概率信念逻辑的语义

THE SEMANTICS OF PROBABILISTIC BELIEF LOGIC

在信念逻辑基础上 ,引入概率 ,给出了一种概率信念逻辑 PBL ,增强了信念逻辑的表述能力和推理能力 .并为 PBL 建立了两种语义 :首先将知识逻辑的 Aum ann语义进行推广 ,给出 PBL 逻辑的概率 Aum ann语义 .其次为 PBL 建立了一种正规概率模态语义 ,这是一种适于刻画概率模态逻辑的语义模型 .证明了 PBL 的概率 Aum ann语义和正规概率模态语义的可靠性 ,并讨论了正规概率模态语义与 Kripke语义的关系 .最后 ,通过一个例子说明了 PBL的描述能力和推理能力 .

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.