Abstract
Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The
seminal work of Darwiche and Pearl (DP approach,
for short) remains the most dominant, despite its
well-documented shortcomings. In this article, we
make further observations on the DP approach.
Firstly, we prove that the DP postulates are, in a
strong sense, inconsistent with Parikh’s relevancesensitive axiom (P), extending previous initial con-
flicts. Immediate consequences of this result are
that an entire class of intuitive revision operators,
which includes Dalal’s operator, violates the DP
postulates, as well as that the Independence postulate and Spohn’s conditionalization are inconsistent
with (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can
be captured by identifying belief states with total
preorders over possible worlds, a fact implying that
a preference ordering (over possible worlds) is an
insufficient representation for a belief state