Characterizing and Computing Semantically Correct Answers from Databases with Annotated Logic and Answer Sets

  • Pablo Barceló
  • Leopoldo Bertossi
  • Loreto Bravo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2582)

Abstract

A relational database may not satisfy certain integrity constraints (ICs) for several reasons. However most likely most of the information in it is still consistent with the ICs. The answers to queries that are consistent with the ICs can be considered sematically correct answers, and are characterized [2] as ordinary answers that can be obtained from every minimally repaired version of the database. In this paper we address the problem of specifying those repaired versions as the minimal models of a theory written in Annotated Predicate Logic [27]. It is also shown how to specify database repairs using disjunctive logic program with annotation arguments and a classical stable model semantics. Those programs are then used to compute consistent answers to general first order queries. Both the annotated logic and the logic programming approaches work for any set of universal and referential integrity constraints. Optimizations of the logic programs are also analyzed.

Keywords

Logic Program Minimal Model Logic Programming Stable Model Belief Revision 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abiteboul, S., Hull, R. and Vianu, V. Foundations of Databases. Addison-Wesley, 1995.Google Scholar
  2. 2.
    Arenas, M., Bertossi, L. and Chomicki, J. Consistent Query Answers in Inconsistent Databases. In Proc. ACM Symposium on Principles of Database Systems (ACM PODS’99), 1999, pp. 68–79.Google Scholar
  3. 3.
    Arenas, M., Bertossi, L. and Kifer, M. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In ‘Computational Logic-CL2000’ Stream: 6th International Conference on Rules and Objects in Databases (DOOD’2000). Springer Lecture Notes in Artificial Intelligence 1861, 2000, pp. 926–941.Google Scholar
  4. 4.
    Arenas, M., Bertossi, L. and Chomicki, J. Specifying and Querying Database Repairs using Logic Programs with Exceptions. In Flexible Query Answering Systems. Recent Developments, H. L. Larsen, J. Kacprzyk, S. Zadrozny, H. Christiansen (eds.), Springer, 2000, pp. 27–41.Google Scholar
  5. 5.
    Arenas, M., Bertossi, L. and Chomicki, J. Scalar Aggregation in FD-Inconsistent Databases. In Database Theory-ICDT 2001, Springer, LNCS 1973, 2001, pp. 39–53.CrossRefGoogle Scholar
  6. 6.
    Arenas, M., Bertossi, L. and Chomicki, J. Answer Sets for Consistent Query Answers. To appear in Theory and Practice of Logic Programming.Google Scholar
  7. 7.
    Baral, C. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, 2003.Google Scholar
  8. 8.
    Barcelo, P. and Bertossi, L. Repairing Databases with Annotated Predicate Logic. In Proc. Nineth International Workshop on Non-Monotonic Reasoning (NMR’2002), Special session: Changing and Integrating Information: From Theory to Practice, S. Benferhat and E. Giunchiglia (eds.), 2002, pp. 160–170.Google Scholar
  9. 9.
    Barcelo, P. and Bertossi, L. Logic Programs for Querying Inconsistent Databases. Proc. Practical Aspects of Declarative Languages (PADL03), Springer LNCS 2562, 2003, pp. 208–222.Google Scholar
  10. 10.
    Ben-Eliyahu, R. and Dechter, R. Propositional Semantics for Disjunctive Logic Programs. Annals of Mathematics in Artificial Intelligence, 1994, 12:53–87.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Bertossi, L., Chomicki, J., Cortes, A. and Gutierrez, C. Consistent Answers from Integrated Data Sources. In ‘Flexible Query Answering Systems’, Proc. of the 5th International Conference, FQAS 2002. T. Andreasen, A. Motro, H. Christiansen, H. L. Larsen (eds.). Springer LNAI 2522, 2002, pp. 71–85.Google Scholar
  12. 12.
    Blair, H. A. and Subrahmanian, V. S. Paraconsistent Logic Programming. Theoretical Computer Science, 1989, 68:135–154.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Buccafurri, F., Leone, N. and Rullo, P. Enhancing Disjunctive Datalog by Constraints. IEEE Transactions on Knowledge and Data Engineering, 2000, 12(5):845–860.CrossRefGoogle Scholar
  14. 14.
    Celle, A. and Bertossi, L. Querying Inconsistent Databases: Algorithms and Implementation. In ‘Computational Logic-CL 2000’, J. Lloyd et al. (eds.). Stream: 6th International Conference on Rules and Objects in Databases (DOOD’2000). Springer Lecture Notes in Artificial Intelligence 1861, 2000, pp. 942–956.Google Scholar
