A Fuzzy Take on Graded Beliefs

International audienceGraded beliefs increase the expressiveness of any model representing beliefs, by allowing the introduction of modulation: it is then possible to model different levels of belief. The increased expressiveness raises issues regarding the interpretation of these levels as well as their combination. This paper addresses this issue proposing a fuzzy interpretation of graded beliefs, viewed as a fuzzy subset of the universe of well formed formulae, considering belief degrees as membership degrees to a belief set. It studies the consequences of this interpretation , for the definition of graded belief manipulation rules and of graded variants of the doxastic axioms KD45, leading to the proposition of conjunction, disjunc-tion, negation, implication and introspection rules for graded beliefs