Belief Revision and Rational Inference

TL;DR

This paper introduces a new postulate for belief revision that links AGM revision to rational, consistency-preserving relations, providing a clearer understanding of how theories are revised and related.

Contribution

It proposes a novel postulate for belief revision, establishing a one-to-one correspondence with rational, consistency-preserving relations and analyzing iterative revision viewpoints.

Findings

New postulate aligns AGM revisions with rational relations

Explicit correspondence between revisions and rational relations

Discussion of iterative revision perspectives

Abstract

The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and compared with other similar postulates that have been proposed in the literature. The AGM revisions that satisfy this new postulate stand in one-to-one correspondence with the rational, consistency-preserving relations. This correspondence is described explicitly. Two viewpoints on iterative revisions are distinguished and discussed.