Andreas Ecke

Similarity-based relaxed instance queries

In Description Logics (DL) knowledge bases (KBs), information is typically captured by clear-cut concepts. For many practical applications querying the KB by crisp concepts is too restrictive; a user might be willing to lose some precision in the query, in exchange of a larger selection of answers. Similarity measures can offer a controlled way of gradually relaxing a query concept within a user-specified limit.In this paper we formalize the task of instance query answering for DL KBs using concepts relaxed by concept similarity measures (CSMs). We investigate computation algorithms for this task in the DL EL , their complexity and properties for the CSMs employed regarding whether unfoldable or general TBoxes are used. For the case of general TBoxes we define a family of CSMs that take the full TBox information into account, when assessing the similarity of concepts.

Computing Role-Depth Bounded Generalizations in the Description Logic \(\mathcal{ELOR}\)

Description Logics (DLs) are a family of knowledge representation formalisms, that provides the theoretical basis for the standard web ontology language OWL. Generalization services like the least common subsumer (lcs) and the most specific concept (msc) are the basis of several ontology design methods, and form the core of similarity measures. For the DL \(\mathcal{ELOR}\), which covers most of the OWL 2 EL profile, the lcs and msc need not exist in general, but they always exist if restricted to a given role-depth. We present algorithms that compute these role-depth bounded generalizations. Our method is easy to implement, as it is based on the polynomial-time completion algorithm for \(\mathcal{ELOR}.\)

Reasoning with Prototypes in the Description Logic \({\mathcal {ALC}}\) Using Weighted Tree Automata

We introduce an extension to Description Logics that allows us to use prototypes to define concepts. To accomplish this, we introduce the notion of prototype distance functions (pdfs), which assign to each element of an interpretation a distance value. Based on this, we define a new concept constructor of the form \(P_{\sim n}(d)\) for \({\sim }\in \{ ,\ge \}\), which is interpreted as the set of all elements with a distance \({}\sim n\) according to the pdf d. We show how weighted alternating parity tree automata (wapta) over the non-negative integers can be used to define pdfs, and how this allows us to use both concepts and pointed interpretations as prototypes. Finally, we investigate the complexity of reasoning in \(\mathcal {ALCP} (\text {wapta})\), which extends the Description Logic \(\mathcal {ALC}\) with the constructors \(P_{\sim n}(d)\) for pdfs defined using wapta.

Completion-based generalization inferences for the Description Logic ELOR with subjective probabilities

Description Logics (DLs) are a well-established family of knowledge representation formalisms. One of its members, the DL ELOR has been successfully used for representing knowledge from the bio-medical sciences, and is the basis for the OWL 2 EL profile of the standard ontology language for the Semantic Web. Reasoning in this DL can be performed in polynomial time through a completion-based algorithm.In this paper we study the logic Prob- ELOR , that extends ELOR with subjective probabilities, and present a completion-based algorithm for polynomial time reasoning in a restricted version, Prob- ELOR c 01 , of Prob- ELOR . We extend this algorithm to computation algorithms for approximations of (i) the most specific concept, which generalizes a given individual into a concept description, and (ii) the least common subsumer, which generalizes several concept descriptions into one. Thus, we also obtain methods for these inferences for the OWL 2 EL profile. These two generalization inferences are fundamental for building ontologies automatically from examples. The feasibility of our approach is demonstrated empirically by our prototype system Gel. Extend the light-weight DL ELOR to allow subjective probabilities.Compute generalization inferences for a probabilistic description logic.Empirical evaluation of a prototypical tool.

Quantitative Methods for Similarity in Description Logics

Description logics (DLs) are a family of logic-based knowledge representation languages used to describe the knowledge of an application domain and reason about it in a formally well-defined way. However, all classical DLs have in common that they can only express exact knowledge, and correspondingly only allow exact inferences. In practice though, knowledge is rarely exact. Many definitions have exceptions or are vaguely formulated in the first place, and people might not only be interested in exact answers, but also in alternatives that are “close enough”. We are interested in tackling how to express that something is “close enough”, and how to integrate this notion into the formalism of DLs. To this end we employ the notion of similarity and dissimilarity measures, we will look at how useful measures can be defined in the context of DLs and two particular applications: Relaxed instance queries will use a similarity measure in order to not just give the exact answer to some query, but all answers that are reasonably similar. Prototypical definitions on the other hand use a measure of dissimilarity or distance between concepts in order to allow the definitions of and reasoning with concepts that capture not just those individuals that satisfy exactly the stated properties, but also those that are “close enough”.