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Completeness theorem for propositional probabilistic models whose measures have only finite ranges. (English) Zbl 1057.03028
Summary: A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form \(P_{\geq s}\) (with the intended meaning “the probability is at least \(s\)”). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.

MSC:
03C70 Logic on admissible sets
03B48 Probability and inductive logic
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