We describe a new inconsistent case which is susceptible to occur while producing consistent answer set using prioritized default logic. We define new semantics for prioritized default logic in order to solve this problem. There is a sign difference between General and Extended logic programs. Extended logic programs are formulated using classical negation, For this reason, an inconsistent answer set can sometimes be produced. For the most part, default reasoning semantics successfully resolved this problem, but a conflict could still arise in one particular case. The purpose of this paper is to present this eventuality, and revise the semantics of default logic in order to give an answer to this problem.

An ATMS (Assumption-based Truth Maintenance System) has been widely used for maintaining the truth of an information by detecting and solving the contradictions in rule-based systems. However, the ATMS cannot correctly maintain the truth of the information in case that the generated information is satisfied within a time interval or includes data about temporal relations of events in time varying situations, because it has no mechanism manipulating temporal data. In this paper, we propose the extended ATMS that can maintain the truth of the information in the knowledge-based system using information changing over time or temporal relations of events. To maintain the contexts generated by relations of events, we modify the label representation method, the disjunction and conjunction simplification method in the label-propagation procedure and the nogood handling method of the conventional ATMS.