Completeness theorem for propositional probabilistic models whose measures have only finite ranges. (English) Zbl 1057.03028

Đordević, Radosav; Rašković, Miodrag; Ognjanović, Zoran

Arch. Math. Logic 43, No. 4, 557-563 (2004).

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

Keywords:

probabilistic logic; finite ranges of probabilities; completeness