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Some probability logics with new types of probability operators. (English) Zbl 0941.03022
Summary: We introduce new types of probability operators of the form $$Q_F$$, where $$F$$ is a recursive rational subset of $$[0,1]$$. A formula $$Q_F \alpha$$ is satisfied in a probability model if the measure of the set of worlds that satisfy $$\alpha$$ is in $$F$$. The new operators are suitable for describing events in discrete sample spaces. We provide sound and complete axiomatic systems for a number of probability logics augmented with the $$Q_F$$-operators. We show that the new operators are not definable in languages of probability logics that have been used so far. We study decidability of the presented logics. We describe a relation of ‘being more expressive’ between the new probability logics.

##### MSC:
 03B48 Probability and inductive logic
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