On the Logic of Iterated Belief Revision

Abstract

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by augmenting the AGM system with four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Finally, we establish a model–based representation theorem which characterizes the augmented system of postulates and constrains, in turns, the way in which entrenchment orderings may be transformed under iterated belief revisions.