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Title: Coherence and correction of belief and necessity assessments Authors:  Davide Petturiti - University of Perugia (Italy) [presenting]
Barbara Vantaggi - University La Sapienza (Italy)
Abstract: Belief functions are uncertainty measures simultaneously close to finitely additive probability measures in terms of properties and able to deal with ambiguity. The elicitation of a belief assessment on a set of events without a particular algebraic structure requires a suitable notion of coherence. De Finetti's work on finitely additive coherent probabilities has shown three possible approaches to coherence: coherence as a consistency notion, coherence as a fair betting scheme, and coherence in terms of penalty criterion. We present generalized notions of coherence for a belief assessment in all the forms recalled above, and prove their equivalence. In turn, this allows us to single out different interpretations of a belief assessment. We further introduce the specialization of such conditions to work in the sub-framework of finitely minitive necessity measures. Finally, we propose a general penalty criterion based on a (strictly) proper scoring rule and investigate the correction of an incoherent assessment in the different frameworks.