  As partial justification of their framework for iterated belief revision
Darwiche and Pearl convincingly argued against Boutiliers natural revision and
provided a prototypical revision operator that fits into their scheme. We show
that the Darwiche-Pearl arguments lead naturally to the acceptance of a smaller
class of operators which we refer to as admissible. Admissible revision ensures
that the penultimate input is not ignored completely, thereby eliminating
natural revision, but includes the Darwiche-Pearl operator, Nayaks
lexicographic revision operator, and a newly introduced operator called
restrained revision. We demonstrate that restrained revision is the most
conservative of admissible revision operators, effecting as few changes as
possible, while lexicographic revision is the least conservative, and point out
that restrained revision can also be viewed as a composite operator, consisting
of natural revision preceded by an application of a "backwards revision"
operator previously studied by Papini. Finally, we propose the establishment of
a principled approach for choosing an appropriate revision operator in
different contexts and discuss future work.
