RDF Surfaces: Enabling Classical Negation on the Semantic Web

TL;DR

RDF Surfaces is introduced, an extension of RDF that incorporates the concept of classic negation, known from first-order logic, offering an abstract, visual approach to negation within the Semantic Web, offering a more general and widely applicable approach than previous attempts at incorporating negation.

Abstract

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.

Figures (15)

• Figure 1: A positive surface with the symbols $A$ and $B$, a nested negative surface with the symbol $A$, and a deeper nested negative surface with the symbol $C$. The logical interpretation of this diagram is $A \land B \land \lnot (A \land \lnot C)$. The parity of the surface is the number of "negative borders" one needs to cross to reach the symbols modulo 2. The positive surfaces has parity 0, the negative surfaces with $A$ parity 1, and the negative surface with $C$ parity 0.
• Figure 2: The first inner nested negative surface (the one with odd parity) of \ref{['fig:s4_positive_negative']} has a containment of 5 symbols/nested surfaces.
• Figure 3: Using rule R4 a copy of a symbol or nested surface can be placed in at any surface level which is contained by the origin surface. But, it is not possible to place a copy of a nested surface within itself.
• Figure 4: (a) A representation of $A \land B \land \lnot ( A \land \lnot C )$ ; (b) the deiterate rule R4 is applied to erase a copy of $A$ from the nested negative surface; (c) the double cut rule R3 is applied to erase the double nested surface; (d) the result of the deduction $A \land B \land C$.
• Figure 5: Diagram representations of (a) $A \land B$, (b) $\lnot A$, (c) $A \lor B$, and (d) $A \rightarrow B$

Theorems & Definitions (4)

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