Advertisement

Adding For-Loops to First-Order Logic

Extended Abstract
  • Frank Neven
  • Martin Otto
  • Jurek Tyszkiewicz
  • Jan Van den Bussche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1540)

Abstract

We study the query language BQL: the extension of the relational algebra with for-loops. We also study FO(FOR): the extension of first-order logic with a for-loop variant of the partial fixpoint operator. In contrast to the known situation with query languages which include while-loops instead of for-loops, BQL and FO(FOR) are not equivalent. Among the topics we investigate are: the precise relationship between BQL and FO(FOR); inflationary versus non-inflationary iteration; the relationship with logics that have the ability to count; and nested versus unnested loops.

Keywords

Query Language Expressive Power Relational Algebra Winning Strategy Modular Equation 
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. AHV95.
    S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.Google Scholar
  2. AV95.
    S. Abiteboul and V. Vianu. Computing with first-order logic. Journal of Computer and System Sciences, 50(2):309–335, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  3. CH82.
    A. Chandra and D. Harel. Structure and complexity of relational queries. Journal of Computer and System Sciences, 25(1):99–128 1982.zbMATHCrossRefGoogle Scholar
  4. Cha81.
    A. Chandra. Programming primitives for database languages. In Conference Record, 8th ACM Symposium on Principles of Programming Languages, pages 50–62 1981.Google Scholar
  5. Cha88.
    A. Chandra. Theory of database queries. In Proceedings of the Seventh ACM Symposium on Principles of Database Systems, pages 1–9. ACM Press, 1988.Google Scholar
  6. EF95.
    H.-D. Ebbinghaus and J. Flum. Finite Model Theory. Springer, 1995.Google Scholar
  7. EFT94.
    H.-D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic. Undergraduate Texts in Mathematics. Springer-Verlag, second edition 1994.Google Scholar
  8. GO93.
    E. Grädel and M. Otto. Inductive definability with counting on finite structures. In E. Börger, editor, Computer Science Logic, volume 702 of Lecture Notes in Computer Science, pages 231–247. Springer-Verlag, 1993.Google Scholar
  9. HKL96.
    L. Hella, Ph. G. Kolaitis, and K. Luosto. Almost everywhere equivalence of logics in finite model theory. Bulletin of Symbolic Logic, 2(4):422–443 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  10. KV95.
    Ph. G. Kolaitis and Jouko A. Väänänen. Generalized quantifiers and pebble games on finite structures. Annals of Pure and Applied Logic, 74(1):23–75, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  11. Ott96.
    M. Otto. The expressive power of fixed-point logic with counting. Journal of Symbolic Logic, 61(1):147–176 1996.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Frank Neven
    • 1
  • Martin Otto
    • 2
  • Jurek Tyszkiewicz
    • 3
  • Jan Van den Bussche
    • 1
  1. 1.Limburgs Universitair CentrumGermany
  2. 2.RWTH AachenGermany
  3. 3.Warsaw Universitygermany

Personalised recommendations