Issues of circulations in nonmonotonic reason maintenance systems

This paper discusses the circulation problems in nonmonotonic reason maintenance systems (NMRMS) which is a consistency maintenance system for nonmonotonic belief bases. When a new justification of a node is inferred and added into the belief base, the NMRMS checks up the affect on the states of the nodes in the belief base. If the new justification results in any inconsistency of node states, the system manages to remove the contradictions and maintain the consistency of the belief base. However, the circulations among the relations of nodes' premises and consequences will likely make the consistency maintenance fail. This paper, first, gives the formal descriptions of nodes in NMRMS, and then presents a circulation model which classifies the circulations in nonmonotonic belief bases into simple circulations, overlap circulations, tangent circulations, bridge circulations and link circulations. Further, the mechanism of recognition and handling of these circulations are discussed. Finally, the algorithms for recognition and handling of some circulations are given.