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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