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The field of iterated belief change has focused mainly on revision, with theother main operator of AGM belief change theory, i.e. contraction, receivingrelatively little attention. In this paper we extend the Harper Identity fromsingle-step change to define iterated contraction in terms of iteratedrevision. Specifically, just as the Harper Identity provides a recipe fordefining the belief set resulting from contracting A in terms of (i) theinitial belief set and (ii) the belief set resulting from revision by not-A, welook at ways to define the plausibility ordering over worlds resulting fromcontracting A in terms of (iii) the initial plausibility ordering, and (iv) theplausibility ordering resulting from revision by not-A. After noting that themost straightforward such extension leads to a trivialisation of the space ofpermissible orderings, we provide a family of operators for combiningplausibility orderings that avoid such a result. These operators arecharacterised in our domain of interest by a pair of intuitively compellingproperties, which turn out to enable the derivation of a number of iteratedcontraction postulates from postulates for iterated revision. We finish byobserving that a salient member of this family allows for the derivation ofcounterparts for contraction of some well known iterated revision operators, aswell as for defining new iterated contraction operators.

Extending the Harper Identity to Iterated Belief Change