Extended Lambek calculi enlarge the type language with adjoint pairs of unary modalities. In previous work, modalities have been used as licensors for controlled forms of restructuring, reordering and copying. Here, we study a complementary use of the modalities as dependency features coding for grammatical roles. The result is a multidimensional type logic simultaneously inducing dependency and function argument structure on the linguistic material. We discuss the new perspective on constituent structure suggested by the dependency-enhanced type logic, and we experimentally evaluate how well a neural language model like BERT can deal with the subtle interplay between logical and structural reasoning that this type logic gives rise to.