Skip to main content
SpringerLink
Log in

Incomplete deductive databases

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

We investigate the complexity of query processing in databases which have both incompletely specified data and deductive rules. The paper is divided into two parts: in the first we consider databases in which incompletely specified data occurs only in the database intension; in the second we consider databases in which incomplete information is represented only in database extension. We prove that, in general, the query processing problem for databases with incomplete intensions is undecidable. A number of classes of rules for which all conjunctive queries can be processed in polynomial time is then characterized. For databases with incomplete extensions we prove a number of CoNP completeness results. For instance, we demonstrate that processing disjunctions which are restricted to individual columns of database predicates can, in general, be as bad as processing arbitrary disjunctions (i.e. CoNP-complete). This falsifies the conjecture that such limited disjunctions could be computationally beneficial. We also show two simple examples of situations in which query processing is guaranteed to be polynomial. These situations are linked to certain assumptions about database updates.

Finally, we provide a summary of the data complexity of queries depending on the type of database extension, intension, query sublanguage and Open World vs Closed World assumption.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Abiteboul, K. Kannellakis and G. Grahne, On the representation and querying of sets of possible worlds, in:Proc. ACM SIGMOD 87 (1987).

  2. K. Apt and M. Van Emden, Contributions to the theory of logic programming, J. ACM 29 (1982).

  3. F. Bancihlon and R. Ramakrishnan, An amateur introduction to recursive queries, in:Proc. ACM SIGMOD (1986).

  4. C. Beeri and M. Vardi, A proof procedure for data dependencies, J. ACM (October 1984).

  5. M.A. Casanova, R. Fagin and C.H. Papadimitriou, Inclusion dependencies and their interaction with functional dependencies, J. Comp. Syst. Sci. (1984).

  6. E.F. Codd, A relational model of data for large shared data banks, CACM 13 (1970) 377–387.

    Google Scholar 

  7. H. Gallaire, J. Minker and J. Nicholas, Logic and databases — A deductive approach, ACM Comp. Surveys (1984) 153–185.

  8. M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, 1979).

  9. Y. Gurewich and H. Lewis, The inference problem for template dependencies, in:ACM PODS Symp. (1982).

  10. Hardy and Wright,An Introduction to the Theory of Numbers (Clarendon, Oxford, 1938).

    Google Scholar 

  11. T. Imielinski and W. Lipski, Incomplete information in relational databases, J. ACM 31 (1984) 761–791.

    Google Scholar 

  12. T. Imielinski, Query processing in deductive databases with incomplete information, in:ACM SIGMOD Conf. (May, 1986).

  13. T. Imielinski and K. Vadaparty, Complexity of query processing in databases with OR-objects, in:Proc. ACM Symp. on Principles of Database Systems (1989).

  14. R. Kowalski,Logic for Problem Solving (1979).

  15. H. Levesque, Computer and Thought lecture at IJCAI 85 (1985).

  16. D. Doveland,Automated Theorem Proving (Springer, 1979).

  17. J. Minker, Generalized Closed World Assumption, in:Conf. on Automated Deduction (1982).

  18. R. Reiter, On closed world databases, in:Logic and Databases (Plenum, 1978).

  19. R. Reiter, A sound and sometimes complete query evaluation algorithm for relational databases with null values, J. ACM (1985).

  20. J. Ullman,Principles of Database Systems (Computer Science Press, 1982).

  21. M. Vardi, The complexity of relational query languages, in:Proc. IEEE Conf. on Foundations of Computer Science (1982).

  22. M. Vardi, The implication and finite implication problems for typed template dependencies, in:ACM PODS Symp. (1982).

  23. M. Vardi, Querying logical databases, J. Comp. Syst. Sci. 33 (1986).

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Rutgers University, 08903, New Brunswick, NJ, USA

    Tomasz Imielinski

Authors
  1. Tomasz Imielinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by NSF grant DCR 85-04140.

More precisely, we can say this only in the presence of the closed world assumption [18].

Rights and permissions

Reprints and permissions

About this article

Cite this article

Imielinski, T. Incomplete deductive databases. Ann Math Artif Intell 3, 259–293 (1991). https://doi.org/10.1007/BF01530927

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01530927

Keywords

Search

Navigation