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

Alvaro del Val

Two recent, papers, (Ggrdenfors 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.

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