Type-theoretic extensions of Abstract Categorial Grammars

Philippe de Groote (1) , Sarah Maarek (1)

1 CALLIGRAMME - Linear logic, proof networks and categorial grammars

Abstract Categorial Grammars (ACG), in their original definition, are based on the linear λ-calculus. This choice derives from the traditional categorial grammars, which are based on resource sensitive logics. From a language-theoretic standpoint, this linearity constraint does not result in a weak expressive power of the formalism. For instance, the string languages generated by the second-order ACGs (whose parsing is known to be polynomial) corresponds to the class of mildly context sensitive lan- guages. From a more practical point of view, however, it would be interesting to increase the intentional expressive power of the formalism by providing high level constructs. For instance, one would like to provide the ACGs with feature structures, as it is the case in most current grammatical formalisms. In previous paper, a possible way of extending the ACGs is suggested. It consists of enriching the type system of the formalism with new type constructors. The present paper elaborates on this proposal.

Domaines: Informatique et langage [cs.CL]

Philippe de Groote, Sarah Maarek. Type-theoretic extensions of Abstract Categorial Grammars. 2007. ⟨inria-00187759⟩