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

Booth, Richard ORCID: https://orcid.org/0000-0002-6647-6381 and Chandler, Jake 2020. On strengthening the logic of iterated belief revision: proper ordinal interval operators. Artificial Intelligence 285 , 103289. 10.1016/j.artint.2020.103289

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Abstract

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. However, most of the suggestions for doing so have been radical enough to result in a dubious ‘reductionist’ principle that identifies belief states with orderings of worlds. The present paper offers a more modest strengthening of Darwiche and Pearl’s proposal. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the family that these principles characterise, which subsumes both lexicographic and restrained revision, can be represented as relating belief states that are associated with a ‘proper ordinal interval’ 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 a large number of AGM era postulates.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Publisher:	Elsevier
ISSN:	0004-3702
Date of First Compliant Deposit:	5 May 2020
Date of Acceptance:	29 April 2020
Last Modified:	17 Nov 2024 21:00
URI:	https://orca.cardiff.ac.uk/id/eprint/131371

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