Epistemic Equivalence and Bisimulation

Bisimulation is an equivalence relation over Kripke models. It is often claimed, but little argued for, that bisimulation captures a ‘natural’ notion of similarity in epistemic semantics, in the sense that the differences between bisimilar models are, from an epistemic point of view, irrelevant. In this paper we examine three types of arguments pertaining to the view that bisimilar models are ‘epistemically equivalent.’ We start with examining an ‘ontological arguments’ having to do with what a Kripke model is, or is meant to do, and use a theorem from co-algebra to argue that bisimilar models should, under certain assumptions, represent the same epistemic situations. We then examine the relationship between bisimulation and the expressive power of epistemic logic, and conclude that the two notions do not fit in any precise way. Finally, we identify a number of desirable properties of a notion of epistemic equivalence, and conclude that although bisimulation satisfies all of these properties, the properties themselves do not characterize bisimulation.