We provide a behavioural logic for configuration structures, a model due to van Glabbeek and Plotkin which generalises the families of (finite) configurations of event structures. The logic is a conservative extension of a logic provided by Baldan and Crafa for prime event structures. We show that logical equivalence can be characterized as a form of hereditary history preserving bisimilarity. We compare such a notion of bisimilarity with an equivalence proposed by van Glabbeek in the setting of higher-dimensional automata, showing that, in general, it is finer, while the two notions coincide in the framework of general event structures. Finally, we explore how to restrict the general logic to capture a notion of history preserving bisimilarity.