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Proof systems for probabilistic uncertain reasoning. (English) Zbl 0918.03015
In the paper several deductive systems for reasoning about uncertain knowledge are proposed. Belief is identified with subjective probability, while knowledge consists of consistent finite sets of linear constraints on a belief function. The deductive systems correspond to classes of inference processes satisfying certain conditions like equivalence, renaming, obstinacy, or minimum information principle. An inference process is a function \(N\) on a knowledge \(CL\) such that for every set \(K\in CL\), \(N(K)\) is a probability function satisfying \(K\). The main results of the paper are the completeness theorems for the considered deductive systems.

MSC:
03B48 Probability and inductive logic
68T30 Knowledge representation
03B60 Other nonclassical logic
68T27 Logic in artificial intelligence
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