We leverage theoretical advances and the multi-user nature of \emph{argumentation}. The overall contributions of our work are as follows. We model the schema matching network and the reconciliation process, where we relate the experts' assertions and the constraints of the matching network to an \emph{argumentation framework}. Our representation not only captures the experts' belief and their explanations, but also enables to reason about these captured inputs. On top of this representation, we develop support techniques for experts to detect conflicts in a set of their assertions. Then we guide the conflict resolution by offering two primitives: \emph{conflict-structure interpretation} and \emph{what-if analysis}. While the former presents meaningful interpretations for the conflicts and various heuristic metrics, the latter can greatly help the experts to understand the consequences of their own decisions as well as those of others. Last but not least, we implement an argumentation-based negotiation support tool for schema matching (ArgSM), which realizes our methods to help the experts in the collaborative task.