Practical Reasoning for Expressive

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problemat-ical. We present an algorithm that decides satissability of the DL ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. Finally, we investigate the limits of decidability for this family of DLs. 1 Motivation Description Logics (DLs) are a well-known family of knowledge representation formalisms DLNS96]. They are based on the notion of concepts (unary predicates , classes) and roles (binary relations), and are mainly characterised by constructors that allow complex concepts and roles to be built from atomic ones. Sound and complete algorithms for the interesting inference problems such as subsumption and satissability of concepts are known for a wide variety of DLs SS91; DLNdN91; Sat96; DL96; CDL99]. To be used in a speciic application, the expressivity of the DL must be suucient to describe relevant properties of objects in the application domain. For example, transitive roles (e.g. \ancestor") and inverse roles (e.g. \succes-sor"/\predecessor") play an important r^ ole not only in the adequate representation of complex, aggregated objects HS99], but also for reasoning with conceptual data models CLN94]. Moreover, reasoning with respect to cyclic deenitions is crucial for applying DLs to reasoning with database schemata CDL98a]. The relevant inference problems for (extensions of) DLs that allow for transitive and inverse roles are known to be decidable DL96], and appropriate inference algorithms have been described DM98], but their high degree of non-determinism appears to prohibit their use in realistic applications. This is mainly y Part of this work was carried out while being a guest at IRST, Trento.