THE SEMANTICS OF PROBABILISTIC BELIEF LOGIC

In this paper, probability is introduced based on belief logic, and a probabilistic belief logic—PBL is given, which can improve the expressive power and deductive power of belief logic. Two kinds of semantics for PBL are also given. Firstly, the Aumann semantics of knowledge logic is generalized to give the semantics of PBL. Secondly, a new semantics of PBL—normal probabilistic modal semantics is given, which is a new semantics suited for modeling probabilistic modal logic. The soundness of PBL about normal probabilistic modal semantics is proved and the relation of normal probabilistic modal semantics and Kripke semantics is discussed. Finally, the expressive power and deductive power of PBL are shown by an example.