A Semantic Framework for Language Layering in WSML

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