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

Authors:
Christian Retoré;Sylvain Salvati
Affiliations:
INRIA Bordeaux Sud-Ouest, LaBRI (Université de Bordeauxet C.N.R.S.), Talence cedex, France 33405;INRIA Bordeaux Sud-Ouest, LaBRI (Université de Bordeauxet C.N.R.S.), Talence cedex, France 33405
Venue:
Journal of Logic, Language and Information
Year:
2010

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Abstract

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.