Hybrid logics were proposed in  as a way of boosting the expressivity of modal logics via a novel mechanism: Adding labels for states in Kripke models and viewing these labels as formulae. In addition, hybrid logics may contain quantifiers to bind the labels. Thus, hybrid logics have both Kripke semantics and a first-order binding apparatus. We present prefixed tableau calculi for weak hybrid logics (proper fragments of classical logic) as well as for hybrid logics having full first-order expressive power, and give a general method for proving completeness.
Tzakova, M. (1999). Tableau calculi for hybrid logics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1617, pp. 278–292). Springer Verlag. https://doi.org/10.1007/3-540-48754-9_24