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 quasi-classical description logic is closer to that of classical logic. Quasi-classical description logic combines three inclusions (i.e., material inclusion, internal inclusion and strong inclusion) of four-valued 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.