A fuzzy take on graded beliefs

Abstract

Graded 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, disjunction, negation, implication and introspection rules for graded beliefs.