Errors in knowledge bases (KBs) written in a Description Logic (DL) are usually detected when reasoning derives an inconsistency or a consequence that does not hold in the application domain modelled by the KB. Whereas classical repair approaches produce maximal subsets of the KB not implying the inconsistency or unwanted consequence, optimal repairs maximize the consequence sets. In this paper, we extend previous results on how to compute optimal repairs from the DL EL to its extension EL⊥, which in contrast to EL can express inconsistency. The problem of how to deal with inconsistency in the context of optimal repairs was addressed previously, but in a setting where the (fixed) terminological part of the KB must satisfy a restriction on cyclic dependencies. Here, we consider a setting where this restriction is not required. We also show how the notion of optimal repairs obtained this way can be used in inconsistency- and error-tolerant reasoning.

In der vorliegenden Arbeit wurde ein Unternehmen der IT-Branche bei der Durchführung eines Wissensmanagement-Projektes (Einführung einer Wissensdatenbank) von den ersten Überlegungen zu möglichen Zielsetzungen bis zur Umsetzung von Maßnahmen und ihrer Etablierung im Arbeitsalltag begleitet. Anhand des konkreten Falls und unter Berücksichtigung der Erkenntnisse aus Theorie und bisheriger Erfahrungsberichte aus der Praxis wurden auftretende Probleme und Reaktionen darauf, aber auch Erfolge in den verschiedenen Phasen eines Wissensmanagementprojektes aufgezeigt und abschließend die Zielerreichung der umgesetzten Maßnahmen evaluiert. Dazu wurden drei Erhebungen ((1) Aufnahme der Ist-Situation vor Datenbank-Einführung, (2) Stimmungsbild kurz nach Datenbank-Einführung, (3) Abschlussevaluation zur Messung der Zielerreichung) konzipiert und durchgeführt. Die zweite Erhebung brachte überraschender Weise eine Spaltung der Anwender in Viel- und Wenig-Nutzer zu Tage. Diese Gruppenteilung wurde ebenfalls im Rahmen der Arbeit untersucht und erklärt. Es zeigte sich, dass die Nutzung der Datenbank signifikant von der Erfüllung der Vorbildfunktion des jeweiligen direkten Vorgesetzten abhängig war. Außerdem wirkte sich die bereits vor Datenbank-Einführung vorhandene Einstellung der jeweiligen Mitarbeiter zu der eingesetzten Software signifikant auf ihre spätere Zufriedenheit mit der Lösung aus. Als maßgeblich für den Erfolg der Wissensdatenbank konnten in Übereinstimmung mit anderen, in der Literatur beschriebenen Fallbespielen die vertrauensvolle und wissensfreundliche Unternehmenskultur, die partizipative Einbindung der Mitarbeiter in den Entwicklungsprozess sowie die Integration der Wissensmanagement-Aktivitäten in die täglichen Arbeitsroutinen identifiziert werden. Im Gegensatz zu anderen Projekten zeigte sich hier jedoch, dass weder Kontrolle noch Sanktionen eine Auswirkung auf das Nutzerverhalten der Mitarbeiter hatten und einzig und alleine weiche Faktoren wie das Lob und die Anerkennung des Vorgesetzten und eine Priorisierung von Wissensmanagement durch Einräumen von Zeit zu einer vermehrten Nutzung der Datenbank führten. Die finale Evaluation ergab, dass die Datenbank Einführung insgesamt erfolgreich war, auch wenn durch die anhaltende Gruppenspaltung die angestrebte Nutzungshäufigkeit und Mitarbeiterzufriedenheit nicht vollständig erreicht werden konnten. / This thesis accompanied a knowledge management project (implementation of a know-ledge database) of an IT infrastructure services provider from the first conceptualization of project goals to the final implementation into the everyday usage. Following one exclusive case and considering the results of other case studies in combination with theoretical background knowledge, the problems, reaction to the problems and successes in different stages of the knowledge management project were described and analyzed. Finally the success of the project was evaluated. In order to do this, three different surveys were designed and conducted: (1) Description of the primary situation, (2) review of the general opinion shortly after the roll-out of the database and (3) the final evaluation which measured success. The second survey showed the surprising result of the group dividing into two sub-groups: frequent and rare users. An explanation of the resulting phenomenon was integrated into the finale evaluation. It showed that the frequency of database-usage is significantly dependent on the example of the direct manager. Additionally, the pre-impression (before starting the knowledgebase project) of the running software influenced significantly the degree of satisfaction with the solution. In accordance with other case studies this example illustrated that the positive influence of organizational culture, employee participation as well as the integration of knowledge management activities in the daily labor-routines are essential to the success of a knowledge management project. Contrary to the findings of others, case control and negative sanctions had no impact on the user habits. Instead praise and recognition from the manager combined with the prioritization of the knowledge management activities through adequate time allocation in the daily routine proved to be of significant influence. The final evaluation verified the overall success of the knowledge database implementation, although due to the continuing separation of the group, the initially hoped for usage-frequency and employee satisfaction could not be fully achieved.

