Possibility Theory, Belief Revision and Nonmonotonic Logic

This paper is a brief overview of joint work done with Salem Benferhat and Jerome Lang, at IRIT in Toulouse on the application of possibility theory to automated reasoning under uncertainty. A noticeable aspect of this research is that although first motivated by Zadeh's interpretation of fuzzy sets as elastic constraints, possibilistic logic has developed in close connection with the mainstream research in belief revision and nonmonotonic reasoning. Especially, Gardenfors' revision postulates leads to an epistemic entrenchment ordering of pieces of knowledge that can be encoded by means of a necessity measure only. And possibilistic logic turns out to belong to the family of preferential logics after Shoham, that unify most of the existing nonmonotonic logics.

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