基于完备拟序的开放逻辑

开放逻辑是一个可以刻画知识的增长，更新以及假说的进化的逻辑理论，它开辟了常识推理研究一条新途径，并在机器学习，知识获取，故障诊断及知识库维护等领域有广泛的应用，基本的开放逻辑不能体现认知主体对所拥有的知识在相信程度上的区别，为此，文中给出了基于完备拟序的开放逻辑，该文采用假说上的完备拟序刻画信度区别，给出了新的重构概念，讨论了假说及完备拟序在知识进化过程中的更新，定义了新的认识进程并证明了所定义的认识进程具有收敛性。

Open Logic Based on a Complete Preorder

Open Logic is a formal system for modeling the growing and updating of knowledge and the dynamics of formal theories. It serves as a logical foundation for knowledge maintenance and software evolution. Open Logic has many similarities with belief revision theory, however, there are three essential differences between them. firstly, reconstruction in Open Logic does not need to operate on a logical closed set, nor does its output; secondly, reconstruction is not a function because its output does not need to be unique; thirdly, the limit theorem of cognitive process is given in Open Logic while this is not considered in belief revision theory. In this paper, a new kind of open logic called Open Logic based a complete preorder is proposed. Firstly, A new notion of reconstruction and the method to revise the complete preorder are given, the basic idea is that the change of the epistemic state of the agent must be as minimal as possible when the new knowledge is learned. It is then shown that the cognitive process newly defined will converge, which means that the evolution of the epistemic state can lead the knowledge of agent evolve to an ideal state. Finally, the method given in this paper is compared and contrasted with related works in the literature. The result given in this paper provide an extension to the basic Open Logic and is more suitable to the situations in which the belief degrees of the epistemic agents are different.