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On strengthening the logic of iterated belief revision: Proper ordinal interval operators

Booth, Richard ORCID: and Chandler, Jake 2018. On strengthening the logic of iterated belief revision: Proper ordinal interval operators. Presented at: 16th International Conference on Principles of Knowledge Representation and Reasoning, Tempe, AZ, USA, 27 October - 2 November 2018.

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Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general.

Item Type: Conference or Workshop Item (Paper)
Date Type: Completion
Status: Published
Schools: Computer Science & Informatics
Date of First Compliant Deposit: 22 August 2018
Last Modified: 24 Oct 2022 07:12

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