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Query Answering in Inconsistent Databases

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Logics for Emerging Applications of Databases

Abstract

In this chapter, we summarize the research on querying inconsistent databases that we have been conducting during the last five years. The formal framework that we have used is based on two concepts: repair and consistent query answer. We describe different approaches to the issue of computing consistent query answers: query transformation, logic programming, inference in annotated logics, and specialized algorithms. We also characterize the computational complexity of this problem. Finally, we discuss related research in artificial intelligence, databases, and logic programming.

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References References

  1. S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, Reading, Mass., 1995.

    Google Scholar 

  2. S. Agarwal, A. M. Keller, G. Wiederhold, and K. Saraswat. Flexible Relation: An Approach for Integrating Data from Multiple, Possibly Inconsistent Databases. In 11th IEEE International Conference on Data Engineering, 1995.

    Google Scholar 

  3. M. Arenas, L. Bertossi, and J. Chomicki. Consistent Query Answers in Inconsistent Databases. In 18th ACM Symposium on Principles of Database Systems, pp. 68–79, 1999

    Google Scholar 

  4. M. Arenas, L. Bertossi, and J. Chomicki. Specifying and Querying Database Repairs Using Logic Programs with Exceptions. In 4th International Conference on Flexible Query Answering Systems, pp. 27–41. Springer-Verlag, 2000.

    Google Scholar 

  5. M. Arenas, L. Bertossi, and J. Chomicki. Scalar Aggregation in FD-Inconsistent Databases. In 8th International Conference on Database Theory, pp. 39–53. Springer-Verlag, LNCS 1973, 2001.

    Google Scholar 

  6. M. Arenas, L. Bertossi, and J. Chomicki. Answer Sets for Consistent Query Answering in Inconsistent Databases. Technical Report arXiv:cs.DB/0204094, arXiv.org e-Print archive, July 2002. To appear in Theory and Practice of Logic Programming.

    Google Scholar 

  7. M. Arenas, L. Bertossi, J. Chomicki, X. He, V. Raghavan, and J. Spinrad. Scalar Aggregation in Inconsistent Databases. Theoretical Computer Science, 296(3): 405–434, 2003. Special issue: selected papers from ICDT 2001.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Arenas, L. Bertossi, and M. Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In International Conference on Computational Logic, pp. 926–941. Springer-Verlag, LNCS 1861, 2000.

    Google Scholar 

  9. O. Arieli and A. Avron. A Model-Theoretic Approach for Recovering Consistent Data from Inconsistent Knowledge Bases. Journal of Automated Reasoning, 22(2):263–309, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  10. O. Arieli, M. Denecker, B. Van Nuffelen, and M. Bruynooghe. Repairing Inconsistent Databases: A Model-Theoretic Approach. In Decker et al. [37].

    Google Scholar 

  11. P. Asirelli, P. Inverardi, and G. Plagenza. Integrity Constraints as Views in Deductive Databases. In S. Conrad, H-J. Klein, and K-D. Schewe, editors, International Workshop on Foundations of Models and Languages for Data and Objects, pp. 133–140, September 1996.

    Google Scholar 

  12. B. Balzer. Tolerating Inconsistency. In 13th International Conference on Software Engineering, pp. 158–165. IEEE Computer Society Press, 1991.

    Google Scholar 

  13. C. Baral, S. Kraus, J. Minker, and V. S. Subrahmanian. Combining Knowledge Bases Consisting of First-Order Theories. Computational Intelligence, 8:45–71, 1992.

    Article  Google Scholar 

  14. P. Barcelo and L. Bertossi. Repairing Databases with Annotated Predicate Logic. In S. Benferhat and E. Giunchiglia, editors, Ninth International Workshop on Non-Monotonic Reasoning (NMR02), Special Session: Changing and Integrating Information: Prom Theory to Practice., pages 160-170, 2002.

    Google Scholar 

  15. P. Barcelo and L. Bertossi. Logic Programs for Querying Inconsistent Databases. In International Symposium on Practical Aspects of Declarative Languages, pp. 208–222. Springer-Verlag, LNCS 2562, 2003.

    Google Scholar 

  16. R. Ben-Eliyahu and R. Dechter. Propositional semantics for disjunctive logic programs. Annals of Mathematics and Artificial Intelligence, 12:53–87, 1994.

