Zoran Ognjanović, Logics with probability operators
We demonstrate probability logics whose languages include probability operators. Intuitively, probability operators are used to formalize statements of the form "the probability of a formula is equal to or greater than s" or "the probability of a formula belongs to a set S". These operators possess qualities reminiscent of modal operators, and their semantics is captured by Kripke-like models with possible worlds. Instead of the typical accessibility relation, probabilities over sets of worlds are considered. Due to non-compactness, which normally holds for the logics we consider, axiomatizations with infinite rules are given and admit corresponding theorems of strong completeness.
We discuss the decidability of probability logics.