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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.

MSC:
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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