Notions of Bisimulation for Heyting-Valued Modal Languages
Pantelis E. Eleftheriou, Costas D. Koutras, Christos Nomikos · Journal of Logic and Computation · 2010
Abstract. We define notions 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 ac-cessibility relation. We investigate the correct notion of bisimulation in this context: we define two variants of bisimulation relations and derive relative (to a truth value) modal equivalence results for bisimilar states. We further investigate game semantics for our bisimulation, Hennessy-Milner classes and other relevant properties. If the underlying algebra H is finite, Heyting-valued modal models can be equivalently reformu-lated to a form relevant to epistemic situations with many interrelated experts. Our definitions and results draw from this formulation, which is of independent interest to Knowledge Representation applications.