The Resource Description Framework (RDF) is a fundamental technology in the Semantic Web, enabling the representation and interchange of structured data. However, RDF lacks the capability to express negated statements in a generic way. As a result, exchanging negative information on a Web scale is thus far restricted to specific cases and predefined statements. The ability to negate (virtually) any RDF statement allows for a comprehensive way to refute, deny or otherwise invalidate claims on a Web scale. Via an intermediate step of a diagrammatic approach to logical expressions called Peirce graphs, we introduce RDF Surfaces, an extension of RDF that incorporates the concept of classic negation, known from first-order logic. Overall, RDF Surfaces provides an abstract, visual approach to negation within the Semantic Web, offering a more general and widely applicable approach than previous attempts at incorporating negation. Aside from a (traditional) programmatic syntax, RDF Surfaces can also be represented visually by means of diagrams inspired by Peirce graphs. We demonstrate negation via RDF Surfaces and how to reason upon it in illustrative use cases drawn from the domains of academic publishing and eHealth. We hope this vision paper attracts new implementers and opens the discussion to its formal specification.

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