When agents communicate they do not necessarily use the same vocabulary or ontology. For them to interact successfully they must find correspondences between the terms used in their ontologies. While many proposals for matching two agent ontologies have been presented in the literature, the resulting alignment may not be satisfactory to both agents and can become the object of further negotiation between them. This paper describes our work constructing a formal framework for reaching agents' consensus on the terminology they use to communicate. In order to accomplish this, we adapt argument-based negotiation used in multi-agent systems to deal specifically with arguments that support or oppose candidate correspondences between ontologies. Each agent can decide according to its interests whether to accept or refuse the candidate correspondence. The proposed framework considers arguments and propositions that are specific to the matching task and related to the ontology semantics. This argumentation framework relies on a formal argument manipulation schema and on an encoding of the agents preferences between particular kinds of arguments. The former does not vary between agents, whereas the latter depends on the interests of each agent. Therefore, this work distinguishes clearly between the alignment rationales valid for all agents and those specific to a particular agent.