On the membership problem for non-linear abstract categorial grammars

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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DOI 10.1007/s10849-009-9110-0
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Jean-Yves Girard (1989). Proofs and Types. Cambridge University Press.

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