Motivated by the need for semantically well-founded and algorithmically managable formalism that is based on description logics (DLs), but is also firmly grounded on research in the reasoning about action community. Our main contribution is an analysis of how the choice of the DL influences the complexity of standard reasoning tasks such as projection and executability, which are important for Web service discovery and composition.

Recent applications of description logics (DLs) strongly suggest the integration of non-monotonic features into DLs, with particular attention to defeasible inheritance. However, the existing non-monotonic extensions of DLs are usually based on default logic or autoepistemic logic, and have to be seriously restricted in expressive power to preserve the decidability of reasoning. In particular, such DLs allow the modelling of defeasible inheritance only in a very restricted form, where non-monotonic reasoning is limited to individuals that are explicitly identified by constants in the knowledge base. In this paper, we consider non-monotonic extensions of expressive DLs based on circumscription. We prove that reasoning in such DLs is decidable even without the usual, strong restrictions in expressive power. We pinpoint the exact computational complexity of reasoning as complete for NPNEXP and NEXPNP, depending on whether or not the number of minimized and fixed predicates is assumed to be bounded by a constant. These results assume that only concept names (and no role names) can be minimized and fixed during minimization. On the other hand, we show that fixing role names during minimization makes reasoning undecidable.

Whereas matching in Description Logics is now relatively well investigated, there are only very few formal results on matching under additional side conditions, though these side conditions were already present in the original paper by Borgida and McGuinness introducing matching in DLs. The present report closes this gap for the DL ALN and its sublanguages.

Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL₀, which allows for conjunction, value restriction, and the top concept only, is already ExpTime-complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in FL₀) is PSpace-complete in the extended description logic. These results are proved via a reduction to linear equations over regular languages, which are then solved using automata. The obtained results are also of interest in formal language theory. / An abridged version will appear in Proc. LPAR'01.

Approximation is a new inference service in Description Logics first mentioned by Baader, Küsters, and Molitor. Approximating a concept, defined in one Description Logic, means to translate this concept to another concept, defined in a second typically less expressive Description Logic, such that both concepts are as closely related as possible with respect to subsumption. The present paper provides the first in-depth investigation of this inference task. We prove that approximations from the Description Logic ALC to ALE always exist and propose an algorithm computing them. As a measure for the accuracy of the approximation, we introduce a syntax-oriented difference operator, which yields a concept description that contains all aspects of the approximated concept that are not present in the approximation. It is also argued that a purely semantical difference operator, as introduced by Teege, is less suited for this purpose. Finally, for the logics under consideration, we propose an algorithm computing the difference.

Recently, the Description Logic (DL) SHIQ has found a large number of applications. This success is due to the fact that SHIQ combines a rich expressivity with efficient reasoning, as is demonstrated by its implementation in DL systems such as FaCT and RACER. One weakness of SHIQ, however, limits its usability in several application areas: numerical knowledge such as knowledge about the age, weight, or temperature of real-world entities cannot be adequately represented. In this paper, we propose an extension of SHIQ that aims at closing this gap. The new Description Logic Q-SHIQ, which augments SHIQ by additional, 'concrete domain' style concept constructors, allows to refer to rational numbers in concept descriptions, and also to define concepts based on the comparison of numbers via predicates such as < or =. We argue that this kind of expressivity is needed in many application areas such as reasoning about the semantic web. We prove reasoning with Q-SHIQ to be EXPTIME-complete (thus not harder than reasoning with SHIQ) by devising an automata-based decision procedure.

Cyclic definitions in description logics have until now been investigated only for description logics allowing for value restrictions. Even for the most basic language FL₀, which allows for conjunction and value restrictions only, deciding subsumption in the presence of terminological cycles is a PSPACE-complete problem. This report investigates subsumption in the presence of terminological cycles for the language EL, which allows for conjunction and existential restrictions. In contrast to the results for FL₀, subsumption in EL remains polynomial, independent of wether we use least fixpoint semantics, greatest fixpoint semantics, or descriptive semantics. These results are shown via a characterization of subsumption through the existence of certain simulation relations between nodes of the description graph associated with a given cyclic terminology. / This is an updated version of the original report, in which some errors in Section 3.1 of the original report have been corrected.

Many description logics (DLs) combine knowledge representation on an abstract, logical level with an interface to 'concrete' domains such as numbers and strings with built-in predicates such as <, +, and prefix-of. These hybrid DLs have turned out to be quite useful for reasoning about conceptual models of information systems, and as the basis for expressive ontology languages. We propose to further extend such DLs with key constraints that allow the expression of statements like 'US citizens are uniquely identified by their social security number'. Based on this idea, we introduce a number of natural description logics and perform a detailed analysis of their decidability and computational complexity. It turns out that naive extensions with key constraints easily lead to undecidability, whereas more careful extensions yield NEXPTIME-complete DLs for a variety of useful concrete domains.

We analyze the complexity of finite model reasoning in the description logic ALCQI, i.e. ALC augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that all relevant reasoning tasks such as concept satisfiability and ABox consistency are EXPTIME-complete, regardless of whether the numbers in number restrictions are coded unarily or binarily. Thus, finite model reasoning with ALCQI is not harder than standard reasoning with ALCQI.

Motivated by medical terminology applications, we investigate the decidability of an expressive and prominent DL, SHIQ, extended with role inclusion axioms of the form RoS⊑T. It is well-known that a naive such extension leads to undecidability, and thus we restrict our attention to axioms of the form RoS⊑R or SoR⊑R, which is the most important form of axioms in the applications that motivated this extension. Surprisingly, this extension is still undecidable. However, it turns out that restricting our attention further to acyclic sets of such axioms, we regain decidability. We present a tableau-based decision procedure for this DL and report on its implementation, which behaves well in practise and provides important additional functionality in a medical terminology application.