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 Q F , where s ? 0 , 1 Q = 0 , 1 ? Q and F is a recursive subset of 0 , 1 Q . The intended meaning of P ? s α is that the probability of α is at least s, while the intended meaning of Q F α 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.

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