Negation of graded beliefs

Abstract : Negation is a key element in the construction of logical systems and plays a central role in reasoning and information manipulation tools. This paper considers the issue of negating graded beliefs, in the framework of a graded doxastic logic. It studies three interpretations of negation for these high level pieces of information, where negation is transferred to the three components of graded beliefs: the formula about which a belief is expressed, the belief modality and the belief level. The paper discusses the choice of appropriate formal frameworks for each of them, considering modal, fuzzy and many-valued logics; it characterises their use and underlines their relations, in particular regarding their effects on the belief degrees.
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Bénédicte Legastelois, Marie-Jeanne Lesot, Adrien Revault d'Allonnes. Negation of graded beliefs. Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2016, Jun 2016, Eindhoven, Netherlands. ⟨hal-01340493⟩

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