The vision underlying the development of the Semantic Web is that the whole complex of our knowledge forms a huge semantic network, which should be represented and made explicit by means of languages such as RDF, RDFS or OWL. However, these languages have important expressive limits, since none of them reaches the full expressive power of a first-order language. As a result, large parts of our knowledge—in particular, mathematical and scientific theories—cannot currently be made available on the Semantic Web as (...) linked data, not even in principle. In this work, we are going to define FOOL (first-order ontology language), a new ontological language compatible with RDF, which allows the expression of any formula of a first-order language as a connected RDF graph. FOOL is as expressive as a first-order language, but unlike it, its statements do not have a serialized form. Instead, like a RDF statement, each statement of a FOOL knowledge base is a connected graph, and different statements link to each other through the meaningful nodes they share. In this way, the semantic relationships between statements are made explicit, and given FOOL’s compatibility with RDF, virtually the entire complex of our knowledge can in principle be made available on the Semantic Web as linked data. The semantic relationships made explicit by a FOOL ontology are not those of logical consequence, but they are meaning connections between statements represented as graphs. It is not far-fetched to think that, by devising appropriate measures of the linking patterns between statements, such relations can be mechanized, thus opening the way to new and possibly unforeseen results and applications. (shrink)