01470nas a2200205   4500008004100000245006600041210006600107300001400173490000700187520083300194653002001027653003301047653002901080653002801109653002901137100001801166700001601184700002001200856004401220       2013                        eng d00aReasoning with Inconsistencies in Hybrid MKNF Knowledge Bases0 aReasoning with Inconsistencies in Hybrid MKNF Knowledge Bases  a263–2900 v213 aThis 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.10aData complexity10aDescription logics and rules10aKnowledge representation10aNon-monotonic reasoning10aParaconsistent reasoning1 aHuang, Shasha1 aLi, Qingguo1 aHitzler, Pascal  uhttp://dx.doi.org/10.1093/jigpal/jzs04301542nas a2200181   4500008004100000245006100041210006100102260003000163300001300193490000900206520099500215100001801210700001601228700002001244700002301264700002301287856005001310       2011                        eng d00aParaconsistent Semantics for Hybrid MKNF Knowledge Bases0 aParaconsistent Semantics for Hybrid MKNF Knowledge Bases  aGalway, IrelandbSpringer  a93–1070 v69023 a<p class="rtejustify">Hybrid MKNF knowledge bases, originally based on the stable model semantics, is a mature method of combining rules and Description Logics (DLs). The well-founded semantics for such knowledge bases has been proposed subsequently for better efficiency of reasoning. However, integration of rules and DLs may give rise to inconsistencies, even if they are respectively consistent. Accordingly, reasoning systems based on the previous two semantics will break down. In this paper, we employ the four-valued logic proposed by Belnap, and present a paraconsistent semantics for Hybrid MKNF knowledge bases, which can detect inconsistencies and handle it effectively. Besides, we transform our proposed semantics to the stable model semantics via a linear transformation operator, which indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide a fixpoint algorithm for computing paraconsistent MKNF models.</p>
1 aHuang, Shasha1 aLi, Qingguo1 aHitzler, Pascal1 aRudolph, Sebastian1 aGutierrez, Claudio  uhttp://dx.doi.org/10.1007/978-3-642-23580-1_8