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Darwiche and Pearl's seminal 1997 article outlined a number of baselineprinciples for a logic of iterated belief revision. These principles, the DPpostulates, have been supplemented in a number of alternative ways. Most of thesuggestions made have resulted in a form of `reductionism' that identifiesbelief states with orderings of worlds. However, this position has recentlybeen criticised as being unacceptably strong. Other proposals, such as thepopular principle (P), aka `Independence', characteristic of `admissible'revision operators, remain commendably more modest. In this paper, wesupplement both the DP postulates and (P) with a number of novel conditions.While the DP postulates constrain the relation between a prior and a posteriorconditional belief set, our new principles notably govern the relation betweentwo posterior conditional belief sets obtained from a common prior by differentrevisions. We show that operators from the resulting family, which subsumesboth lexicographic and restrained revision, can be represented as relatingbelief states that are associated with a `proper ordinal interval' (POI)assignment, a structure more fine-grained than a simple ordering of worlds. Weclose the paper by noting that these operators satisfy iterated versions of alarge number of AGM era postulates, including Superexpansion, that are notsound for admissible operators in general.

On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators