The complexity of hybrid logics over equivalence relations

This paper examines and classifies the computational complexity of model checking and satisfiability for hybrid logics over frames with equivalence relations. The considered languages contain all possible combinations of the downarrow binder, the existential binder, the satisfaction operator, and the global modality, ranging from the minimal hybrid language to very expressive languages. In the model-checking case, we separate polynomial-time solvable from PSPACE-complete cases, and for satisfiability, we exhibit cases complete for NP, PSpace, NExp, and even N2Exp. Our analysis also includes the versions without atomic propositions of all these languages.