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A three-valued semantics for querying and repairing inconsistent databases

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Abstract

The problem of managing and querying inconsistent databases has been deeply investigated in the last few years. As the problem of consistent query answering is hard in the general case, most of the techniques proposed so far have an exponential complexity. Polynomial techniques have been proposed only for restricted forms of constraints (such as functional dependencies) and queries. In this paper, a technique for computing “approximate” consistent answers in polynomial time is proposed, which works in the presence of a wide class of constraints (namely, full constraints) and Datalog queries. The proposed approach is based on a repairing strategy where update operations assigning an undefined truth value to the “reliability” of tuples are allowed, along with updates inserting or deleting tuples. The result of a repair can be viewed as a three-valued database which satisfies the specified constraints. In this regard, a new semantics (namely, partial semantics) is introduced for constraint satisfaction in the context of three-valued databases, which aims at capturing the intuitive meaning of constraints under three-valued logic. It is shown that, in order to compute “approximate” consistent query answers, it suffices to evaluate queries by taking into account a unique repair (called deterministic repair), which in some sense “summarizes” all the possible repairs. The so obtained answers are “approximate” in the sense that are safe (true and false atoms in the answers are, respectively, true and false under the classical two-valued semantics), but not complete.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley (1994)

  2. Andritsos, P., Fuxman, A., Miller, R.: Clean answers over dirty databases. IEEE International Conference on Data Engineering (ICDE) (2006)

  3. Arenas, M., Bertossi, L., Chomicki, J.: Consistent query answers in inconsistent databases. In: Proceedings ACM Symposium on Principles of Database Systems (PODS), pp. 68–79 (1999)

  4. Arenas, M., Bertossi, L.E., Chomicki, J.: Specifying and querying database repairs using logic programs with exceptions. In: Proceedings International Conference on Flexible Query Answering Systems (FQAS), pp. 27–41 (2000)

  5. Arenas, M., Bertossi, L.E., Chomicki, J., He, X., Raghavan, V., Spinrad, J.: Scalar aggregation in inconsistent databases. Theor. Comp. Sci. (TCS) 3(296), 405–434 (2003)

    Article  MathSciNet  Google Scholar 

  6. Arenas, M., Bertossi, L., Chomicki, J.: Answer sets for consistent query answering in inconsistent databases. Theor. Pract. Log. Prog. 3(45), 393–424 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Baral, C., Zhang, Y.: On the semantics of knowledge update. In: Proceedings International Joint Conference on Artificial Intelligence, pp. 97–102 (2001)

  8. Bertossi, L.: Consistent query answering in databases. SIGMOD Record, 35(2), 68–76 (2006)

    Article  Google Scholar 

  9. Bohannon, P., Flaster, M., Fan, W., Rastogi, R.: A cost-based model and effective heuristic for repairing constraints by value modification. In: Proceedings ACM SIGMOD International Conference on Management of Data (SIGMOD), pp. 143–154 (2005)

  10. Cali, A., Lembo, D., Rosati, R.: On the decidability and complexity of query answering over inconsistent and incomplete databases. In: Proceedings ACM Symposium on Principles of Database Systems (PODS), pp. 260–271 (2003)

  11. Caroprese, L., Greco, S., Sirangelo, S., Zumpano, E.: Declarative semantics of production rules for integrity maintenance. In: Proceedings International Conference on Logic Programming, pp. 26–40 (2006)

  12. Chomicki, J., Lobo, J., Naqvi, S.A.: Conflict resolution using logic programming. IEEE Trans. Knowl. Data Eng. (TKDE) 15(1), 244–249 (2003)

    Article  Google Scholar 

  13. Chomicki, J., Marcinkowski, J.: Minimal-change integrity maintenance using tuple deletions. Inf. Comput 197(1–2), 90–121 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Chomicki, J.: Consistent query answering: five easy pieces. In: Proceedings International Conference on Database Theory (ICDT), pp. 1–17 (2007)

  15. Corts-Calabuig, A., Denecker, M., Arieli, O., Bruynooghe, M.: Representation of partial knowledge and query answering in locally complete databases. In: Proceedings International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), pp. 407–421 (2006)

  16. Flesca, S., Furfaro, F., Parisi, F.: Consistent query answers on numerical databases under aggregate constraints. In: Proceedings International Workshop on Database Programming Languages, pp. 279–294 (2005)

  17. Fuxman, A., Miller, J.R.: First-order query rewriting for inconsistent databases. J. Comput. Syst. Sci. 73(4), 610–635 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings International Conference on Logic Programming (ICLP), pp. 1070–1080 (1988)

