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.

The recently introduced series of description logics under the common moniker ‘DL-Lite ’ has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and the ability to represent conceptual modeling formalisms, on the other. The main aim of this article is to carry out a thorough and systematic investigation of inference in extensions of the original DL-Lite logics along five axes: by (i) adding the Boolean connectives and (ii) number restrictions to concept constructs, (iii) allowing role hierarchies, (iv) allowing role disjointness, symmetry, asymmetry, reflexivity, irreflexivity and transitivity constraints, and (v) adopting or dropping the unique name assumption. We analyze the combined complexity of satisfiability for the resulting logics, as well as the data complexity of instance checking and answering positive existential queries. Our approach is based on embedding DL-Lite logics in suitable fragments of the one-variable first-order logic, which provides useful insights into their properties and, in particular, computational behavior.

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.

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.

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).

Abstract not found

Least Common Subsumers (LCS) have been proposed in Description Logics (DL) to capture the commonalities between two or more concepts. Since its introduction in 1992, LCS have been successfully employed as a logical tool for a variety of applications, spanning from inductive learning, to bottom-up construction of knowledge bases, information retrieval, to name a few. The best known algorithm for computing LCS uses structural comparison on normal forms, and the most expressive DL it is applied to is ALEN. We provide a general tableau-based calculus for computing LCS, via substitutions on concept terms containing concept variables. We show the applicability of our method to an expressive DL (but without disjunction and full negation), discuss complexity issues, and show the generality of our proposal.