Reasoning and Query Answering with Complete Data and Ontologies

Combining relational databases and ontologies is necessary for modern query answering systems. To deal with the problem, the ontology-based data access approach uses ontologies to capture databases, i.e. databases are considered under the open-world assumption. This leads to many issues including the necessity of restricting to only positive queries, and the failure of query composition. In our research, we focus on a combined setting that allows data in databases stay completely (so-called complete data) as under the closed-world assumption while knowledge provided by ontologies can be incomplete. To this purpose, we ?rst study the complexity of query answering problem under description logic constraints in the presence of complete data and show that complete data makes query answering harder than query answering over incomplete data only. We then provide a query rewriting technique that supports deciding the existence of a safe-range ?rst-order equivalent reformulation of a query regarding the database schema. If such a reformulation exists, it provides an e?cient approach to construct the reformulation which is e?ectively executable as an SQL query. In the third part of the thesis, we study the de?nability abduction problem which aims to identify the least committing extensions of ontological constraints to gain the equivalent reformulation of queries. We ?nally apply this idea to data exchange - where we want to characterize the case of lossless transformations of data.