On the Complexity of Hybrid Logics with Binders

Hybrid logic refers to a group of logics lying between modal and first-order logic in which one can refer to individual states of the Kripke structure. In particular, the hybrid logic HL(@, ↓) is an appealing extension of modal logic that allows one to refer to a state by means of the given names and to dynamically create new names for a state. Unfortunately, as for the richer first-order logic, satisfiability for the hybrid logic HL(@, ↓) is undecidable and model checking for HL(@, ↓) is PSpace-complete. We carefully analyze these results and we isolate large fragments of HL(@, ↓) for which satisfiability is decidable and model checking is below PSpace.