  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.
