Quasi-classical Semantics and Tableau Calculus of Description Logics for Paraconsistent Reasoning in the Semantic Web

The knowledge and data in the semantic Web are large-scale, dispersive, multi-authored and therefore usually inconsistent. It is reasonable to develop practical reasoning techniques for inconsistent ontologies. We propose a new type of paraconsistent description logics based on quasi-classical logic (QCL), called quasi-classical description logics (QCDLs). Furthermore, we present a semantic tableau calculus for QCDLs and define a sound, complete and decidable consequence relation based on the calculus. These enable the paraconsistent reasoning in the semantic Web. We also give a comparison with other key paraconsistent description logics and show that QCDLs possess more expressive and stronger semantics and other advantages.