A knowledge base with dependencies

Traditionally, knowledge is defined as justified true belief (JTB). However, Gettier Problem showed that JTB is not sufficient for knowledge. This paper argues that validity of knowledge has to depend on justifications of knowledge. Therefore, justifications of knowledge have to be stored in knowledge base also. Based on Truth Maintenance Systems, this paper presents a novel knowledge representation system, i.e. knowledge bases with dependencies. This paper applies this idea to propositional logic program. Given a logic program, consequences together with their dependencies are computed and recorded. For updating consequences set with dependencies, this paper proposes an algorithm of rule addition and two algorithms of rule deletion. The second algorithm of rule deletion can handle the problem of circular dependency. Knowledge bases with dependencies can provide a new foundation for belief revision and argument.