.INRIA Bordeaux Sud-Ouest, LaBRI (Université de Bordeauxet C.N.R.S.)Talence cedexFrance

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