Hierarchies of probabilistic logics

Our aim is to present what we call the lower and the upper hierarchy of the real valued probability logics with probability operators of the form P⩾s and QF, where s∈[0,1]Q=[0,1]∩Q and F is a recursive subset of [0,1]Q. The intended meaning of P⩾sα is that the probability of α is at least s, while the intended meaning of QFα is that the probability of α is in F. •We consider probability logics with two types of probability operators.•The first type expresses assertions of the form “the probability of α is at least r”.•The second type expresses assertions of the form “the probability of α is in the set F”.•We provide a classification of studied logics and show that they form a proper hierarchy.