Simple K-star Categorial Dependency Grammars and their Inference

We propose a novel subclass in the family of Categorial Dependency Grammars (CDG), based on a syntactic criterion on categorial types associated to words in the lexicon and study its learnability. This proposal relies on a linguistic principle and relates to a former non-constructive condition on iterated dependencies. We show that the projective CDG in this subclass are incrementally learnable in the limit from dependency structures. In contrast to previous proposals, our criterion is both syntactic and does not impose a (rigidity) bound on the number of categorial types associated to a word.