On the expressive power of abstract categorial grammars: Representing context-free formalisms [Book Review]

Abstract
We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order operation in the case of linear context-free rewriting systems. This suggest the possibility of defining an Abstract Categorial Hierarchy.
Keywords Abstract categorial grammars  context-free grammars  formal language theory  lambda-calculus
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Michael Moortgat (2009). Symmetric Categorial Grammar. Journal of Philosophical Logic 38 (6):681 - 710.
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