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On the Data Complexity of Consistent Query Answering

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Abstract

The framework of database repairs is a principled approach to managing inconsistency in databases. In particular, the consistent answers of a query on an inconsistent database provide sound semantics and the guarantee that the values obtained are those returned by the query on every repair of the given inconsistent database. In this paper, we carry out a systematic investigation of the data complexity of the consistent answers of conjunctive queries for set-based repairs and with respect to classes of constraints that, in recent years, have been extensively studied in the context of data exchange and data integration. Our results, which range from polynomial-time computability to undecidability, complement or improve on earlier work, and provide a fairly comprehensive picture of the data complexity of consistent query answering. We also address the problem of finding a “representative” or “useful” repair of an inconsistent database. To this effect, we introduce the notion of a universal repair, as well as relaxations of it, and then apply it to the investigation of the data complexity of consistent query answering.

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Notes

  1. Proposition 7.1 in [33] asserts the existence of a set of tgds Σ and an instance I, such that I has no 1-universal superset-repair w.r.t. Σ. Unfortunately, there was a mistake in the proof of this proposition. Proposition 3.8 clarifies the situation (note that, by Proposition 2.7, for sets of tgds Σ, every instance has a superset-repair).

  2. For inclusion dependencies, this fact was pointed out in [14].

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Acknowledgments

We thank the anonymous reviewers for their comments and pointers to the literature. This research was partially supported by NSF grants IIS-0905276 and IIS-1217869. Fontaine was visiting UC Santa Cruz while this research was carried out.

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Correspondence to Gaëlle Fontaine.

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ten Cate, B., Fontaine, G. & Kolaitis, P.G. On the Data Complexity of Consistent Query Answering. Theory Comput Syst 57, 843–891 (2015). https://doi.org/10.1007/s00224-014-9586-0

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