Journal of Logic, Language and Information

, Volume 13, Issue 4, pp 421–438

On the Expressive Power of Abstract Categorial Grammars: Representing Context-Free Formalisms

  • Philippe de Groote
  • Sylvain Pogodalla
Original Article

DOI: 10.1007/s10849-004-2114-x

Cite this article as:
de Groote, P. & Pogodalla, S. J Logic Lang Inf (2004) 13: 421. doi:10.1007/s10849-004-2114-x

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.

Key words

Abstract categorial grammars context-free grammars formal language theory lambda-calculus 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Philippe de Groote
    • 1
  • Sylvain Pogodalla
    • 1
  1. 1.INRIA LorraineFrance