Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottom-up " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal value restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. Our approach for computing the lcs is based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisms between these trees. The lcs operation then corresponds to the product operation on trees.

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.

Pattern structures consist of objects with descriptions (called patterns) that allow a semilattice operation on them. Pattern structures arise naturally from ordered data, e.g., from labeled graphs ordered by graph morphisms. It is shown that pattern structures can be reduced to formal contexts, however sometimes processing the former is often more ecient and obvious than processing the latter. Concepts, implications, plausible hypotheses, and classi cations are de ned for data given by pattern structures. Since computation in pattern structures may be intractable, approximations of patterns by means of projections are introduced.

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

Association rules are used to investigate large databases. The analyst is usually confronted with large lists of such rules and has to find the most relevant ones for his purpose. Based on results about knowledge representation within the theoretical framework of Formal Concept Analysis, we present relatively small bases for association rules from which all rules can be deduced. We also provide algorithms for their calculation.

. Computing the most specic concept (msc) is an inference task that allows to abstract from individuals dened in description logic (DL) knowledge bases. For DLs that allow for existential restrictions or number restrictions, however, the msc need not exist unless one allows for cyclic concepts interpreted with the greatest xed-point semantics. Since such concepts cannot be handled by current DL-systems, we propose to approximate the msc. We show that for the DL ALE , which has concept conjunction, a restricted form of negation, existential restrictions, and value restrictions as constructors, approximations of the msc always exist and can eectively be computed. 1

Abstract. Least Common Subsumers in Description Logics have shown their usefulness for discovering commonalities among all concepts of a collection. Several applications are nevertheless focused on searching for properties shared by significant portions of a collection rather than by the collection as a whole. Actually, this is an issue we faced in a real case scenario that provided initial motivation for this study, namely the process of Core Competence extraction in knowledge intensive companies. The paper defines four reasoning services for the identification of meaningful common subsumers describing partial commonalities in a collection. In particular Common Subsumers adding informative content to the Least Common Subsumer are investigated, with reference to ALN and ELN. 1

For description logics with existential restrictions, the size of the least common subsumer (lcs) of concept descriptions may grow exponentially in the size of the concept descriptions. To reduce the size of the output descriptions and the run-time of the lcs algorithm we present an optimized algorithm for computing the lcs in ALE using lazy unfolding. A first evaluation of the performance of the naive algorithm in comparison to the performance of the algorithm using lazy unfolding indicates a performance gain for both concept sizes as well as run-times.

The problem of finding commonalities characterizes several Knowledge Management scenarios involving collection of resources. The automatic extraction of shared features in a collection of resource descriptions formalized in accordance with a logic language has been in fact widely investigated in the past. In particular, with reference to Description Logics concept descriptions, Least Common Subsumers have been specifically introduced. Nevertheless, such studies focused on identifying features shared by the whole collection. The paper proposes instead novel reasoning services in Description Logics, aimed at identifying commonalities in a significant portion of the collection, rather than in the collection as a whole. In particular, common subsumers adding informative content to the one provided by the Least Common Subsumer are here investigated. The new services are useful in all scenarios where features are not required to be fully shared, like the one motivating our research: Core Competence extraction in knowledge intensive companies.

Abstract. Core Competence evaluation is crucial for strategical choices in knowledge intensive companies. Such a process is usually manually performed by the management on the basis of subjective criteria, which can then cause non-optimal decisions, especially in wide companies. We propose here a semantic-based approach for the automatic evaluation of Core Competence, exploiting novel reasoning services in Description Logics, extracting commonalities in a collection of resource descriptions. Such inferences aim at identifying features shared at least by a significant portion of a collection of professional profiles formalized in accordance with a logic language. We are in fact not necessarily interested in competence shared by the whole company personnel. 1