Rational Closure For All Description Logics (Extended Abstract)

Many modern applications of description logics (DLs, for short), such as biomedical ontologies and semantic web policies, provide compelling motivations for extending DLs with an overriding mechanism analogous to the homonymous feature of object-oriented programming. Rational closure (RC) is one of the candidate semantics for such extensions, and one of the most intensively studied. So far, however, it has been limited to strict fragments of SROIQ(D) – the logic on which OWL2 is founded. In this paper we prove that RC cannot be extended to logics that do not satisfy the disjoint model union property, including SROIQ(D). Then we introduce a refinement of RC called stable rational closure that overcomes the dependency on the disjoint model union property. Our results show that stable RC is a natural extension of RC. However, its positive features come at a price: stable RC re-introduces one of the undesirable features of other nonmonotonic logics, namely, deductive closures may not exist and may not be unique.