A fundamental interoperability problem is caused by the semantic heterogeneity of agents'ontologies in open multi-agent systems. In this paper, we propose a formal framework for agents debating over heterogeneous terminologies. For this purpose, we propose an argumentation-based representation framework to manage conflicting descriptions. Moreover, we propose a model for the reasoning of agents where they justify the description to which they commit and take into account the description of their interlocutors. Finally, we provide a dialectical system allowing agents to participate in a dialogue in order to reach an agreement over heterogeneous descriptions.
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