Elsevier

Artificial Intelligence

Volume 277, December 2019, 103171
Artificial Intelligence

From iterated revision to iterated contraction: Extending the Harper Identity

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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.

Keywords

Belief revision
Iterated belief change
Belief contraction
Harper Identity
Rational closure

Cited by (0)

This paper is a substantially extended and updated version of [1], presented at the IJCAI-16 conference.