On the expressive power of Abstract Categorial Grammars: Representing context-free formalisms

Philippe de Groote 1 Sylvain Pogodalla 1
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
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Philippe de Groote, Sylvain Pogodalla. On the expressive power of Abstract Categorial Grammars: Representing context-free formalisms. Journal of Logic, Language and Information, Springer Verlag, 2004, 13 (4), pp.421-438. ⟨10.1007/s10849-004-2114-x⟩. ⟨inria-00112956⟩

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