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Hoare's Logic is incomplete when it does not have to be

  • J. Bergstra
  • A. Chmielinska
  • J. Tiuryn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 131)

Abstract

If Hoare's Logic, HL(A), is complete on a structure A, then the set PC(A) of all asserted programs true over A is recursive in the first order theory of A, Th(A). We show that this implication cannot be reversed.

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References

  1. 1.
    Bergstra, J.A., & J.V. Tucker, "Some natural structures which fail to possess a sound and decidable Hoare-like logic for their while-programs" (to appear in TCS. An earlier edition of this paper is registered at the Mathematical Centre as report IW 136/80).Google Scholar
  2. 2.
    Bergstra, J.A. & J.F. Tucker, "Expressiveness and the completeness of Hoare's logic", Mathematical Centre Report IW 143/80.Google Scholar
  3. 3.
    Bergstra, J.A., & J.V. Tucker, "Two theorems on the completeness of Hoare's Logic" Mathematical Centre Report IW?/81.Google Scholar
  4. 4.
    Cook, S.A., "Soundness and completeness of an axiom system for program verification", SIAM J. Computing? (1978) 70–90.Google Scholar
  5. 5.
    Harel, D., "First order dynamic logic", Lecture notes in Computer Science 68, Springer 1978.Google Scholar
  6. 6.
    Wand, M., "A new incompleteness result for Hoare's system", JACM 25(1978) 168–175.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • J. Bergstra
    • 1
  • A. Chmielinska
    • 2
  • J. Tiuryn
    • 3
    • 4
    • 5
  1. 1.Department of Computer ScienceUniversity of LeidenThe Netherlands
  2. 2.Department of MathematicsUniversity of TorunPoland
  3. 3.M.I.T., Laboratory for Computer ScienceUSA
  4. 4.Department of MathematicsBoston UniversityUSA
  5. 5.Department of MathematicsUniversity of WarsawPoland

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