Some Probability Logics with New Types of Probability Operators

We introduce new types of probability operators of the form QF , whereF is a recursive rational subset of [0; 1]. A formulaQF is satisfied in a probability model if the measure of the set of worlds that satisfy 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 QF -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.