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

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Journal of Logic Language and Information 19 (2):185-200 (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.

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10.1007/s10849-009-9111-z

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Proofs and types.Jean-Yves Girard - 1989 - New York: Cambridge University Press.
Mathematical linguistics and proof theory.Wojciech Buszkowski - 1997 - In J. F. A. K. Van Benthem, Johan van Benthem & Alice G. B. Ter Meulen (eds.), Handbook of Logic and Language. Elsevier. pp. 683--736.
Lambda Grammars and the Syntax-Semantics Interface.Reinhard Muskens - 2001 - In Robert Van Rooij & Martin Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium. Amsterdam: ILLC. pp. 150-155.

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