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Second-order probability logic. (English) Zbl 0829.03021
Summary: We introduce the second-order probability logic \(L^2_{{\mathcal A}P \forall}\) which possesses the probability quantifiers \((P\vec x\geq r)\) on the individual variables and the ordinary quantifiers \((\forall X)\) and \((\exists X)\) on the set variables. The aim of the paper is to prove the completeness theorem for second-order probability models.
MSC:
03C80 Logic with extra quantifiers and operators
03B48 Probability and inductive logic
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