Query processing in incomplete logical databases

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


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.


Relational Database Query Processing Data Dependency Order Theory Query Evaluation 
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.


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  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 Berlin Heidelberg 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

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