OWL (Web Ontology Language) was proposed by W3C in 2003 as a standard language for representing Web ontologies. It is intended to facilitate the machine interpret-ability of the Webcontent by providing a vocabulary with a formal semantics, which is missing in XML, RDF, or RDF Schema.The original definition of OWL comes with a standardmodel-theoretic semantics. Meanwhile many other paradigms were used to give semantics to web ontologies, such as description logic (DL), Datalog, logic programming (LP), first-order logic (FOL), autoepistemic DL (ADL) etc.Some of these semantics (DL, FOL) interpret OWL ontologies under Open World Assumption (OWA), whereas the others (LP, ADL) interpret OWL ontologies under Closed World Assumption (CWA).A main problem which arise here is to find out theconditions under which an agent interpreting an OWL ontology under OWA can interoperate with an agent which interpret thesame ontology under CWA. We supply a solution to this problem by defining integratedsemantics for OWL. Integrated semantics interprets an OWL ontologyby a diagram of target logics rather than just one logic.The arrows in the diagram represent the relationships between logics formalised as comorphisms. We claim that the interoperability is possible only if a morphism between the two models exists in theintegrated semantics.
In our talk we consider the case of DL, as an interpretationunder OWA, and LP, as an interpretation under CWA. We point out which are the difficulties in organising an LP paradigm as a logic and in formalising the relationship between DL and LP.For the case of LP with stable semantics, we show that the”closing the world” relationship can be expressed by a set of constraints expressed as MKNF rules.