In this paper we study the class of consistent belief functions, as counterparts of consistent knowledge bases in classical logic. We prove that such class can be defined univocally no matter our definition of proposition implied by a belief function. As consistency can be desirable in decision making, the problem of mapping an arbitrary belief function to a consistent one arises, and can be posed in a geometric setup. We analyze here all the consistent transformations induced by minimizing L_p distances between belief functions, represented by the vectors of their basic probabilities.
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