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A propositional \(p\)-adic probability logic. (English) Zbl 1265.03011
The author introduces a probability logic such that the range of probability functions is the set \(S\) of all \(p\)-adic integers which are algebraic over \(Q\). The logical language contains Boolean combinations of formulas of the form \(P_{=s}\alpha\), where \(s\in S\), and \(\alpha\) is a propositional formula. A semantics is given by a class of Kripke-like structures enriched by finitely additive \(p\)-adic probabilities. An infinitary axiom system is provided and proven to be sound and strongly complete with respect to that class of models. A decidability procedure which checks satisfiability of formulas is presented.

03B48 Probability and inductive logic
03B25 Decidability of theories and sets of sentences
03B42 Logics of knowledge and belief (including belief change)
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