Theory of Belief Degrees for Reasoning about Knowledge

In many of the application areas for reasoning about knowledge, it is important to reason about the possibility of certain events as well as the knowledge of agents. This paper introduces the concept of belief degree of an agent i with respect to a fact. Moreover, based on the belief degree of agent i , the similarity degree between agent i ´s graded knowledge and a pseudo metric on the set of agent i ´s graded knowledge are established, which provide a possible framework for agent i to develop approximate reasoning by taking advantage of its graded knowledge.