01311nas a2200169 4500008004100000245003900041210003900080260003300119300001400152490000900166520084400175100001201019700002001031700001901051700002001070856005101090 2009 eng d00aParaconsistent Reasoning for OWL 20 aParaconsistent Reasoning for OWL 2 aChantilly, VA, USAbSpringer a197–2110 v58373 a

A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basid description logic ALC. In this paper, we further study how to extend the four-valued semantics to the more expressive description logic SROIQ which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapated to tractable description logics including EL++, DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for ALC and show that we can retain most of the desired properties.

1 aMa, Yue1 aHitzler, Pascal1 aPolleres, Axel1 aSwift, Terrance uhttp://dx.doi.org/10.1007/978-3-642-05082-4_1401436nas a2200169 4500008004100000245006200041210006000103260003300163300001200196490000900208520092100217100001901138700002001157700001901177700002001196856005001216 2009 eng d00aA Preferential Tableaux Calculus for Circumscriptive ALCO0 aPreferential Tableaux Calculus for Circumscriptive ALCO aChantilly, VA, USAbSpringer a40–540 v58373 a

Nonmonotonic extensions of description logics (DLs) allow for default and local closed-world reasoning and are an acknowledged desired feature for applications, e.g. in the Semantic Web. A recent approach to such an extension is based on McCarthy’s circumscription, which rests on the principle of minimising the extension of selected predicates to close off dedicated parts of a domain model. While decidability and complexity results have been established in the literature, no practical algorithmisation for circumscriptive DLs has been proposed so far. In this paper, we present a tableaux calculus that can be used as a decision procedure for concept satisfiability with respect to conceptcircumscribed ALCO knowledge bases. The calculus builds on existing tableaux for classical DLs, extended by the notion of a preference clash to detect the non-minimality of constructed models.

1 aGrimm, Stephan1 aHitzler, Pascal1 aPolleres, Axel1 aSwift, Terrance uhttp://dx.doi.org/10.1007/978-3-642-05082-4_4