Query processing in incomplete logical databases

  • Nadine Lerat
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 243)

Abstract

An incomplete database T combines two types of information about the real world modeled by the database : (a) the relational database with null values ("value not known") represented by axioms of a First Order Theory T0 and (b) the data dependencies that are known to be satisfied in the real world. For a given set of dependencies (functional and inclusion dependencies), a chase process transforms in two steps ("forward" and "backward" chase) type (b) information into an equivalent type (a) form. This yields a new first order theory T1 ; for a class Γ of queries (subclass of monotone queries) the evaluation on T and on T1 are equivalent. A technique involving both algebraic and theorem-proving methods provides for a sound and complete evaluation of the query.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Gra]
    M. H. Graham, A new proof that the chase is a Church-Rosser replacement system, June 1980.Google Scholar
  2. [Grh]
    G. Grahne, Dependency satisfaction in databases with incomplete information. Proc. 10th Symp. on Very Large Data Bases, Singapore, Aug. 1984, 37–47.Google Scholar
  3. [Hon]
    P. Honeyman, Testing Satisfaction of Functional Dependencies. J. Assoc. Comput. Mach. 29, 3(July 1982), 668–677.Google Scholar
  4. [IL1]
    T. Imielinski, W. Lipski, Incomplete information in Relational Databases. J. Assoc. Comput. Mach. 31, 4(Oct. 1984), 761–791.Google Scholar
  5. [IL2]
    T. Imielinski, W. Lipski, Dependencies in relational databases with incomplete information. To appear.Google Scholar
  6. [Imi]
    T. Imielinski, On algebraic query processing in logical databases. In Advances in Data Base Theory, vol 2 (H. Gallaire, J. Minker, J.-M. Nicolas, eds), Plenum Press, New York, 1984, 285–318.Google Scholar
  7. [Im85]
    T. Imielinski, Abstraction in Query Processing. 1985.Google Scholar
  8. [Jan]
    J. Janas, On the feasibility of informative answers. In Advances in Database Theory, vol. 1 (H. Gallaire, J. Minker and J. M. Nicolas, eds), Plenum Press, New York, 1981, pp. 397–414.Google Scholar
  9. [JK]
    D. S. Johnson and A. Klug, Testing Containment of Conjunctive Queries under Functional and Inclusion Dependencies. J. Computer Syst. Sci. 28, 167–189 (1984).Google Scholar
  10. [LL]
    N. Lerat, W. Lipski, Non-applicable nulls. To appear in Theoretical Computer Science.Google Scholar
  11. [Nic]
    J.-M. Nicolas, First order logic formalization for functional, multivalued, and mutual dependencies. Proc. ACM SIGMOD Symp. on Management of Data, 1978, 40–46.Google Scholar
  12. [Rei1]
    R. Reiter, Towards a logical reconstruction of relational database theory. In Conceptual Modelling: Perspectives from Artificial Intelligence, Databases and Programming Languages (M. L. Brodie, J. Mylopoulos and J. Schmidt, eds), Springer-Verlag, to appear.Google Scholar
  13. [Rei2]
    R. Reiter, A sound and sometimes complete query evaluation algorithm for relational databases with null values. Techn. Rep., Dept. of Computer Science, Univ. of British Columbia, Vancouver, BC, June 1983.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Nadine Lerat
    • 1
  1. 1.Laboratoire de Recherche en Informatique U.A. 410 du C.N.R.S. "Al Khowarizmi"Université de Paris-Sud, Centre d'OrsayOrsay CédexFrance

Personalised recommendations