Abstract
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.
Highlights
In recent times, one has to manage huge amounts of data that arise from multiple sources, scattered across many different databases, so data is often incomplete and of heterogeneous quality
We focus on two areas: 1. Get a deeper understanding of the complexities of answering Horn Description logics (DLs) ontology-mediated query (OMQ)
The main result of the thesis regarding data complexity and rewritability of OMQs is a complete characterization of OMQs based on an EL-ontology and a conjunctive query (CQ) as the actual query: For every such OMQ, the query answering problem is either in AC0 or NL-complete or PTIME-complete
Summary
One has to manage huge amounts of data that arise from multiple sources, scattered across many different databases, so data is often incomplete and of heterogeneous quality. Ontologies store background knowledge about certain domains by defining terminology and describing how different terms relate to each other. When answering an OMQ, one does not speak of answers to the query, but of certain answers, which are all answers to the query that are logically entailed by the database and the ontology. This approach has been studied extensively, see for example [6, 11, 12]. Note that finding the certain answers to an OMQ is a logical reasoning problem, which can in general be much harder than computing the answers to a traditional query (like an SQL query) in the absence of an ontology, which is merely a model checking problem
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