High-Level Why-Not Explanations using Ontologies
  We propose a novel foundational framework for why-not explanations, that is, explanations for why a tuple is missing from a query result. Our why-not explanations leverage concepts from an ontology to provide high-level and meaningful reasons for why a tuple is missing from the result of a query. A key algorithmic problem in our framework is that of computing a most-general explanation for a why-not question, relative to an ontology, which can either be provided by the user, or it may be automatically derived from the data and/or schema. We study the complexity of this problem and associated problems, and present concrete algorithms for computing why-not explanations. In the case where an external ontology is provided, we first show that the problem of deciding the existence of an explanation to a why-not question is NP-complete in general. However, the problem is solvable in polynomial time for queries of bounded arity, provided that the ontology is specified in a suitable language, such as a member of the DL-Lite family of description logics, which allows for efficient concept subsumption checking. Furthermore, we show that a most-general explanation can be computed in polynomial time in this case. In addition, we propose a method for deriving a suitable (virtual) ontology from a database and/or a data workspace schema, and we present an algorithm for computing a most-general explanation to a why-not question, relative to such ontologies. This algorithm runs in polynomial-time in the case when concepts are defined in a selection-free language, or if the underlying schema is fixed. Finally, we also study the problem of computing short most-general explanations, and we briefly discuss alternative definitions of what it means to be an explanation, and to be most general. 
Balder ten Cate and Cristina Civili and Evgeny Sherkhonov and   Wang-Chiew Tan
cs.DB