Quasi-Classical Description Logic

In this paper, we present a paraconsistent description logic based on quasi-classical logic. Compared to the four-valued description logic, quasi-classical description logic satisfies all of the three basic inference rules (i.e., modus ponens, modus tollens and disjunctive syllogism) so that the inference ability of quasiclassical description logic is closer to that of classical logic. Quasiclassical description logic combines three inclusions (i.e., material inclusion, internal inclusion and strong inclusion) of fourvalued description logic so that quasi-classical description logic satisfies the intuitive equivalence. Moreover, we develop a terminable, sound and complete tableau algorithm for quasi-classical description logic. As an important result, the complexity of reasoning problems in quasi-classical description logic is proved to be no higher than that of reasoning problems in description logic.