On the Dynamics of Total Preorders: Revising Abstract Interval Orders

Authors:
Richard Booth;Thomas Meyer
Affiliations:
Faculty of Informatics, Mahasarakham University, Mahasarakham, Thailand 44150;Meraka Institute, CSIR, Pretoria, South Africa
Venue:
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2007

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Abstract

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-steptpo revision only. In this paper we extend that framework to consider double-steptpo 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.