We propose in this paper DIALOCR, i.e. a framework for inter-agents dialogue to reach an ontological agreement, which formalize a debate in which the divergent representations are discussed. For this purpose, we propose an argumentation-based representation framework which manages the conflicts between representations with different relevances for different audiences to compute their acceptance. Moreover, we propose a model for the reasoning of agents where they justify the definition to which they commit and take into account the definitions of their interlocutors. This framework bounds a dialectics system in which two agents play a dialogue to reach an agreement about a conflict of representation.