© 2016 Elsevier Inc. A credal network associates a directed acyclic graph with a collection of sets of probability measures. Usually these probability measures are specified by tables containing probability values. Here we examine the complexity of inference in credal networks when probability measures are specified through formal languages. We focus on logical languages based on propositional logic and on the function-free fragment of first-order logic. We show that sub-Boolean and relational logics lead to interesting complexity results. In short, we explore the relationship between specification language and computational complexity in credal networks.