Knowledge that Transforms

LET Ω ≡ 1 2 n denote a set of states of nature, n ≥ 3. Let C denote a set of cases, the cardinality of which can be uncountably large. A database I is a function that maps C to Z+ and ∑ j∈C I(j) < ∞, where I(j) denotes the number of observations of case j in the database.1 Let I denote the set of all possible databases. A probabilistic belief function p : I → (Ω) maps databases to probability distributions over Ω. BGSS axiomatized a class of probabilistic belief functions that encapsulates the idea of “similarity-weighted frequencies,” that is, each p in this class admits a representation such that, for every I ∈ I ,