Approximate 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 with respect to a fact at a given point. 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. Lastly, two kinds of models for approximate reasoning are proposed, which provides a possible framework for an agent to develop approximate reasoning at a given point by using its graded knowledge.