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/jzs043