Description Logics (DLs) belong to a successful family of knowledge representation formalisms with two key assets: formally well-defined semantics which allows to represent knowledge in an unambiguous way and automated reasoning which allows to infer implicit knowledge from the one given explicitly. This thesis investigates various reasoning techniques for tractable DLs in the EL family which have been implemented in the CEL system. It suggests that the use of the lightweight DLs, in which reasoning is tractable, is beneficial for ontology design and maintenance both in terms of expressivity and scalability. The claim is supported by a case study on the renown medical ontology SNOMED CT and extensive empirical evaluation on several large-scale biomedical ontologies.

Description Logics (DLs) belong to a successful family of knowledge representation formalisms with two key assets: formally well-defined semantics which allows to represent knowledge in an unambiguous way and automated reasoning which allows to infer implicit knowledge from the one given explicitly. This thesis investigates various reasoning techniques for tractable DLs in the EL family which have been implemented in the CEL system. It suggests that the use of the lightweight DLs, in which reasoning is tractable, is beneficial for ontology design and maintenance both in terms of expressivity and scalability. The claim is supported by a case study on the renown medical ontology SNOMED CT and extensive empirical evaluation on several large-scale biomedical ontologies.

Building and mantaining large-scale ontologies is an error-prone task. It is thus not uncommon to find unwanted or unexpected consequences that follow implicitely from the restrictions in the ontology. To understand and correct these consequences, it is helpful to find the specific portions of the ontology that are responsible for them. Axiom-pinpointing is the task of finding minimal subontologies that entail a given consequence, also called MinAs. In this work we look at the task of computing all the MinAs by means of modified decision procedures. We first show that tableaux- and automata-based decision procedures can be transformed into pinpointing algorithms that output a (compact) representation of the set of all MinAs. We then explore the complexity of the problem.

The work in this paper is motivated by a privacy scenario in which the identity of certain persons (represented as anonymous individuals) should be hidden.We assume that factual information about known individuals (i.e., individuals whose identity is known) and anonymous individuals is stored in an ABox and general background information is expressed in a TBox, where both the TBox and the ABox are publicly accessible. The identity problem then asks whether one can deduce from the TBox and the ABox that a given anonymous individual is equal to a known one. Since this would reveal the identity of the anonymous individual, such a situation needs to be avoided. We first observe that not all Description Logics (DLs) are able to derive any such equalities between individuals, and thus the identity problem is trivial in these DLs. We then consider DLs with nominals, number restrictions, or function dependencies, in which the identity problem is non-trivial. We show that in these DLs the identity problem has the same complexity as the instance problem. Finally, we consider an extended scenario in which users with different rôles can access different parts of the TBox and ABox, and we want to check whether, by a sequence of rôle changes and queries asked in each rôle, one can deduce the identity of an anonymous individual.

Ontology-based data access (OBDA) augments classical query answering in databases by including domain knowledge provided by an ontology. An ontology captures the terminology of an application domain and describes domain knowledge in a machine-processable way. Formal ontology languages additionally provide semantics to these specifications. Systems for OBDA thus may apply logical reasoning to answer queries; they use the ontological knowledge to infer new information, which is only implicitly given in the data. Moreover, they usually employ the open-world assumption, which means that knowledge not stated explicitly in the data or inferred is neither assumed to be true nor false. Classical OBDA regards the knowledge however only w.r.t. a single moment, which means that information about time is not used for reasoning and hence lost; in particular, the queries generally cannot express temporal aspects. We investigate temporal query languages that allow to access temporal data through classical ontologies. In particular, we study the computational complexity of temporal query answering regarding ontologies written in lightweight description logics, which are known to allow for efficient reasoning in the atemporal setting and are successfully applied in practice. Furthermore, we present a so-called rewritability result for ontology-based temporal query answering, which suggests ways for implementation. Our results may thus guide the choice of a query language for temporal OBDA in data-intensive applications that require fast processing, such as context recognition.

Building and mantaining large-scale ontologies is an error-prone task. It is thus not uncommon to find unwanted or unexpected consequences that follow implicitely from the restrictions in the ontology. To understand and correct these consequences, it is helpful to find the specific portions of the ontology that are responsible for them. Axiom-pinpointing is the task of finding minimal subontologies that entail a given consequence, also called MinAs. In this work we look at the task of computing all the MinAs by means of modified decision procedures. We first show that tableaux- and automata-based decision procedures can be transformed into pinpointing algorithms that output a (compact) representation of the set of all MinAs. We then explore the complexity of the problem.

We examine the complexity and expressivity of the combination of the Description Logic ALCQI with a terminological formalism based on cardinality restrictions on concepts. This combination can naturally be embedded into C², the two variable fragment of predicate logic with counting quantifiers. We prove that ALCQI has the same complexity as C² but does not reach its expressive power. / An abriged version of this paper has been submitted to CSL'99

Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of description logics, originally to help filter out unimportant aspects of large concepts appearing in industrial-strength knowledge bases. Previous work has concentrated on (sub-)languages of CLASSIC, which in particular do not allow for existential restrictions. In this work, we present sound and complete decision algorithms for the solvability of matching problems and for computing sets of matchers for matching problems in description logics with existential restrictions.

The description logic ALCQI extends the 'standard' description logic ALC by qualifying number restrictions and converse roles. We show that conept satisfiability for this DL is still decidable in polynomial space. The presented algorithm combines techniques from [Tob99a] to deal with qualifying number restrictions and from [HST99] to deal with converse roles. Additionally, we extend the result to ALCQIR, which extends ALCQI by role intersections. This solves an open problem from [DLNN97]. The result for ALCQI has already been presented in the seperate technical report [Tob99b]. In this report we use the same techniques to obtain the stronger result for ALCQIR.

Unification of concept terms is a new kind of inference problem for Description Logics, which extends the equivalence problem by allowing to replace certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present first decidability and complexity results for a small concept description language. / This revised version of LTCS-Report 97-02 provides a stronger complexity result in Section 6. An abridged version will appear in Proc. ECAI'98 .