Iterated revision and the axiom of recovery: A unified treatment via epistemic states

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom— while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This provides a framework in which iterated revision becomes possible and makes explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem that connects the semantic conditions that we impose on iterated revision and the additional syntactical properties mentioned. We also show some interesting similarities between our framework and that of Darwiche-Pearl [4]. In particular, we show that the intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2).