In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7. CSLI Publications. pp. 111-132 (2008)

Abstract
In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the paper. Our results show that many-valued hybrid logic is indeed a natural enterprise.
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DOI 10.1093/logcom/exv040
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Merging Frameworks for Interaction.Johan van Benthem, Jelle Gerbrandy, Tomohiro Hoshi & Eric Pacuit - 2009 - Journal of Philosophical Logic 38 (5):491-526.

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