Journal of Logic, Language and Information

, Volume 19, Issue 2, pp 163–183

On the Membership Problem for Non-Linear Abstract Categorial Grammars

Article

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.

Keywords

Lambda-calculus Intersection types Montague semantics  Text generation Formal grammars 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.INRIA Bordeaux Sud-Ouest, LaBRIUniversité de Bordeaux, Unité Mixte de Recherche CNRS (UMR 5800)Talence cedexFrance

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