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Self-conditional probabilities and probabilistic interpretations of belief functions. (English) Zbl 1314.68307
Summary: We present an interpretation of belief functions within a pure probabilistic framework, namely as normalized self-conditional expected probabilities, and study their mathematical properties. Interpretations of belief functions appeal to partial knowledge. The self-conditional interpretation does this within the traditional probabilistic framework by considering surplus belief in an event emerging from a future observation, conditional on the event occurring. Dempster’s original interpretation, in contrast, involves partial knowledge of a belief state. The modal interpretation, currently gaining popularity, models the probability of a proposition being believed (or proved, or known). The versatility of the belief function formalism is demonstrated by the fact that it accommodates very different intuitions.
68T37 Reasoning under uncertainty in the context of artificial intelligence
03B48 Probability and inductive logic
60A05 Axioms; other general questions in probability
68T30 Knowledge representation
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