Relevant minimal change in belief update
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
Belief revision within fragments of propositional logic
Journal of Computer and System Sciences
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This article discusses Parikh's axiom of relevance in belief revision, and recalls some results from Kourousias and Makinson (2007, J. Symbolic Logic, 72, 994–1002) in this context. The crucial distinction is emphasized between the uniqueness of the finest splitting of K and the fact that K has several normal forms associated with that finest splitting. The main new result of this article is a new proof for the theorem that the set of prime implicates of K is a normal form for the finest splitting of K. It is explained how this proof avoids a mistake in an earlier proof from Wu and Zhang (2010, Knowledge-Based Syst., 23, 70–76). As a corollary, relevance can be re-defined without reference to the finest splitting, using the notion of path-relevance from Makinson (2009, J. Appl. Logic, 7, 377–387). Finally, a weak yet sufficient condition for irrelevance is presented.