  15. 15.
    Chomicki, J. and Marcinkowski, J. On the Computational Complexity of Consistent Query Answers. Submitted in 2002 (CoRR paper cs.DB/0204010).Google Scholar
  16. 16.
    Chou, T. and Winslett, M. A Model-Based Belief Revision System. Journal of Automated Reasoning, 1994, 12:157–208.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Damasio, C. V. and Pereira, L. M. A Survey on Paraconsistent Semantics for Extended Logic Programas. In Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 2, D. M. Gabbay and Ph. Smets (eds.), Kluwer Academic Publishers, 1998, pp. 241–320.Google Scholar
  18. 18.
    Dantsin, E., Eiter, T., Gottlob, G. and Voronkov, A. Complexity and Expressive Power of Logic Programming. ACM Computing Surveys, 2001, 33(3): 374–425.CrossRefGoogle Scholar
  19. 19.
    Eiter, T. and Gottlob, G. Propositional Circumscription and Extended Closed World Assumption are Πp 2-complete. Theoretical Computer Science, 1993, 114, pp. 231–245.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Eiter, T., Leone, N., Mateis, C., Pfeifer, G. and Scarcello, F. A Deductive System for Non-Monotonic Reasoning. Proc. LPNMR’97, Springer LNAI 1265, 1997, pp. 364–375.Google Scholar
  21. 21.
    Eiter, T., Faber, W.; Leone, N. and Pfeifer, G. Declarative Problem-Solving in DLV. In Logic-Based Artificial Intelligence, J. Minker (ed.), Kluwer, 2000, pp. 79–103.Google Scholar
  22. 22.
    Fagin, R., Kuper, G., Ullman, J. and Vardi, M. Updating Logical Databases. In Advances in Computing Research, JAI Press, 1986, Vol. 3, pp. 1–18.Google Scholar
  23. 23.
    Gelfond, M. and Lifschitz, V. The Stable Model Semantics for Logic Programming. In Logic Programming, Proceedings of the Fifth International Conference and Symposium, R. A. Kowalski and K. A. Bowen (eds.), MIT Press, 1988, pp. 1070–1080.Google Scholar
  24. 24.
    Gelfond, M. and Lifschitz, V. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing, 1991, 9:365–385.CrossRefGoogle Scholar
  25. 25.
    Giannotti, F., Greco, S.; Sacca, D. and Zaniolo, C. Programming with Nondeterminism in Deductive Databases. Annals of Mathematics and Artificial Intelligence, 1997, 19(3–4).Google Scholar
  26. 26.
    Greco, G., Greco, S. and Zumpano, E. A Logic Programming Approach to the Integration, Repairing and Querying of Inconsistent Databases. In Proc. 17th International Conference on Logic Programming, ICLP’01, Ph. Codognet (ed.), LNCS 2237, Springer, 2001, pp. 348–364.Google Scholar
  27. 27.
    Kifer, M. and Lozinskii, E. L. A Logic for Reasoning with Inconsistency. Journal of Automated reasoning, 1992, 9(2):179–215.MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Kifer, M. and Subrahmanian, V. S. Theory of Generalized Annotated Logic Programming and its Applications. Journal of Logic Programming, 1992, 12(4):335–368.CrossRefMathSciNetGoogle Scholar
  29. 29.
    Leone, N., Rullo, P. and Scarcello, F. Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation. Information and Computation, 1997, 135(2):69–112.MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Lloyd, J. W. Foundations of Logic Programming. Springer Verlag, 1987.Google Scholar
  31. 31.
    Marek, V. W. and Truszczynski, M. Revision Programming. Theoretical Computer Science, 1998, 190(2):241–277.MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Pradhan, S. Reasoning with Conflicting Information in Artificial Intelligence and Database Theory. PhD thesis, Department of Computer Science, University of Maryland, 2001.Google Scholar
  33. 33.
    Reiter, R. Towards a Logical Reconstruction of Relational Database Theory. In On Conceptual Modelling, M. L. Brodie, J. Mylopoulos, J. W. Schmidt (eds.), Springer, 1984.Google Scholar
  34. 34.
    Sagonas, K. F., Swift, T. and Warren, D. S. XSB as an Efficient Deductive Database Engine. In Proc. of the 1994 ACM SIGMOD International Conference on Management of Data, ACM Press, 1994, pp. 442–453.Google Scholar
  35. 35.
    Winslett, M. Reasoning about Action using a Possible Models Approach. In Proc. Seventh National Conference on Artificial Intelligence (AAAI’88), 1988, pp. 89–93.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pablo Barceló
    • 1
  • Leopoldo Bertossi
    • 2
  • Loreto Bravo
    • 2
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

Personalised recommendations