We study learnability of Categorial Dependency Grammars (CDG), a family of categorial grammars expressing all kinds of projective, discontinuous and repeatable dependencies. For these grammars, it is known that they are not learnable from dependency structures.
We propose two different ways of modelling the repeatable dependencies through iterated types and the two corresponding families of CDG which cannot distinguish between the dependencies repeatable at least
times and those repeatable
number of times. For both we show that they are incrementally learnable in the limit from dependency structures.