Open Logic Based on a Complete Preorder
Da Liu · Chinese Journal of Computers · 2002
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.