On the properties of the languages specified by the multimodal categorial dependency grammars

In the paper we continue to investigate the categorial dependency grammars (CDG). A multimodal version of these grammars with negative mode pairing rules (mmCDG) is considered. It is proved that the set of mmCDG-languages is closed under iteration and it is an abstract family of languages. We also establish that the class of mmCDG-languages is closed under intersection, but it is not closed under projection. An example of a non-semilinear mmCDG-language is presented. It is established that there exists a mmCDG with NP-complete membership problem.