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Hierarchies of probabilistic logics. (English) Zbl 1433.03061
Summary: Our aim is to present what we call the lower and the upper hierarchy of the real valued probability logics with probability operators of the form \(P_{\geqslant s}\) and \(Q_F\), where \(s \in [0, 1]_{\mathbb{Q}} = [0, 1] \cap \mathbb{Q}\) and \(F\) is a recursive subset of \([0, 1]_{\mathbb{Q}}\). The intended meaning of \(P_{\geqslant s} \alpha\) is that the probability of \(\alpha\) is at least \(s\), while the intended meaning of \(Q_F \alpha\) is that the probability of \(\alpha\) is in \(F\).

MSC:
03B48 Probability and inductive logic
03D55 Hierarchies of computability and definability
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