Elementary Iterated Revision and the Levi Identity
  Recent work has considered the problem of extending to the case of iterated
belief change the so-called `Harper Identity' (HI), which defines single-shot
contraction in terms of single-shot revision. The present paper considers the
prospects of providing a similar extension of the Levi Identity (LI), in which
the direction of definition runs the other way. We restrict our attention here
to the three classic iterated revision operators--natural, restrained and
lexicographic, for which we provide here the first collective characterisation
in the literature, under the appellation of `elementary' operators. We consider
two prima facie plausible ways of extending (LI). The first proposal involves
the use of the rational closure operator to offer a `reductive' account of
iterated revision in terms of iterated contraction. The second, which doesn't
commit to reductionism, was put forward some years ago by Nayak et al. We
establish that, for elementary revision operators and under mild assumptions
regarding contraction, Nayak's proposal is equivalent to a new set of
postulates formalising the claim that contraction by $\neg A$ should be
considered to be a kind of `mild' revision by $A$. We then show that these, in
turn, under slightly weaker assumptions, jointly amount to the conjunction of a
pair of constraints on the extension of (HI) that were recently proposed in the
literature. Finally, we consider the consequences of endorsing both suggestions
and show that this would yield an identification of rational revision with
natural revision. We close the paper by discussing the general prospects for
defining iterated revision in terms of iterated contraction.
