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Borchmann D.,TU Dresden | Borchmann D.,Center for Advancing Electronics Dresden
Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) | Year: 2015

Within formal concept analysis, attribute exploration is a powerful tool to semi-automatically check data for completeness with respect to a given domain. However, the classical formulation of attribute exploration does not take into account possible errors which are present in the initial data. To remedy this, we present in this work a generalization of attribute exploration based on the notion of confidence, that will allow for the exploration of implications which are not necessarily valid in the initial data, but instead enjoy a minimal confidence therein. © 2015 Springer International Publishing Switzerland. Source


Borgwardt S.,TU Dresden | Distel F.,TU Dresden | Penaloza R.,TU Dresden | Penaloza R.,Center for Advancing Electronics Dresden
Artificial Intelligence | Year: 2015

Fuzzy description logics (DLs) can be used to represent and reason with vague knowledge. This family of logical formalisms is very diverse, each member being characterized by a specific choice of constructors, axioms, and triangular norms, which are used to specify the semantics. Unfortunately, it has recently been shown that the consistency problem in many fuzzy DLs with general concept inclusion axioms is undecidable. In this paper, we present a proof framework that allows us to extend these results to cover large classes of fuzzy DLs. On the other hand, we also provide matching decidability results for most of the remaining logics. As a result, we obtain a near-universal classification of fuzzy DLs according to the decidability of their consistency problem. © 2014 Elsevier B.V. All rights reserved. Source


Ceylan I.I.,TU Dresden | Penaloza R.,TU Dresden | Penaloza R.,Center for Advancing Electronics Dresden
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

We introduce the probabilistic Description Logic. In, axioms are required to hold only in an associated context. The probabilistic component of the logic is given by a Bayesian network that describes the joint probability distribution of the contexts. We study the main reasoning problems in this logic; in particular, we (i) prove that deciding positive and almost-sure entailments is not harder for than for the BN, and (ii) show how to compute the probability, and the most likely context for a consequence. © 2014 Springer International Publishing Switzerland. Source


Mailis T.,TU Dresden | Penaloza R.,TU Dresden | Penaloza R.,Center for Advancing Electronics Dresden | Turhan A.-Y.,TU Dresden
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

Fuzzy Description Logics (DLs) generalize crisp ones by providing membership degree semantics for concepts and roles. A popular technique for reasoning in fuzzy DL ontologies is by providing a reduction to crisp DLs and then employ reasoning in the crisp DL. In this paper we adopt this approach to solve conjunctive query (CQ) answering problems for fuzzy DLs. We give reductions for Godel, and Łukasiewicz variants of fuzzy SROIQ and two kinds of fuzzy CQs. The correctness of the proposed reduction is proved and its complexity is studied for different fuzzy variants of SROIQ. © Springer International Publishing Switzerland 2014. Source


Ecke A.,TU Dresden | Penaloza R.,TU Dresden | Penaloza R.,Center for Advancing Electronics Dresden | Turhan A.-Y.,TU Dresden
International Journal of Approximate Reasoning | Year: 2014

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-ELORc01, 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. © 2014 Elsevier Inc. Source

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