On the Dynamics of Total Preorders: Revising Abstract Interval Orders

Total preorders (tpos) are often used in belief revision to encode an agent’s strategy for revising its belief set in response to new information. Thus the problem of tpo-revision is of critical importance to the problem of iterated belief revision. Booth et al. [1] provide a useful framework for revising tpos by adding extra structure to guide the revision of the initial tpo, but this results in single-step tpo revision only. In this paper we extend that framework to consider double-step tpo revision. We provide new ways of representing the structure required to revise a tpo, based on abstract interval orders, and look at some desirable properties for revising this structure. We prove the consistency of these properties by giving a concrete operator satisfying all of them.