  Ontologies and automated reasoning are the building blocks of the Semantic
Web initiative. Derivation rules can be included in an ontology to define
derived concepts, based on base concepts. For example, rules allow to define
the extension of a class or property, based on a complex relation between the
extensions of the same or other classes and properties. On the other hand, the
inclusion of negative information both in the form of negation-as-failure and
explicit negative information is also needed to enable various forms of
reasoning. In this paper, we extend RDF graphs with weak and strong negation,
as well as derivation rules. The ERDF stable model semantics of the extended
framework (Extended RDF) is defined, extending RDF(S) semantics. A distinctive
feature of our theory, which is based on Partial Logic, is that both truth and
falsity extensions of properties and classes are considered, allowing for truth
value gaps. Our framework supports both closed-world and open-world reasoning
through the explicit representation of the particular closed-world assumptions
and the ERDF ontological categories of total properties and total classes.
