Abstract not found

The vision of a Semantic Web has recently drawn considerable attention, both from academia and industry. Description logics are often named as one of the tools that can support the Semantic Web and thus help to make this vision reality.

Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottom-up construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attention to concept descriptions or acyclic TBoxes. In this paper, we extend the notions les and msc to cyclic TBoxes. For the description logic EC (which allows for conjunctions, existential restrictions, and the top-concept), we show that the les and msc always exist and can be computed in polynomial time if we interpret cyclic definitions with greatest fixpoint semantics.

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.

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology.

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 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.

Matching of concepts against patterns is a new inference task in Description Logics, which was originally motivated by applications of the Classic system. Consequently, the work on this problem was until now mostly concerned with sublanguages of the Classic language, which does not allow for existential restrictions. This paper extends the existing work on matching in two directions. On the one hand, the question of what are the most "interesting " solutions of matching problems is explored in more detail. On the other hand, for languages with existential restrictions both, the complexity of deciding the solvability of matching problems and the complexity of actually computing sets of "interesting " matchers are determined. The results show that existential restrictions make these computational tasks more complex. Whereas for sublanguages of Classic both problems could be solved in polynomial time, this is no longer possible for languages with existential restrictions.

Computing the least common subsumer (lcs) has proved to be useful in a variety of different applications. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an lcs algorithm for the description logic ALEN , which allows for both constructors, thereby correcting previous algorithms proposed in the literature. 1

We study the problem of deciding whether two ontologies are inseparable w.r.t. a signature Σ, i.e., whether they have the same consequences in the signature Σ. A special case is to decide whether an extension of an ontology is conservative. By varying the language in which ontologies are formulated and the query language that is used to describe consequences, we obtain different versions of the problem. We focus on the lightweight description logic EL as an ontology language, and consider query languages based on (i) subsumption queries, (ii) instance queries over ABoxes, (iii) conjunctive queries over ABoxes, and (iv) second-order logic. For query languages (i) to (iii), we establish ExpTime-completeness of both inseparability and conservative extensions. Case (iv) is equivalent to a model-theoretic version of inseparability and conservative extensions, and we prove it to be undecidable. We also establish a number of robustness properties for inseparability.

Description logics (DLs) are a successful family of logic-based knowledge representation formalisms that can be used to represent the terminological knowledge of an application domain in a structured and formally well-founded way. DL systems provide their users with inference procedures that allow to reason about the represented knowledge. Standard inference problems (such as the subsumption and the instance problem) are now well-understood. Their computational properties (such as decidability and complexity) have been investigated in detail, and modern DL systems are equipped with highly optimized implementations of these inference procedures, which—in spite of their high worst-case complexity—perform quite well in practice. In applications of DL systems it has turned out that building and maintaining large DL knowledge bases can be further facilitated by procedures for other, nonstandard inference problem, such as computing the least common subsumer and the most specific concept, and rewriting and matching of concepts. While the research concerning these non-standard inferences is not as mature as the one for the standard inferences, it has now reached a point where it makes sense to motivate these inferences within a uniform application framework, give an overview of the results obtained so far, describe the remaining open problems, and give perspectives for future research in this direction. 1