In this paper we present a mediating algorithm to provide a conflict resolution in the knowledge management system K-DSS which is a decision support system for identifying crucial knowledge. In the knowledge base of K-DSS, inconstancies can appear because of conflicts between decision makers evolved in the process of identification of crucial knowledge. Our objective is to solve conflicts by the mean of argumentative agents representing decision makers. Multiagent theory is suitable to our context due to the autonomous character of agents able to represent faithfully each human actor evolved in the process of identification of crucial knowledge.