Probabilistic Belief Logic and Its Probabilistic Aumann Semantics

In this paper, we present a logic system forprobabilistic belief named PBL, which expands the language of belieflogic by introducing probabilistic belief. Furthermore, we give theprobabilistic Aumann semantics of PBL. We also list some validproperties of belief and probabilistic belief, which form the deductionsystem of PBL. Finally, we prove the soundness and completeness ofthese properties with respect to probabilistic Aumann semantics.