Jos de Bruijn and Stijn Heymans. WSML ontology semantics. Final Draft d28.3, WSML Working Group, 2007.

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 firstorder 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 (the Well-Founded Semantics can be seen as an approximation), and WSML-Core to DHL(D) (without nominals), a Horn subset of SHIQ(D).

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