Ontologies have been widely used in various application domains such as the Semantic Web, information systems and bio-informatics. Ontology is often modelled using description logics (DLs) to provide the mechanisms for repre- senting knowledge of a domain, defining its semantics and reasoning upon it. Lightweight DL ontologies are those which purposefully designed to have high performance on standard reasoning tasks, including satisfiability, subsump- tion and query answering, while sacrificing to certain degree their expressive power. Along with the vast use of ontologies, non-standard reasoning tasks have started to emerge, namely abductive and inductive reasoning. Abductive reasoning is the process of inferring the best explanation from the given ob- servations according to a background knowledge. Inductive reasoning is the process of deriving general logical theory from the given example data. For abductive reasoning, we study one important explanation problem for DL ontologies, referred to as query abduction. Ontology-based data access appli- cations show that query abduction is among the most important tools that reasoning systems have to be equipped to support debugging incomplete data. Hence, we study query abduction that aims to find explanations for the given observations (i.e. a query with answers) that together with the knowledge base will be satisfied if the explanations add to the knowledge base.