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Incoherency problems in a combination of description logics and rules. (English) Zbl 1404.03026

Summary: 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.

MSC:

03B53 Paraconsistent logics
68T27 Logic in artificial intelligence
03B70 Logic in computer science
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