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.