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 make a first step towards adapting an existing approach for privacypreserving publishing of linked data to Description Logic (DL) ontologies. We consider the case where both the knowledge about individuals and the privacy policies are expressed using concepts of the DL EL, which corresponds to the setting where the ontology is an EL instance store. We introduce the notions of compliance of a concept with a policy and of safety of a concept for a policy, and show how optimal compliant (safe) generalizations of a given EL concept can be computed. In addition, we investigate the complexity of the optimality problem.

We present some initial results on ontology-based query answering with description logic ontologies that may employ temporal and probabilistic operators on concepts and axioms. Speci_cally, we consider description logics extended with operators from linear temporal logic (LTL), as well as subjective probability operators, and an extended query language in which conjunctive queries can be combined using these operators. We first show some complexity results for the setting in which either only temporal operators or only probabilistic operators may be used, both in the ontology and in the query, and then show a 2ExpSpace lower bound for the setting in which both types of operators can be used together. / This is an extended version of an article accepted at Description Logics 2019.

Projection is the problem of checking whether the execution of a given sequence of actions will achieve its goal starting from some initial state. In this paper, we study a setting where we combine a two-dimensional Description Logic of context (ConDL) with an action formalism. We choose a well-studied ConDL where both: the possible states of a dynamical system itself (object level) and also different context-dependent views on this system state (context level) are organised in relational structures and can be described using usual DL constructs. To represent how such a system and its views evolve we introduce a suitable action formalism. It allows to describe change on both levels. Furthermore, the observable changes on the object level due to an action execution can also be contextdependent. We show that the formalism is well-behaved in the sense that projection has the same complexity as standard reasoning tasks in case ALCO is the underlying DL.

We present a method for answering ontology-mediated queries for DL-Lite extended with a concrete domain, where we allow concrete domain predicates to be used in the query as well. Our method is based on query rewriting, a well-known technique for ontology-based query answering (OBQA), where the knowledge provided by the ontology is compiled into the query so that the rewritten query can be evaluated directly over a database. This technique reduces the problem of query answering w.r.t. an ontology to query evaluation over a database instance. Specifically, we consider members of the DL-Lite family extended with unary and binary concrete domain predicates over the real numbers. While approaches for query rewriting DL-Lite with these concrete domain have been investigated theoretically, these approaches use a combined approach in which also the data is processed, and require the concrete domain values occurring in the data to be known in advance, which makes the procedure data-dependent. In contrast, we show how rewritings can be computed in a data-independent fashion.

Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. One contribution of this paper is to strengthen the existing undecidability results further by showing that concrete domains even weaker than the ones considered in the previous proofs may cause undecidability. To regain decidability in the presence of GCIs, quite strong restrictions, in sum called w-admissiblity, need to be imposed on the concrete domain. On the one hand, we generalize the notion of w-admissiblity from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate w-admissiblity to well-known notions from model theory. In particular, we show that finitely bounded, homogeneous structures yield w-admissible concrete domains. This allows us to show w-admissibility of concrete domains using existing results from model theory.

Concrete domains have been introduced in Description Logics (DLs) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. To retain decidability when integrating a concrete domain into a decidable DL, the domain must satisfy quite strong restrictions. In previous work, we have analyzed the most prominent such condition, called w-admissibility, from an algebraic point of view. This provided us with useful algebraic tools for proving w-admissibility, which allowed us to find new examples for concrete domains whose integration leaves the prototypical expressive DL ALC decidable. When integrating concrete domains into lightweight DLs of the EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. In the present paper, we investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical padmissible concrete domain based on the rational numbers. Although w-admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into ALC yields decidable DLs.

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining Description Logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there has recently been a growing interest in extending this work to the quantitative case. In this paper, we complement existing results on the combination of DLs with metric temporal logics over the natural numbers by introducing interval-rigid names. This allows to state that elements in the extension of certain names stay in this extension for at least some specified amount of time.

We investigate ontology-based query answering (OBQA) in a setting where both the ontology and the query can refer to concrete values such as numbers and strings. In contrast to previous work on this topic, the built-in predicates used to compare values are not restricted to being unary. We introduce restrictions on these predicates and on the ontology language that allow us to reduce OBQA to query answering in databases using the so-called combined rewriting approach. Though at first sight our restrictions are different from the ones used in previous work, we show that our results strictly subsume some of the existing first-order rewritability results for unary predicates. / This is an extended version of a paper published in the proceedings of IJCAI 2017.

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.