This paper demonstrates the potential of the Semantic Web as a platform for representing, navigating and processing arguments on a global scale. We use the RDF Schema (RDFS) ontology language to specify the ontology of the recently proposed Argument Interchange Format (AIF) and an extension thereof to Toulmin's argument scheme. We build a prototype Web-based system for demonstrating basic querying for argument structures expressed in the Resource Description Framework (RDF). An RDF repository is created using the Sesame open source RDF server, and can be accessed via a user interface that implements various user-defined queries.