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Explaining why an answer is in the result of a query or why it is missingfrom the result is important for many applications including auditing,debugging data and queries, and answering hypothetical questions about data.Both types of questions, i.e., why and why-not provenance, have been studiedextensively. In this work, we present the first practical approach foranswering such questions for queries with negation (first-order queries). Ourapproach is based on a rewriting of Datalog rules (called firing rules) thatcaptures successful rule derivations within the context of a Datalog query. Weextend this rewriting to support negation and to capture failed derivationsthat explain missing answers. Given a (why or why-not) provenance question, wecompute an explanation, i.e., the part of the provenance that is relevant toanswer the question. We introduce optimizations that prune parts of aprovenance graph early on if we can determine that they will not be part of theexplanation for a given question. We present an implementation that runs on topof a relational database using SQL to compute explanations. Our experimentsdemonstrate that our approach scales to large instances and significantlyoutperforms an earlier approach which instantiates the full provenance tocompute explanations.

Efficiently Computing Provenance Graphs for Queries with Negation