Bisimulation for Single-Agent Plausibility Models

Epistemic plausibility models are Kripke models agents use to reason about the knowledge and beliefs of themselves and each other. Restricting ourselves to the single-agent case, we determine when such models are indistinguishable in the logical language containing conditional belief, i.e., we define a proper notion of bisimulation, and prove that bisimulation corresponds to logical equivalence on image-finite models. We relate our results to other epistemic notions, such as safe belief and degrees of belief. Our results imply that there are only finitely many non-bisimilar single-agent epistemic plausibility models on a finite set of propositions. This gives decidability for single-agent epistemic plausibility planning.