Uncertainty That Counts

  • Dany Maslowski
  • Jef Wijsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7022)


Uncertainty is modeled by a multibase (db,μ) where db is a database with zero or more primary key violations, and μ associates a multiplicity (a positive integer) to each fact of db. In data integration, the multiplicity of a fact g can indicate the number of data sources in which g was found. In planning databases, facts with the same primary key value are alternatives for each other, and the multiplicity of a fact g can denote the number of people in favor of g.

A repair of db is obtained by selecting a maximal number of facts without ever selecting two distinct facts of the same relation that agree on their primary key. Every repair has a support count, which is the product of the multiplicities of its facts.

For a fixed Boolean query q, we define σ CERTAINTY(q) as the following counting problem: Given a multibase (db,μ), determine the weighted number of repairs of db that satisfy q. Here, every repair is weighted by its support count. We illustrate the practical significance of this problem by means of examples.

For conjunctive queries q without self-join, we provide a syntactic characterization of the class of queries q such that σ CERTAINTY(q) is in P; for queries not in this class, σ CERTAINTY(q) is \(\sharp\) P-hard (and hence highly intractable).


Conjunctive Query Weighted Number Support Count Source Database Query Answering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)zbMATHGoogle Scholar
  2. 2.
    Arenas, M., Bertossi, L.E., Chomicki, J.: Consistent query answers in inconsistent databases. In: PODS, pp. 68–79. ACM Press, New York (1999)Google Scholar
  3. 3.
    Arenas, M., Bertossi, L.E., Chomicki, J., He, X., Raghavan, V., Spinrad, J.: Scalar aggregation in inconsistent databases. Theor. Comput. Sci. 296(3), 405–434 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dalvi, N.N., Ré, C., Suciu, D.: Probabilistic databases: diamonds in the dirt. Commun. ACM 52(7), 86–94 (2009)CrossRefGoogle Scholar
  5. 5.
    Dalvi, N.N., Re, C., Suciu, D.: Queries and materialized views on probabilistic databases. J. Comput. Syst. Sci. 77(3), 473–490 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dalvi, N.N., Suciu, D.: Management of probabilistic data: foundations and challenges. In: Libkin, L. (ed.) PODS, pp. 1–12. ACM, New York (2007)Google Scholar
  7. 7.
    Fan, W., Geerts, F., Wijsen, J.: Determining the currency of data. In: Lenzerini, M., Schwentick, T. (eds.) PODS, pp. 71–82. ACM, New York (2011)Google Scholar
  8. 8.
    Fuxman, A., Miller, R.J.: First-order query rewriting for inconsistent databases. J. Comput. Syst. Sci. 73(4), 610–635 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Greco, S., Molinaro, C.: Approximate probabilistic query answering over inconsistent databases. In: Li, Q., Spaccapietra, S., Yu, E.S.K., Olivé, A. (eds.) ER 2008. LNCS, vol. 5231, pp. 311–325. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Maslowski, D., Wijsen, J.: On counting database repairs. In: Proceedings of the 4th International Workshop on Logic in Databases, LID 2011, pp. 15–22. ACM, New York (2011), Google Scholar
  11. 11.
    Pema, E., Kolaitis, P.G., Tan, W.C.: On the tractability and intractability of consistent conjunctive query answering. In: Proceedings of the 2011 Joint EDBT/ICDT Ph.D. Workshop, PhD 2011, pp. 38–44. ACM, New York (2011), Google Scholar
  12. 12.
    Toda, S.: PP is as hard as the polynomial-time hierarchy. SIAM J. Comput. 20(5), 865–877 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Wijsen, J.: On the consistent rewriting of conjunctive queries under primary key constraints. Inf. Syst. 34(7), 578–601 (2009)CrossRefGoogle Scholar
  14. 14.
    Wijsen, J.: On the first-order expressibility of computing certain answers to conjunctive queries over uncertain databases. In: Paredaens, J., Gucht, D.V. (eds.) PODS, pp. 179–190. ACM, New York (2010)Google Scholar
  15. 15.
    Wijsen, J.: A remark on the complexity of consistent conjunctive query answering under primary key violations. Inf. Process. Lett. 110(21), 950–955 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dany Maslowski
    • 1
  • Jef Wijsen
    • 1
  1. 1.Université de MonsMonsBelgium

Personalised recommendations