Multiple Iterated Belief Revision Without Independence

Multiple iterated revision needs advanced belief revision techniques beyond the classical AGM theory that are able to integrate several (propositional) pieces of new information into epistemic states. A crucial feature of this kind of revision is that the multiple pieces of information should be dealt with separately, which has usually been understood as requiring some kind of independence among the different propositions under revision. Therefore, previous works have proposed several independence postulates which should ensure this. In this paper, we present an approach to multiple iterated revision that can do without those independence postulates. More precisely, we propose a method to revise ordinal conditional functions (so-called Spohn’s ranking functions) by a set of propositional beliefs that satisfies the epistemic AGM postulates and the Darwiche and Pearl postulates for iterated revision, as well as some other postulates for multiple iterated revision, but none of the independence postulates that have been proposed so far. This shows that those independence postulates are not necessary for ensuring the adequate handling of multiple pieces of information under revision.