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An extension of semantic resolution is proposed. It is also an extension of the set of support as it can be considered as a particular case of semantic resolution. It is proved sound and refutationally complete. The extension is based on our former method for model building. The approach uses constrained clauses (or c-clauses), i.e. couples [clause : constraint]. Two important new features are introduced with respect to semantic resolution. Firstly, the method builds its own (finite ordblp:conf/ijcai/CaferraP95 fatcat:bcbea3dhnzfd3f4slugvv36cda