A Bad Day Surfing Is Better than a Good Day Working: How to Revise a Total Preorder

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 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 take a step towards addressing that deficiency by providing a formal framework which goes beyond the first revision step. The framework is obtained by enriching the preference information starting from the following intuitive idea: we associate to each world x two abstract objects x and x−, with the intuition that x represents x “on a good day”, while x− represents x “on a bad day”, 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 metainformation which enables us to go beyond the first revision step of the revision operator being applied.