This article 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 para-MKNF knowledge bases.
& Hitzler, P.
(2013). Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases. Logic Journal of the IGPL, 21 (2), 263-290.