On the generative capacity of multi-modal Categorial Grammars

Abstract

In Moortgat (1996) the Lambek Calculus L(Lambek, 1958) is extended by a pair of residuation modalities ♦ and □↓. Categorial Grammars based on the resulting logic L♦ are attractive for the purpose of modelling linguistic phenomena since they offer a compromise between the strict constituent structures imposed by context free grammars and related formalisms on the one hand, and the complete absence of hierarchical information in Lambek grammars on the other hand. The paper contains some results on the generative capacity of Categorial Grammars based on L♦. First it is shownthat adding residuation modalities does not extend the weak generative capacity. This is proved by extending the proof for the context freeness of L-grammars from Pentus (1993) to L♦. Second, the strong generative capacity of L♦-grammars is compared to context free grammars. The results are mainly negative; the set of tree languages generated by L♦-grammars neither contains nor is contained in the class of context free tree languages.