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Extending the Harper identity to iterated belief change

Booth, Richard and Chandler, Jake 2016. Extending the Harper identity to iterated belief change. Presented at: 25th International Joint Conference on Artificial Intelligence, New York, USA, 9-15 July 2016. Published in: Brewka, Gerard ed. IJCAI'16: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence. Association for Computing Machinery, pp. 987-993.

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Abstract

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e., contraction receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators.

Item Type: Conference or Workshop Item (Paper)
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher: Association for Computing Machinery
ISBN: 9781577357704
Date of First Compliant Deposit: 22 April 2016
Date of Acceptance: 5 April 2016
Last Modified: 31 Jan 2018 14:36
URI: http://orca.cardiff.ac.uk/id/eprint/89679

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