We discuss two ways of using abduction to explain missing entailments from description logic knowledge bases, one more common, one more unusual, and then have a closer look at how current results/implementations on abduction could be used towards generating such explanations, and what still needs to be done. / This is an extended version of an article submitted to XLoKR 2021.

In Description Logics the reasoning service most specific concept (msc) constructs a concept description that generalizes an ABox individual into a concept description. For the Description Logic EL the msc may not exist, if computed with respect to general EL-TBoxes or cyclic ABoxes. However, it is still possible to find a concept description that is the msc up to a fixed role-depth, i.e. with respect to a maximal nesting of quantifiers. In this report we present a practical approach for computing the roledepth bounded msc, based on the polynomial-time completion algorithm for EL. We extend these methods to Prob-EL⁰¹c , which is a probabilistic variant of EL. Together with the companion report [9] this report devises computation methods for the bottom-up construction of knowledge bases for EL and Prob-EL⁰¹c .

Description logics in their standard setting only allow for representing and reasoning with crisp knowledge without any degree of uncertainty. Of course, this is a serious shortcoming for use cases where it is impossible to perfectly determine the truth of a statement. For resolving this expressivity restriction, probabilistic variants of description logics have been introduced. Their model-theoretic semantics is built upon so-called probabilistic interpretations, that is, families of directed graphs the vertices and edges of which are labeled and for which there exists a probability measure on this graph family. Results of scientific experiments, e.g., in medicine, psychology, or biology, that are repeated several times can induce probabilistic interpretations in a natural way. In this document, we shall develop a suitable axiomatization technique for deducing terminological knowledge from the assertional data given in such probabilistic interpretations. More specifically, we consider a probabilistic variant of the description logic EL⊥, and provide a method for constructing a set of rules, so-called concept inclusions, from probabilistic interpretations in a sound and complete manner.

We consider ontology-based query answering in a setting where some of the data are numerical and of a probabilistic nature, such as data obtained from uncertain sensor readings. The uncertainty for such numerical values can be more precisely represented by continuous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing approaches using discrete probability distributions over facts by continuous probability distributions over numerical values. We determine the exact (data and combined) complexity of query answering in extensions of the well-known description logics EL and ALC with numerical comparison operators in this probabilistic setting. / This is an extended version of the article in: Proceedings of the 11th International Symposium on Frontiers of Combining Systems. This version has been revised based on the comments of the reviewers.

For a probabilistic extension of the description logic EL⊥, we consider the task of automatic acquisition of terminological knowledge from a given probabilistic interpretation. Basically, such a probabilistic interpretation is a family of directed graphs the vertices and edges of which are labeled, and where a discrete probabilitymeasure on this graph family is present. The goal is to derive so-called concept inclusions which are expressible in the considered probabilistic description logic and which hold true in the given probabilistic interpretation. A procedure for an appropriate axiomatization of such graph families is proposed and its soundness and completeness is justified.

Formulae of linear temporal logic (LTL) can be used to specify (wanted or unwanted) properties of a dynamical system. In model checking, the system’s behaviour is described by a transition system, and one needs to check whether all possible traces of this transition system satisfy the formula. In runtime verification, one observes the actual system behaviour, which at any point in time yields a finite prefix of a trace. The task is then to check whether all continuations of this prefix to a trace satisfy (violate) the formula. More precisely, one wants to construct a monitor, i.e., a finite automaton that receives the finite prefix as input and then gives the right answer based on the state currently reached. In this paper, we extend the known approaches to LTL runtime verification in two directions. First, instead of propositional LTL we use the more expressive temporal logic ALC-LTL, which can use axioms of the Description Logic (DL) ALC instead of propositional variables to describe properties of single states of the system. Second, instead of assuming that the observed system behaviour provides us with complete information about the states of the system, we assume that states are described in an incomplete way by ALC-knowledge bases. We show that also in this setting monitors can effectively be constructed. The (double-exponential) size of the constructed monitors is in fact optimal, and not higher than in the propositional case. As an auxiliary result, we show how to construct Büchi automata for ALC-LTL-formulae, which yields alternative proofs for the known upper bounds of deciding satisfiability in ALC-LTL.