A faithful representation of non-associative Lambek grammars in abstract categorial grammars

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.
Keywords Lambda calculus  Formal language theory  Categorial grammar
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DOI 10.1007/s10849-009-9111-z
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Jean-Yves Girard (1989). Proofs and Types. Cambridge University Press.

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