    Google Scholar 

  17. L. Bertossi and J. Chomicki, editors. Working Notes of the IJCAI’O1 Workshop on Inconsistency in Data and Knowledge. AAAI Press, 2001.

    Google Scholar 

  18. L. Bertossi, J. Chomicki, A. Cortes, and C. Gutierrez. Consistent Answers from Integrated Data Sources. In 5th International Conference on Flexible Query Answering Systems, pp. 71–85, Springer-Verlag, LNCS 2522, 2002.

    Google Scholar 

  19. L. Bertossi and C. Schwind. Analytic Tableaux and Database Repairs: Foundations. In 2nd International Symposium on Foundations of Information and Knowledge Systems, pp. 32–48. Springer-Verlag, LNCS 2284, 2002.

    Google Scholar 

  20. L. Bertossi and C. Schwind. Database Repairs and Analytic Tableaux. Technical Report arXiv:cs.DB/021l042, arXiv.org e-Print archive, November 2002. To appear in a special issue of Annals of Mathematics and Artificial Intelligence.

    Google Scholar 

  21. H. Blair and V. S. Subrahmanian. Paraconsistent Logic Programming. Theoretical Computer Science, 68(2):135–154, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Brandstädt, V. B. Le, and J. P. Spinrad. Graph Classes: A Survey. SIAM, 1999.

    Google Scholar 

  23. L. Bravo and L. Bertossi. Logic Programs for Consistently Querying Data Integration Systems. In International Joint Conference on Artificial Intelligence, 2003. To appear.

    Google Scholar 

  24. F. Bry. Query Answering in Information Systems with Integrity Constraints. In IFIP WG 11.5 Working Conference on Integrity and Control in Information Systems. Chapman & Hall, 1997.

    Google Scholar 

  25. A. Celle and L. Bertossi. Querying Inconsistent Databases: Algorithms and Implementation. In International Conference on Computational Logic, pp. 942–956. Springer-Verlag, LNCS 1861, 2000.

    Google Scholar 

  26. U. S. Chakravarthy, J. Grant, and J. Minker. Logic-Based Approach to Semantic Query Optimization. ACM Transactions on Database Systems, 15(2):162–207, 1990.

    Article  Google Scholar 

  27. A. Chandra and P. Merlin. Optimal Implementation of Conjunctive Queries in Relational Databases. In 9th ACM SIGACT Symposium on the Theory of Computing, pp. 77–90, 1977.

    Google Scholar 

  28. L. Cholvy. Querying an Inconsistent Database. In Proceedings of Artificial Intelligence: Methodology, Systems and Applications (AIMSA). orth-Holland, 1990.

    Google Scholar 

  29. J. Chomicki and J. Marcinkowski. Minimal-Change Integrity Maintenance Using Tuple Deletions. Technical Report cs.DB/0212004, arXiv.org e-Print archive, December 2002.

    Google Scholar 

  30. J. Chomicki and J. Marcinkowski. On the Computational Complexity of Consistent Query Answers. Technical Report arXiv:cs.DB/020401O, arXiv.org e-Print archive, April 2002.

    Google Scholar 

  31. T. Chou and M. Winslett. A Model-Based Belief Revision System. Journal of Automated Reasoning, 12:157–208, 1994.

    Article  MathSciNet  Google Scholar 

  32. N. C. A. da Costa, J-Y. Beziau, and O. Bueno. Paraconsistent Logic in a Historical Perspective. Logique & J Analyse, 150/151/152:111–125, 1995.

    Google Scholar 

  33. M. Dalal. Investigations into a Theory of Knowledge Base Revision. In 7th National Conference on Artificial Intelligence, August 1988.

    Google Scholar 

  34. C. V. Damasio and L. M. Pereira. A Survey of Paraconsistent Semantics for Extended Logic Programs. In Gabbay and Smets [44], pp. 241–320.

    Google Scholar 

  35. E. Dantsin, T. Eiter, G. Gottlob, and A. Voronkov. Complexity and Expressive Power of Logic Programming. ACM Computing Surveys, 33(3):374–425, 2001.

