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A \(p\)-adic probability logic. (English) Zbl 1251.03027
In this paper a propositional logic \(\mathcal L_{\mathbb Q_p}\) is introduced which is a generalization of Khrennikov’s \(p\)-adic probability theory. It is shown that \(\mathcal L_{\mathbb Q_p}\) is sound and complete with respect to appropriate notions.
The first sections give background and motivation.
Thereafter, the main notions, such as \(\mathcal L_{\mathbb Q_p}\)-model and the satisfiability relation, are introduced.
The main content of Section three are five axioms and six inference rules, and a short discussion of these axioms and rules is given. In the next section, soundness and strong completeness of \(\mathcal L_{\mathbb Q_p}\) with respect to these axioms and rules are shown.
Section five contains decidability considerations. In the sixth and final section, the authors give their conclusions.

MSC:
03B48 Probability and inductive logic
03B25 Decidability of theories and sets of sentences
03B42 Logics of knowledge and belief (including belief change)
68T27 Logic in artificial intelligence
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