Incoherency Problems in a Combination of Description Logics and Rules

A paraconsistent semantics has been presented for hybrid MKNF knowledge bases-a combination method for description logics and rules. However, it is invalid when incoherency occurs in the knowledge base. In this paper, we introduce a semi-S-5 semantics for hybrid MKNF knowledge bases on the basis of nine-valued lattice, such that it is paraconsistent for incoherent knowledge base. It is shown that a semi-S-5 model can be computed via a fixpoint operator and is in fact a paraconsistent MKNF model when the knowledge base is incoherent. Moreover, we apply six-valued lattice to hybrid MKNF knowledge bases and present a suspicious semantics to distinguish different trust level information. At last, we investigate the relationship between suspicious semantics and paraconsistent semantics.