Quasi-Classical Semantics for Expressive Description Logics

Inconsistency handling in expressive description logics is an important problem because inconsistency may naturally occur in an open world. In this paper, we first present the quasi-classical semantics for description logic SHIQ, which is based on quasi-classical logic. We show that this semantics can be used to deal with inconsistency and that it is reduced to the standard semantics when there is no inconsistency. Compared with the existing four-valued semantics for description logics, it strengthens the reasoning capability in the sense that it can satisfy some important inference rules, such as Modus Ponens. Finally, we analyze the computational complexity of consistency checking based on the quasiclassical semantics.