Admissible and Restrained Revision

TL;DR

This paper characterizes a class of belief revision operators called admissible, which balance between natural and lexicographic revision, introducing restrained revision as the most conservative option and providing a framework for selecting suitable operators.

Contribution

It defines admissible revision operators, introduces restrained revision, and analyzes their properties and relationships, advancing the theory of iterated belief revision.

Findings

Restrained revision is the most conservative admissible operator.

Lexicographic revision is the least conservative among admissible operators.

Restrained revision can be viewed as natural revision preceded by backward revision.

Abstract

As partial justification of their framework for iterated belief revision Darwiche and Pearl convincingly argued against Boutiliers natural revision and provided a prototypical revision operator that fits into their scheme. We show that the Darwiche-Pearl arguments lead naturally to the acceptance of a smaller class of operators which we refer to as admissible. Admissible revision ensures that the penultimate input is not ignored completely, thereby eliminating natural revision, but includes the Darwiche-Pearl operator, Nayaks lexicographic revision operator, and a newly introduced operator called restrained revision. We demonstrate that restrained revision is the most conservative of admissible revision operators, effecting as few changes as possible, while lexicographic revision is the least conservative, and point out that restrained revision can also be viewed as a composite operator, consisting of natural revision preceded by an application of a "backwards revision" operator previously studied by Papini. Finally, we propose the establishment of a principled approach for choosing an appropriate revision operator in different contexts and discuss future work.