A Fuzzy Take on Graded Beliefs

Bénédicte Legastelois (1) , Marie-Jeanne Lesot (1) , Adrien Revault d'Allonnes (2)

1 LFI - Learning, Fuzzy and Intelligent systems
2 LIASD - Laboratoire d'Informatique Avancée de Saint-Denis

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, disjunc-tion, negation, implication and introspection rules for graded beliefs.

Mots clés: belief reasoning; doxastic logic; fuzzy set theory

Domaines: Intelligence artificielle [cs.AI]

Bénédicte Legastelois, Marie-Jeanne Lesot, Adrien Revault d'Allonnes. A Fuzzy Take on Graded Beliefs. 10th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2017), Sep 2017, Varsovie, Poland. pp.392-404, ⟨10.1007/978-3-319-66824-6_35⟩. ⟨hal-01591903⟩