    Article  Google Scholar 

  36. S. de Amo, W. A. Carnielli, and J. Marcos. A Logical Framework for Integrating Inconsistent Information in Multiple Databases. In 2nd International Symposium on Foundations of Information and Knowledge Systems, pp. 67–84, 2002.

    Google Scholar 

  37. H. Decker, J. Villadsen, and T. Waragai, editors. ICLP 2002 Workshop on Paraconsistent Computational Logic (PCL), July 2002.

    Google Scholar 

  38. Phan Minh Dung. Integrating Data from Possibly Inconsistent Databases. In 1st International Conference on Cooperative Information Systems, Brussels, Belgium, 1996.

    Google Scholar 

  39. O. M. Duschka, M. R. Genesereth, and A. Y. Levy. Recursive Query Plans for Data Integration. Journal of Logic Programming, 43(1):49–73, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  40. T. Eiter, W. Faber, N. Leone, and G. Pfeifer. Declarative Problem-Solving in DLV. In J. Minker, editor, Logic-Based Artificial Intelligence, pp. 79–103. Kluwer, 2000.

    Google Scholar 

  41. T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57(2–3):227–270, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  42. R. Fagin, J. D. Ullman, and M. Y. Vardi. On the semantics of updates in databases. In 2nd ACM Symposium on Principles of Database Systems, 1983.

    Google Scholar 

  43. E. Franconi, A. L. Palma, N. Leone, S. Perri, and F. Scarcello. Census Data Repair: a Challenging Application of Disjunctive Logic Programming. In 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, pp. 561–578. Springer-Verlag, LNCS 2250, 2002.

    Google Scholar 

  44. D. M. Gabbay and P. Smets, editors. Handbook of Defeasible Reasoning and Uncertain Information, Vol. 2. Kluwer, Dordrecht, The Netherlands, 1998.

    Google Scholar 

  45. H. Galhardas, D. Florescu, D. Shasha, E. Simon, and C-A. Saita. Declarative Data Cleaning: Language, Model, and Algorithms. In 27th International Conference on Very Large Data Bases, pp. 371–380, 2001.

    Google Scholar 

  46. P. Gärdenfors. Knowledge in Flux. MIT Press, Cambridge, Mass., 1990.

    Google Scholar 

  47. P. Gärdenfors and H. Rott. Belief Revision. In D. M. Gabbay, J. Hogger, C, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 4, pp. 35–132. Oxford University Press, 1995.

    Google Scholar 

  48. M. R. Garey and D. S. Johnson. Computers and Intractability: a Guide to the Theory of NP-Completeness. W. H. Freeman, New York, 1979.

    Google Scholar 

  49. M. Gelfond and V. Lifschitz. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing, 9(3/4):365–386, 1991.

    Article  Google Scholar 

  50. M. Gertz. A Extensible Framework for Repairing Constraint Violations. In S. Conrad, H-J. Klein, and K-D. Schewe, editors, International Workshop on Foundations of Models and Languages for Data and Objects, pp. 41–56, September 1996.

    Google Scholar 

  51. M. Gertz. Diagnosis and Repair of Constraint Violations in Database Systems. PhD thesis, Universitiit Hannover, 1996.

    Google Scholar 

  52. F. Giannotti, S. Greco, D. Sacca, and C. Zaniolo. Programming with Non-determinism in Deductive Databases. Annals of Mathematics and Artificial Intelligence, 19(3–4), 1997.

    Google Scholar 

  53. F. Giannotti and D. Pedreschi. Datalog with Nondeterministic Choice Computes NDB-PTIME. Journal of Logic Programming, 35:75–101, 1998.

    Article  MathSciNet  Google Scholar 

  54. P. Godfrey, J. Grant, J. Gryz, and J. Minker Integrity Constraints: Semantics and Applications. In J. Chomicki and G. Saake, editors, Logics for Databases and Information Systems, Chapt. 9. Kluwer Academic Publishers, Boston, 1998.

    Google Scholar 

  55. G. Grahne and A. O. Mendelzon. Tableau Techniques for Querying Information Sources through Global Schemas. In 7th International Conference on Database Theory, pp. 332–347. Springer-Verlag, LNCS 1540, 1999.

