Hierarchies of probabilistic logics

• 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.

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⩾sP⩾s and QFQF, where s∈[0,1]Q=[0,1]∩Qs∈[0,1]Q=[0,1]∩Q and F   is a recursive subset of [0,1]Q[0,1]Q. The intended meaning of P⩾sαP⩾sα is that the probability of α is at least s  , while the intended meaning of QFαQFα is that the probability of α is in F.