On the Computation of Common Subsumers in Description Logics

Description logics (DL) knowledge bases are often build by users with expertise in the application domain, but little expertise in logic. To support this kind of users when building their knowledge bases a number of extension methods have been proposed to provide the user with concept descriptions as a starting point for new concept definitions. The inference service central to several of these approaches is the computation of (least) common subsumers of concept descriptions. In case disjunction of concepts can be expressed in the DL under consideration, the least common subsumer (lcs) is just the disjunction of the input concepts. Such a trivial lcs is of little use as a starting point for a new concept definition to be edited by the user. To address this problem we propose two approaches to obtain "meaningful" common subsumers in the presence of disjunction tailored to two different methods to extend DL knowledge bases. More precisely, we devise computation methods for the approximation-based approach and the customization of DL knowledge bases, extend these methods to DLs with number restrictions and discuss their efficient implementation

Formal Concept Analysis Methods for Description Logics

This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets

Reasoning-Supported Quality Assurance for Knowledge Bases

The increasing application of ontology reuse and automated knowledge acquisition tools in ontology engineering brings about a shift of development efforts from knowledge modeling towards quality assurance. Despite the high practical importance, there has been a substantial lack of support for ensuring semantic accuracy and conciseness. In this thesis, we make a significant step forward in ontology engineering by developing a support for two such essential quality assurance activities

Selecting Ontology Entailments for Presentation to Users

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Completion-based computation of least common subsumers with limited role-depth for EL and Prob-EL⁰¹

The least common subsumer (lcs) w.r.t general EL-TBoxes does not need to exists in general due to cyclic axioms. In this report we present an algorithm for computing role-depth bounded EL-lcs based on the completion algorithm for EL. We extend this computation algorithm to a recently introduced probabilistic variant of EL: Prob-EL⁰¹

Model-based Most Specific Concepts in Description Logics with Value Restrictions

Non-standard inferences are particularly useful in the bottom-up construction of ontologies in description logics. One of the more common non-standard reasoning tasks is the most specific concept (msc) for an ABox-individual. In this paper we present similar non-standard reasoning task: most specific concepts for models (model-mscs). We show that, although they look similar to ABox-mscs their computational behaviour can be different. We present constructions for model-mscs in FL₀ and FLE with cyclic TBoxes and for ALC∪∗ with acyclic TBoxes. Since subsumption in FLE with cyclic TBoxes has not been examined previously, we present a characterization of subsumption and give a construction for the least common subsumer in this setting

Computing Least Common Subsumers in ALEN

Computing the least common subsumer (lcs) in description logics is an inference task first introduced for sublanguages of CLASSIC. Roughly speaking, the lcs of a set of concept descriptions is the most specific concept description that subsumes all of the input descriptions. As such, the lcs allows to extract the commonalities from given concept descriptions, a task essential for several applications like, e.g., inductive learning, information retrieval, or the bottom-up construction of KR-knowledge bases. 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 (as well as concept conjunction, primitive negation, and value restrictions). The proof of correctness of our lcs algorithm is based on an appropriate structural characterization of subsumption in ALEN also introduced in this paper.This research was carried out while the second author was still at the LuFG Theoretical Computer Science, RWTH Aachen