an:06446853
Zbl 1314.68307
Cooke, Roger; Smets, Philippe
Self-conditional probabilities and probabilistic interpretations of belief functions
EN
Ann. Math. Artif. Intell. 32, No. 1-4, 269-285 (2001).
1012-2443 1573-7470
2001
j
68T37 03B48 60A05 68T30
belief functions; self-conditional expected probabilities; Dempster's model; probability of modal propositions
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.