Law information retrieval systems use law ontologies to represent semantic objects, to associate them with law documents and to make inferences about them. A number of law ontologies have been proposed in the literature, what shows the variety of approaches pointing to the need of matching systems. We present a proposal based on argumentation to match law ontologies, as an approach to be considered for this problem. Argumentation is used to combine different techniques for ontology matching. Such approaches are encapsulated by agents that apply individual matching algorithms and cooperate in order to exchange their local results (arguments). Next, based on their preferences and confidence, the agents compute their preferred matching sets. The arguments in such preferred sets are viewed as the set of globally acceptable arguments. We show the applicability of our model matching two legal core ontologies: LKIF and CLO.