La Trobe

From iterated revision to iterated contraction: Extending the Harper Identity

journal contribution
posted on 2025-05-09, 06:19 authored by Richard Booth, Jacob ChandlerJacob Chandler
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.

Funding

This research was partially supported by the Australian Government through an Australian Research Council Future Fellowship (project number FT160100092) awarded to Jake Chandler.

History

Publication Date

2019-12-01

Journal

Artificial Intelligence

Volume

277

Article Number

103171

Pagination

20p.

Publisher

Elsevier

ISSN

0004-3702

Rights Statement

© 2019 Elsevier B.V. All rights reserved.