A notion of bisimulation for many-valued modal logic

We introduce a suitable notion of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal language is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language which is interpreted on relational frames with an H-valued accessibility relation. We prove that for each language, an H-indexed family of bisimulations can be defined which implies a relative invariance result for the truth values of modal formulas. A bisimulation game is further defined and relevant results, such as the tree model property are examined. If the underlying algebra H is finite, the modal language can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. In this context, our bisimulations are transformations of Hmodal models which guarantee that the epistemic consensus of a predefined group of the involved experts is invariant under the bisimulation relation.