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This article discusses forms of reasoning (beyond ontology reasoning), and reasoning languages (beyond ontology languages), that are needed for a full deployment of the Semantic Web. We first outline a motivating application scenario, then discuss the logic languages needed on the Semantic Web and related issues. The views reported about in this article underly and have been developed within the EU research project REWERSE (REasoning on the WEb with Rules and SEmantics, cf. http://rewerse.net).