Measuring similarity in belief revision

The Possible Models Approach (PMA) introduced by Winslett, proposes, among other things, a domain-independent criterion for measuring similarity between different states of a dynamic system. The concept of similarity between states (possible worlds) appears also in the area of Belief Revision in the form of a system of spheres. Systems of spheres are in turn connected to epistemic entrenchments by means of the AGM revision functions that the two structures induce. In view of these connections, in this article we study the implications of adopting PMA's criterion of similarity in the context of Belief Revision. More precisely, we formulate conditions that capture PMA's criterion of similarity in terms of systems of spheres (PMA systems of spheres) and we provide an axiomatic characterization of the class of epistemic entrenchments corresponding to systems of spheres that comply with PMA's criterion of similarity (PMA epistemic entrenchments). We also discuss some interesting properties of the class of PMA system of spheres and PMA epistemic entrenchments. Our study is primarily motivated by the role that PMA epistemic entrenchments can play in Reasoning about Action.