Belief Revision and Rational Inference

The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and compared with other similar postulates that have been proposed in the literature. The AGM revisions that satisfy this new postulate stand in one-to-one correspondence with the rational, consistency-preserving relations. This correspondence is described explicitly. Two viewpoints on iterative revisions are distinguished and discussed.