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Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/4950

Title: How to revise a total preorder
Authors: Booth, R
Meyer, T
Keywords: Revision operator
Interval orderings
Preorder
Belief revision
Iterated belief revision
Philosophical logic
Issue Date: Feb-2011
Publisher: Springer
Citation: Booth, R and Meyer, T. 2011. How to revise a total preorder. Journal of Philosophical Logic, Vol. 40(2), pp 193-238.
Series/Report no.: Workflow;6072
Abstract: Most approaches to iterated belief revision are accompanied by some motivation for the use of the proposed revision operator (or family of operators), and typically encode enough information in the epistemic state of an agent for uniquely determining one-step revision. But in those approaches describing a family of operators there is usually little indication of how to proceed uniquely after the first revision step. In this paper we contribute towards addressing that deficiency by providing a formal framework which goes beyond the first revision step in two ways. First, the framework is obtained by enriching the epistemic state of an agent starting from the following intuitive idea: we associate to each world x two abstract objects x+ and x−, and we assume that, in addition to preferences over the set of worlds, we are given preferences over this set of objects as well. The latter can be considered as meta-information encoded in the epistemic state which enables us to go beyond the first revision step of the revision operator being applied, and to obtain a unique set of preferences over worlds. We then extend this framework to consider, not only the revision of preferences over worlds, but also the revision of this extended structure itself. We look at some desirable properties for revising the structure and prove the consistency of these properties by giving a concrete operator satisfying all of them. Perhaps more importantly, we show that this framework has strong connections with two other types of constructions in related areas. Firstly, it can be seen as a special case of preference aggregation which opens up the possibility of extending the framework presented here into a full-fledged framework for preference aggregation and social choice theory. Secondly, it is related to existing work on the use of interval orderings in a number of different contexts.
Description: Copyright: 2011 Springer. This is a pre print version of the work. The definitive version is published in Journal of Philosophical Logic, Vol. 40(2), pp 193-238
URI: http://krr.meraka.org.za/wp-content/uploads/2011/03/jpl-booth-ea-2011.pdf
http://hdl.handle.net/10204/4950
ISSN: 0022-3611
Appears in Collections:Digital intelligence
General science, engineering & technology

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