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The propositional language extended by two families of unary propositional probability operators and the corresponding list of probability measure axioms concerning those operators is the basis of the system preseted here. We describe a Kripke-type possible worlds semantics covering such a kind of logical systems.

The language of the propositional calculus is extended by two families of propositional probability operators, inductively applicable to the formulae, and the set of all formulae provable in an arbitrary superintuitionistic propositional logic is extended by the probability measure axioms concerning those probability operators. A logical system obtained in such a way, similar to a kind of polymodal logic, makes possible to express a probability measure of truthfulness of any formula. The paper contains a description of the Kripke-type possible worlds semantics covering the considered logical systems, being followed by the corresponding completeness results.

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