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The problem of rewriting a concept given a terminology can informally be stated as follows: given a terminology T (i.e., a set of concept definitions) and a concept description C that does not contain concept names defined in T, can this description be rewritten into a "related better " description E by using (some of) the names defined in T? In this paper, we first introduce a general framework for the rewriting problem in description logics, and then concentrate on one specific instance of the framework, namely the minimal rewriting problem (where "better " means shorter, and "related " means equivalent). We investigate the complexity of the decision problem induced by the minimal rewriting problem for the languages FL 0, ALN, ALE, and ALC, and then introduce an algorithm for computing (minimal) rewritings for the language ALE. (In the full paper, a similar algorithm is also developed for ALN.) Finally, we sketch other interesting instances of the framework.

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 paper closes this gap for the DL ALN and its sublanguages: matching under subsumption conditions remains polynomial, while strict subsumption conditions increase the complexity to NP.

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 FL 0 , 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 FL 0 ) is PSpace-complete in the extended description logic.

One approach to integrating knowledge bases is based on finding assertions that relate the expressions in the constituent terminologies. For knowledge bases with many terms this task requires computer support. We set up a formal framework for merging Description Logic TBoxes, and then explore the limits of a purely structural approach to the problem of finding inter-relationships between knowledge bases. Some theoretical notions are empirically examined in a real medical ontology (galen).

First of all I would like to thank Prof. Dr. Bernd Neumann. His encouraging comments and enthusiasm over the years shaped the whole work discussed in this monograph. Always emphasizing the importance of applications to demonstrate the adequacy of theoretical work, he suggested to particularly consider real-world problems. Thus, it is also thanks to him that the description logic system RACE can deal with hard inference problems encountered in real-world applications. We had many interesting discussions during our research on deductive information systems. I also thank Bernd Neumann for valuable comments on a draft of this monograph. For additional reviews of this monograph I thank Prof. Dr. Franz Baader and Prof. Dr. Christopher Habel. I am also particularly grateful to my colleague Dr. Volker Haarslev. Together we have been discussing the topics on description logic systems for the last three years. Many times we have been investigating new optimization strategies, which turned out to effective but were hard to implement. Many long discussions with Volker Haarslev lead to the development of formal proofs of the algorithms implemented in

Abstract. The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, we show that EL-unification is NP-complete, and thus has the same complexity as EL-matching. 1

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Unification of concept descriptions has been introduced by Baader and Narendran [5] as a new inference service for detecting and avoiding redundancies in Description Logic knowledge bases. The technical results in [5] are concerned with unification in the small Description Logic FL 0 , which allows for conjunction of concepts, value restriction, and the top concept. It is shown that uni cation of FL 0 -concept descriptions is equivalent to unification modulo the equational theory ACUIh, which is concerned with a binary associative-commutative idempotent function symbol with a unit and finitely many unary function symbols that behave like endomorphisms for the binary symbol and the unit. Since ACUIh is a commutative/monoidal theory [6], unification modulo this theory can in turn be reduced to solving linear equations in a certain semiring. For the theory ACUIh, this semiring consists of finite sets of words over a finite alphabet...

Ontologies are formalism whose purpose is to support humans or machines to share some common knowledge in a structured way. They allow the concepts and terms relevant to a given domain to be identified and defined in an unambiguous way. As such, ontologies are seen as the key technology used to describe the semantics of information at various sites, overcoming the problem of implicit and hidden knowledge and thus enabling exchange of semantic contents. In this report we survey the work on ontologies that has been carried out in recent years. In particular, we first overview the languages that have been proposed for representing ontologies, and present the work on reasoning over ontologies. We then overview the work on ontologies from four different points of view: (i) We survey methodologies for designing and maintaining ontologies, presenting automated tools suitable for such tasks. (ii) We present languages and architectures for accessing, processing and in general making use of ontologies. (iii) We presents several approaches for integrating and merging ontologies by detecting correspondences among them. (iv)