This paper lays theoretical and software foundations for a World Wide Argument Web (WWAW): a large-scale Web of inter-connected arguments posted by individuals to express their opinions in a structured manner. First, we extend the recently proposed Argument Interchange Format (AIF) to express arguments with a structure based on Walton’s theory of argumentation schemes. Then, we describe an implementation of this ontology using the RDF Schema language, and demonstrate how our ontology enables the representation of networks of arguments on the Semantic Web. Finally, we present a pilot Semantic Web-based system, ArgDF, through which users can create arguments using different argumentation schemes and can query arguments using a Semantic Web query language. Users can also attack or support parts of existing arguments, use existing parts of an argument in the creation of new arguments, or create new argumentation schemes. As such, this initial public-domain tool is intended to seed a var...