  19. Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. J. Intell. Inf. Syst. 27(2), 159–184 (2006)

    Article  Google Scholar 

  20. Grant, J., Subrahmanian, V.S.: Reasoning in inconsistent knowledge bases. IEEE Trans. Knowl. Data Eng. (TKDE) 7(1), 177–189 (1995)

    Article  MathSciNet  Google Scholar 

  21. Greco, S., Zumpano, E.: Querying inconsistent databases. Proceedings International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), pp. 308–325 (2000)

  22. Greco, G., Greco, S., Zumpano, E.: A logical framework for querying and repairing inconsistent databases. IEEE Trans. Knowl. Data Eng. (TKDE) 15(6), 1389–1408 (2003)

    Article  Google Scholar 

  23. Greco, S., Sirangelo, C., Trubitsyna, I., Zumpano, E.: Preferred repairs for inconsistent databases. In: Proceedings International Conference on Database and Expert Systems Applications (DEXA), pp. 44–55 (2004)

  24. Greco, G., Molinaro, C.: Querying and repairing inconsistent databases under three-valued semantics. In: Proceedings International Conference on Logic Programming (ICLP), pp. 149–164 (2007)

  25. Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. Inconsistency Tolerance, pp. 191–236 (2005)

  26. Hunter, A.: Measuring inconsistency in knowledge via quasi-classical models. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), pp. 68–73 (2002)

  27. Hunter, A.: Evaluating significance of inconsistencies. In: Proceedings of the 18th International Joint Conference on Artificial Intellignce (IJCAI), pp. 468–473 (2003)

  28. Leone, N., Pfeifer, G., Faber, W., Calimeri, F., Dell’Armi, T., Eiter, T., Gottlob, G., Ianni, G., Ielpa, G., Koch, K., Perri, S., Polleres, A.: The DLV system. In: Proceedings International Conference on Logics in Artificial Intelligence (JELIA), pp. 537–540 (2002)

  29. Lin, J., Mendelzon, A.O.: Merging databases under constraints. Int. J. Coop. Inf. Syst. 7(1), 55–76 (1998)

    Article  Google Scholar 

  30. Lozinskii, E.L.: Resolving contradictions: a plausible semantics for inconsistent systems. J. Autom. Reason. 12(1), 1–32 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  31. Marek, V.W., Truszczynski, M.: Revision programming. Theor. Comput. Sci. 190(2), 241–277 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  32. Martinez, M.V., Pugliese, A., Simari, G.I., Subrahmanian, V.S., Prade, H.: How dirty is your relational database? An axiomatic approach. In: Proceedings of European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 103–114 (2007)

  33. Rao, P., Sagonas, K.F., Swift, T., Warren, D.S., Freire, J.: XSB: a system for effciently computing WFS. In: Proceedings International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), pp. 431–441 (1977)

  34. Sagonas, K.F., Swift, T., Warren, D.S.: An abstract machine for efficiently computing queries to well-founded models. J. Logic Program. 45(1–3), 1–41 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  35. Staworko, S., Chomicki, J., Marcinkowski, J.: Priority-based conflict resolution in inconsistent relational databases. Current Trends in Database Technology—EDBT Workshops, pp. 318–335 (2006)

  36. Subrahmanian, V.S.: Amalgamating knowledge bases. ACM Trans. Database Syst. (TODS) 19(2), 291–331 (1994)

    Article  MathSciNet  Google Scholar 

  37. Syrjzänen, T., Niemelä, I.: The Smodels system. In: Procedings International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), pp. 434–438 (2001)

  38. Ullman, J.K.: Principles of Database and Knowledge-Base Systems. Computer Science Press (1998)

  39. Van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)

    Article  MATH  Google Scholar 

  40. Wijsen, J.: Database repairing using updates. ACM Trans. Database Syst. (TODS) 30(3), 722–768 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. DEIS—Università della Calabria, Via P. Bucci, 87036, Rende (CS), Italy

    Filippo Furfaro, Sergio Greco & Cristian Molinaro

Authors
  1. Filippo Furfaro
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  2. Sergio Greco
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  3. Cristian Molinaro
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Correspondence to Filippo Furfaro.

Additional information

A preliminary version of this paper appeared in the Proceedings of the International Conference on Logic Programming, 2007. Work partially supported by MUR grants under the projects PILOT and LOGICA.

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Furfaro, F., Greco, S. & Molinaro, C. A three-valued semantics for querying and repairing inconsistent databases. Ann Math Artif Intell 51, 167–193 (2007). https://doi.org/10.1007/s10472-008-9088-3

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Keywords

Mathematics Subject Classification (2000)