A Tableau Algorithm for Paraconsistent and Nonmonotonic Reasoning in Description Logic-Based System

This paper proposes a paraconsistent and nonmonotonic extension of description logic by planting a nonmonotonic mechanism called minimal inconsistency in paradoxical description logics, which is a paraconsistent version of description logics. A precedence relation between two paradoxical models of knowledge bases is firstly introduced to obtain minimally paradoxical models by filtering those models which contain more inconsistencies than others. A new entailment relationship between a KB and an axiom characterized by minimal paradoxical models is applied to characterize the semantics of a paraconsistent and nonmonotonic description logic. An important advantage of our adaptation is simultaneously overtaking proverbial shortcomings of existing two kinds extensions of description logics: the weak inference power of paraconsistent description logics and the incapacity of nonmonotonic description logics in handling inconsistencies. Moreover, our paraconsistent and nonmonotonic extension not only preserves the syntax of description logic but also maintains the decidability of basic reasoning problems in description logics. Finally, we develop a sound and complete tableau algorithm for instance checking with the minimally paradoxical semantics.