    Google Scholar 

  56. J. Grant and J. Minker. A Logic-Based Approach to Data Integration. Theory and Practice of Logic Programming, 2(3):323–368, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  57. G. Greco, S. Greco, and E. Zumpano. A Logic Programming Approach to the Integration, Repairing and Querying of Inconsistent Databases. In 17th International Conference on Logic Programming, pp. 348–364. Springer-Verlag, LNCS 2237, 2001.

    Google Scholar 

  58. S. Greco, D. Sacca, and C. Zaniolo. Datalog Queries with Stratified Negation and Choice: from P to DP. In 5th International Conference on Database Theory, pp. 82–96. Springer-Verlag, 1995.

    Google Scholar 

  59. S. Greco and E. Zumpano. Querying Inconsistent Databases. In 7th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, pp. 308–325. Springer-Verlag, LNCS 1955, 2000.

    Google Scholar 

  60. J. Gryz. Query Rewriting using Views in the Presence of Functional and Inclusion Dependencies. Information Systems, 24(7):597–612, 1999.

    Article  MATH  Google Scholar 

  61. D. S. Hochbaum. Approximating Covering and Packing Problems: Set Cover, Vertex Cover, Independent Set, and Related Problems. In D. S. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems. PWS, 1997.

    Google Scholar 

  62. A. Hunter. Paraconsistent Logics. In Gabbay and Smets [44], pp. 13–44.

    Google Scholar 

  63. T. ImieliÑski, S. Naqvi, and K. Vadaparty. Incomplete Objects-A Data Model for Design and Planning Applications. In ACM SIGMOD International Conference on Management of Data, pp. 288–297, Denver, Colorado, May 1991.

    Google Scholar 

  64. T. ImieliÑski, R. van der Meyden, and K. Vadaparty. Complexity Tailored Design: A New Design Methodology for Databases With Incomplete Information. Journal of Computer and System Sciences, 51(3):405–432, 1995.

    Article  MathSciNet  Google Scholar 

  65. C. Kakas, A, R. A. Kowalski, and F. Toni. Abductive Logic Programming. Journal of Logic and Computation, 2(6):719–770, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  66. P. C. Kanellakis. Elements of Relational Database Theory. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, Chapt. 17, pp. 1073–1158. Elsevier/MIT Press, 1990.

    Google Scholar 

  67. H. Katsuno and A. O. Mendelzon. Propositional Knowledge Base Revision and Minimal Change. Artificial Intelligence, 52(3):263–294, 1992.

    Article  MathSciNet  Google Scholar 

  68. M. Kifer and E. L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 9(2):179–215, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  69. M. Kifer and V. S. Subrahmanian. Theory of Generalized Annotated Logic Programming and its Applications. Journal of Logic Programming, 12(4):335–368, 1992.

    Article  MathSciNet  Google Scholar 

  70. R. Kowalski and F. Sadri. Logic Programs with Exceptions. New Generation Computing, 9(3/4):387–400, 1991.

    Article  Google Scholar 

  71. R. Kowalski, F. Sadri, and P. Soper. Integrity Checking in Deductive Databases. In International Conference on Very Large Data Bases, pp. 61–69. Morgan Kaufmann Publishers, 1987.

    Google Scholar 

  72. S. M. Leach and J. J. Lu. Query Processing in Annotated Logic Programming: Theory and Implementation. Journal of Intelligent Information Systems, 6:33–58, 1996.

    Article  Google Scholar 

  73. D. Lembo, M. Lenzerini, and R. Rosati. Source Inconsistency and Incompleteness in Data Integration. In 9th International Workshop on Knowledge Representation meets Databases (KRDB’02), Toulouse, France, 2002.

    Google Scholar 

  74. M. Lenzerini. Data Integration: A Theoretical Perspective. In 21st ACM Symposium on Principles of Database Systems, 2002. Invited talk.

    Google Scholar 

  75. N. Leone, P. Rullo, and F. Scarcello. Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation. Information and Computation, 135(2):69–112, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  76. A. Y. Levy. Combining Artificial Intelligence and Databases for Data Integration. In Artificial Intelligence Today, pp. 249–268. Springer-Verlag, LNCS 1600, 1999.

    Google Scholar 

  77. A. Y. Levy, A. Rajaraman, and J. J. Ordille. Query-Answering Algorithms for Information Agents. In 13th National Conference on Artificial Intelligence, pp. 40–47, 1996.

