Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explana-tion facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answer-ing. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunc-tive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations. 1