Jos de Bruijn and Stijn Heymans. A semantic framework for language layering in WSML. In Proceedings of the 1st International Conference on Web Reasoning and Rule Systems (RR2007), pages 103-117, Innsbruck, Austria, June 7-8 2007. Springer.

WSML presents a framework encompassing different language variants, rooted in Description Logics and (F-)Logic Programming. So far, the precise relationships between these variants have not been investigated. We take the nonmonotonic first-order autoepistemic logic, which generalizes both Description Logics and Logic Programming, and extend it with frames and concrete domains, to capture all features of WSML; we call this novel formalism FF-AEL. We consider two forms of language layering for WSML, namely loose and strict layering, where the latter enforces additional restrictions on the use of certain language constructs in the rule-based language variants, in order to give additional guarantees about the layering. Finally, we demonstrate that each WSML variant semantically corresponds to its target formalism, i.e. WSML-DL corresponds to SHIQ(D), WSML-Rule to the Stable Model Semantics for Logic Programs, a generalization of the Well-Founded Semantics, and WSML-Core to DHL(D) (without nominals), the Horn subset of SHIQ(D).

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