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From iterated revision to iterated contraction: Extending the Harper Identity

Booth, Richard and Chandler, Jake 2019. From iterated revision to iterated contraction: Extending the Harper Identity. Artificial Intelligence 277 , 103171. 10.1016/j.artint.2019.103171

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Abstract

The study of iterated belief change has principally focused on revision, with the other main operator of AGM belief change theory, namely contraction, receiving comparatively little attention. In this paper we show how principles of iterated revision can be carried over to iterated contraction by generalising a principle known as the ‘Harper Identity’. The Harper Identity provides a recipe for defining the belief set resulting from contraction by a sentence A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A. Here, we look at ways to similarly define the conditional belief set resulting from contraction by A. After noting that the most straightforward proposal of this kind leads to triviality, we characterise a promising family of alternative suggestions that avoid such a result. One member of that family, which involves the operation of rational closure, is noted to be particularly theoretically fruitful and normatively appealing.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher: Elsevier
ISSN: 0004-3702
Date of First Compliant Deposit: 7 October 2019
Date of Acceptance: 5 September 2019
Last Modified: 20 Sep 2020 02:05
URI: http://orca.cf.ac.uk/id/eprint/125889

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