关于概率中序列事件的逻辑

A Logic for Probabilities of Successive Events

在概率论的集合语言中,除了补、交、并等运算之外,还有一个重要的运算:乘积。两个基本事件的乘积表示这些事件连续发生。然而,关于概率的逻辑文献中对序列事件的研究却比较少。在本文中,我们提出了一个模态逻辑(记为DML)来刻画概率论中关于序列事件的推理,然后我们在DML逻辑之上构造了一个概率逻辑(记为PL_(DML))。我们将DML与克里普克语义上的标准模态逻辑进行了比较,并证明了DML等价于确定性模型类上的正规模态逻辑。最后,我们还给出了PL_(DML)的演绎系统并证明了其完备性。

In the set language of probability theory,besides complement,intersection,and union,there is another important operation:product.The product of two basic events expresses that these events occur in succession.However,there is limited research about successive events in the literature on probability logic.In this paper,we propose a modal logic(called DML)to capture the reasoning about successive events in probability theory,and then we construct a probability logic(called PLDML)based on DML.We compare DML with standard modal logic on Kripke semantics and show that DML is equivalent to the normal modal logic on deterministic models.We also give a deductive system of PLDML and show its completeness.