    Google Scholar 

  78. A. Y. Levy, A. Rajaraman, and J. J. Ordille. Querying Heterogeneous Information Sources Using Source Descriptions. In 22nd International Conference on Very Large Data Bases, pp. 251–262, 1996.

    Google Scholar 

  79. J. Lin. A Semantics for Reasoning Consistently in the Presence of Inconsistency. Artificial Intelligence, 86(1–2):75–95, 1996.

    Article  MathSciNet  Google Scholar 

  80. J. Lin and A. O. Mendelzon. Merging Databases under Constraints. International Journal of Cooperative Information Systems, 7(1):55–76, 1996.

    Article  Google Scholar 

  81. J. W. Lloyd. Foundations of Logic Programming. 2nd edition, Springer-Verlag, 1987.

    Google Scholar 

  82. E. L. Lozinskii. Resolving Contradictions: A Plausible Semantics for Inconsistent Systems. Journal of Automated Reasoning, 12(1):1–32, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  83. V. W. Marek and M. Truszczynski. Revision Programming. Theoretical Computer Science, 190(2):241–277, 1998.

    Google Scholar 

  84. A. Motro. Multiplex: A Formal Model for Multidatabases and Its Implementation. In 4th International Workshop on Next Generation Information Technology and Systems, pp. 138–158. Springer-Verlag, LNCS 1649, 1999.

    Google Scholar 

  85. B. A. Nuseibeh, S. M. Easterbrook, and Russo A. Leveraging Inconsistency in Software Development. IEEE Computer, 33(4):24–29, 2000.

    Article  Google Scholar 

  86. S. Pradhan. Semantics of Normal Logic Programs and Contested Information. In 11th IEEE Symposium on Logic in Computer Science, pp. 406–415, 1996.

    Google Scholar 

  87. S. Pradhan. Reasoning with Conflicting Information in Artificial Intelligence and Database Theory. Ph.D. thesis, Department of Computer Science, University of Maryland, College Park, Md., 2001.

    Google Scholar 

  88. R. Reiter. Towards a Logical Reconstruction of Relational Database Theory. In M. L. Brodie, J. Mylopoulos, and J. W. Schmidt, editors, On Conceptual Modeling, pp. 191–233. Springer-Verlag, 1984.

    Google Scholar 

  89. R. Reiter. On Integrity Constraints. In 2nd International Conference on Theoretical Aspects of Rationality and Knowledge, pp. 97–111, 1988.

    Google Scholar 

  90. R. Reiter. What Should A Database Know? In 6th ACM Symposium on Principles of Database Systems, pp. 302–304, 1988.

    Google Scholar 

  91. F. Sadri and R. Kowalski. A Theorem-Proving Approach to Database Integrity. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pp. 313–362. Morgan Kaufmann, 1988.

    Google Scholar 

  92. K. F. Sagonas, T. Swift, and D. S. Warren. XSB as an Efficient Deductive Database Engine. In ACM SIGMOD International Conference on Management of Data, pp. 442–453, 1994.

    Google Scholar 

  93. V. S. Subrahmanian. Amalgamating Knowledge Bases. ACM Transactions on Database Systems, 19(2):291–331, 1994.

    Article  MathSciNet  Google Scholar 

  94. J. D. Ullman. Information Integration Using Logical Views. In 6th International Conference on Database Theory, pp. 19–40. Springer-Verlag, LNCS 1186, 1997.

    Google Scholar 

  95. M. Y. Vardi. The Complexity of Relational Query Languages. In 14th ACM Symposium on Theory of Computing, pp. 137–146, 1982.

    Google Scholar 

  96. J. Wijsen. Condensed Representation of Database Repairs for Consistent Query Answering. In 9th International Conference on Database Theory, pp. 378–393, Springer-Verlag, LNCS 2572, 2003.

    Google Scholar 

  97. M. Winslett. Reasoning about Action using a Possible Models Approach. In 7th National Conference on Artificial Intelligence, 1988.

    Google Scholar 

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Bertossi, L., Chomicki, J. (2004). Query Answering in Inconsistent Databases. In: Chomicki, J., van der Meyden, R., Saake, G. (eds) Logics for Emerging Applications of Databases. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18690-5_2

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