@article {62,
	title = {Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases},
	journal = {Logic Journal of the IGPL},
	volume = {21},
	year = {2013},
	pages = {263{\textendash}290},
	abstract = {This paper is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different paraMKNF knowledge bases.},
	keywords = {Data complexity, Description logics and rules, Knowledge representation, Non-monotonic reasoning, Paraconsistent reasoning},
	doi = {10.1093/jigpal/jzs043},
	url = {http://dx.doi.org/10.1093/jigpal/jzs043},
	author = {Shasha Huang and Qingguo Li and Pascal Hitzler}
}
@article {74,
	title = {Local Closed World Reasoning with Description Logics under the Well-Founded Semantics},
	journal = {Artificial Intelligence},
	volume = {175},
	year = {2011},
	pages = {1528{\textendash}1554},
	abstract = {<p class="rtejustify">An important question for the upcoming Semantic Web is how to best combine open world ontology languages, such as the OWL-based ones, with closed world rule-based languages. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases [52], and it is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. In this paper we propose a well-founded semantics for nondisjunctive hybrid MKNF knowledge bases that promises to provide better efficiency of reasoning, and that is compatible with both the OWL-based semantics and the traditional Well-Founded Semantics for logic programs. Moreover, our proposal allows for the detection of inconsistencies, possibly occurring in tightly integrated ontology axioms and rules, with only little additional effort. We also identify tractable fragments of the resulting language.</p>
},
	keywords = {Description Logic, Knowledge representation, Logic Programming, Non-monotonic reasoning, Ontologies, Semantic Web},
	doi = {10.1016/j.artint.2011.01.007},
	url = {http://dx.doi.org/10.1016/j.artint.2011.01.007},
	author = {Matthias Knorr and Jos{\'e} J{\'u}lio Alferes and Pascal Hitzler}
}
