Darwiche and Pearl’s Iterated Belief Revision: Not Always Spohn-Expressible

The problem of iterated belief revision, which concerns how rational agents modify their beliefs in response to new information over time, lies at the core of understanding rational belief change. This article examines the interplay between the following two prominent frameworks for iterated belief revision: the qualitative Darwiche and Pearl’s approach (abbrev. DP approach) and the quantitative Spohn conditionalization. In particular, we prove that the DP approach is too liberal (under-constrained) to capture Spohn’s conditionalization (confined to revision scenarios); hence, the former cannot be regarded as a precise qualitative counterpart of the latter. Against this background, we provide insights into the essential semantic constraints on total preorders over the possible worlds needed to strengthen the DP approach and achieve alignment with Spohn’s method.