Extending the Harper Identity to Iterated Belief Change
  The field of iterated belief change has focused mainly on revision, with the
other main operator of AGM belief change theory, i.e. contraction, receiving
relatively little attention. In this paper we extend the Harper Identity from
single-step change to define iterated contraction in terms of iterated
revision. Specifically, just as the Harper Identity provides a recipe for
defining the belief set resulting from contracting A in terms of (i) the
initial belief set and (ii) the belief set resulting from revision by not-A, we
look at ways to define the plausibility ordering over worlds resulting from
contracting A in terms of (iii) the initial plausibility ordering, and (iv) the
plausibility ordering resulting from revision by not-A. After noting that the
most straightforward such extension leads to a trivialisation of the space of
permissible orderings, we provide a family of operators for combining
plausibility orderings that avoid such a result. These operators are
characterised in our domain of interest by a pair of intuitively compelling
properties, which turn out to enable the derivation of a number of iterated
contraction postulates from postulates for iterated revision. We finish by
observing that a salient member of this family allows for the derivation of
counterparts for contraction of some well known iterated revision operators, as
well as for defining new iterated contraction operators.
