Abstract
In this work we establish and investigate connections between causes for query answers in databases, database repairs with respect to denial constraints, and consistency-based diagnosis. The first two are relatively new research areas in databases, and the third one is an established subject in knowledge representation. We show how to obtain database repairs from causes, and the other way around. Causality problems are formulated as diagnosis problems, and the diagnoses provide causes and their responsibilities. The vast body of research on database repairs can be applied to the newer problems of computing actual causes for query answers and their responsibilities. These connections are interesting per se. They also allow us, after a transition inspired by consistency-based diagnosis to computational problems on hitting-sets and vertex covers in hypergraphs, to obtain several new algorithmic and complexity results for database causality.
Highlights
When querying a database, a user may not always obtain the expected results, and the system could provide some explanations
For a BCQ Q and database D, they are: (a) The causality problem (CP) that is about computing the actual causes for Q. (b) The responsibility problem (RP) that is about computing the responsibility ρD(t) of a given actual cause t
Since a tuple that is not an actual cause has responsibility 0, the latter problem subsumes the former. (c) Computing the most responsible actual causes (MRC). These problems have corresponding decision versions. Both CP and its decision version, CPD, are solvable in polynomial time [41], which can be extended to union of BCQs (UBCQs)
Summary
A user may not always obtain the expected results, and the system could provide some explanations. These three forms of reasoning, namely inferring causes from databases, consistency-based diagnosis, and consistent query answering (and repairs) are all non-monotonic [49]. Being the causality problems the main focus of this work, we take advantage of algorithms and complexity results both for consistency-based diagnosis; and database repairs and consistent query answering [9]. 1. For a boolean conjunctive query and its associated denial constraint (the former being its violation view), we establish a precise connection (characterization and computational reductions) between actual causes for the query (being true) and the subset- and cardinality-repairs of the instance wrt. Proofs of results without an implicit proof in this paper can be found in [50]
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