Incompatibilities between iterated and relevance-sensitive belief revision

AI Access Foundation
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Journal Article
Journal of Artificial Intelligence Research, 2020, 69, pp. 85-108
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© 2020 AI Access Foundation. The AGM paradigm for belief change, as originally introduced by Alchourron, Gardenfors and Makinson, lacks any guidelines for the process of iterated revision. One of the most inuential work addressing this problem is Darwiche and Pearl's approach (DP approach, for short), which, despite its well-documented shortcomings, remains to this date the most dominant. In this article, we make further observations on the DP approach. In particular, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with axiom (P). The whole study, essentially, indicates that two fundamental aspects of the revision process, namely, iteration and relevance, are in deep conict, and opens the discussion for a potential reconciliation towards a comprehensive formal framework for knowledge dynamics.
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