A special external atom or an entire conjunction of such atoms can be used to achieve hybrid rule-ontology integration, allowing a query-like interface to OWL classes (including their subClassOf subsumption) and properties (including subPropertyOf subsumption). Optional typing of RIF variables (e.g., for a Sorted Horn Logic) can be regarded as the special case of such an interface for OWL-Lite classes. (Predefined classes, such as Integer, can be borrowed from XML Part 2, Datatypes.)
The semantics of such integrations are different for RIF LP, FO, and PR.
In case of FO, there is no semantic mismatch and the overall semantics is first-order. In case of LP, recent work by Rosati (DL+Log, KR2006) provides a semantics for a very general class of rulesets that are tightly integrated with DL-based ontologies. However, even more general, ad hoc interoperability between rules and ontologies might be needed. For PR and RR, interoperability with OWL is likely not to have model-theoretic semantics as it will be ad hoc.