Terminating Tableau Calculi for Hybrid Logics Extending K

This article builds on work by Bolander and Blackburn [Thomas Bolander and Patrick Blackburn. Termination for hybrid tableaus. Journal of Logic and Computation, 17(3):517–554, 2007] on terminating tableau systems for the minimal hybrid logic K. We provide (for the basic uni-modal hybrid language) terminating tableau systems for a number of non-transitive hybrid logics extending K, such as the logic of irreflexive frames, antisymmetric frames, and so on; these systems don't employ loop-checks. We also provide (for hybrid tense logic enriched with the universal modality) a terminating tableau calculus for the logic of transitive frames; this system makes use of loop-checks.