This paper proposes a cooperative approach for composite ontology mapping. We first present an extended classification of automated ontology matching and propose an automatic composite solution for the matching problem based on cooperation. In our proposal, agents apply individual mapping algorithms and cooperate in order to change their individual results. We assume that the approaches are complementary to each other and their combination produces better results than the individual ones. Next, we compare our model with three state of the art matching systems. The results are promising specially for what concerns precision and recall. Finally, we propose an argumentation formalism as an extension of our initial model. We compare our argumentation model with the matching systems, showing improvements on the results.