Some probability logics with new types of probability operators

We introduce new types of probability operators of the form QF, where F is a recursive rational subset of [0,1]. A formula QFα is satisfied in a probability model if the measure of the set of worlds that satisfy α 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.