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An ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that emerge from ontology-mediated querying and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice. In particular, the thesis gives results regarding the data complexity of OMQ evaluation by completely classifying complexity and rewritability questions for OMQs based on an EL ontology and a conjunctive query. Furthermore, the query-by-example problem, and the expressibility and verification problem in ontology-based data access are introduced and investigated.

This report summarises the Digital Ludeme Project, a recently launched 5-year research project being conducted at Maastricht University. This computational study of the world's traditional strategy games seeks to improve our understanding of early games, their development, and their role in the spread of related mathematical ideas throughout recorded human history.

Information systems have to deal with an increasing amount of data that is heterogeneous, unstructured, or incomplete. In order to align and complete data, systems may rely on taxonomies and background knowledge that are provided in the form of an ontology. This survey gives an overview of research work on the use of ontologies for accessing incomplete and/or heterogeneous data.

A most promising approach to answering queries in ontology-based data access (OBDA) is through query rewriting. In this paper we present novel rewriting approaches for several extensions of OBDA. The goal is to understand their relative expressiveness and to pave the way for efficient query answering algorithms.

Recent success in Artificial Intelligence (AI) and Machine Learning (ML) allow problem solving automatically without any human intervention. Autonomous approaches can be very convenient. However, in certain domains, e.g., in the medical domain, it is necessary to enable a domain expert to understand, why an algorithm came up with a certain result. Consequently, the field of Explainable AI (xAI) rapidly gained interest worldwide in various domains, particularly in medicine. Explainable AI studies transparency and traceability of opaque AI/ML and there are already a huge variety of methods. For example with layer-wise relevance propagation relevant parts of inputs to, and representations in, a neural network which caused a result, can be highlighted. This is a first important step to ensure that end users, e.g., medical professionals, assume responsibility for decision making with AI/ML and of interest to professionals and regulators. Interactive ML adds the component of human expertise to AI/ML processes by enabling them to re-enact and retrace AI/ML results, e.g. let them check it for plausibility. This requires new human-AI interfaces for explainable AI. In order to build effective and efficient interactive human-AI interfaces we have to deal with the question of how to evaluate the quality of explanations given by an explainable AI system. In this paper we introduce our System Causability Scale to measure the quality of explanations. It is based on our notion of Causability (Holzinger et al. in Wiley Interdiscip Rev Data Min Knowl Discov 9(4), 2019) combined with concepts adapted from a widely-accepted usability scale.