, Volume 19, Issue 2, pp 163-183
Date: 19 Dec 2009

On the Membership Problem for Non-Linear Abstract Categorial Grammars

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Abstract

In this paper we show that the membership problem for second order non-linear Abstract Categorial Grammars is decidable. A consequence of that result is that Montague-like semantics yield to a decidable text generation problem. Furthermore the proof we propose is based on a new tool, Higher Order Intersection Signatures, which grasps statically dynamic properties of λ-terms and presents an interest in its own.