Complexity of hybrid logics over transitive frames

This paper examines the complexity of hybrid logics over transitive frames and transitive trees. We show that satisfiability over transitive frames for the hybrid language extended with ↓ is NEXPcomplete. This is in contrast to undecidability of satisfiability over arbitrary frames for this language [2]. We also show that adding @ or the past modality leads to undecidability over transitive frames, but not over transitive trees, where we show the richest language to be nonelementarily decidable. Moreover, we establish 2EXP and EXP upper bounds for satisfiability over transitive frames and transitive trees, respectively, for the hybrid Until/Since language. An EXP lower bound is shown to hold for the modal Until language over both frame classes.