On the Relation Between the Coherence and Foundations Theories of Belief Revision

Abstract

Two recent papers, (Gardenfors 1990; Doyle 1992), try to assess the relative merits of the two main approaches to belief revision, the foundations and coherence theories, but leave open the question of the mathematical connections between them. We answer this question by showing that the foundations and coherence theories of belief revision are mathematically equivalent. The result also has consequences for nonmonotonic reasoning, as it entails that Poole's system of default reasoning and Shoham's preferential logic are expressively equivalent, in that they can represent the same set of non monotonic consequence relations. Introduction Two major approaches to belief revision can be distinguished, according to the role assigned in the belief revision process to the agent's reasons for holding his or her beliefs. In the foundations theory of belief revision, the agent's beliefs are seen as having a structure beyond the purely logical relations among them. In particular, certain beliefs ...