A Comparison of Two Proof Critics: Power vs. Robustness

  • Louise A. Dennis
  • Alan Bundy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2410)


Proof critics are a technology from the proof planning paradigm. They examine failed proof attempts in order to extract information which can be used to generate a patch which will allow the proof to go through.

We consider the proof of the “whisky problem”, a challenge problem from the domain of temporal logic. The proof requires a generalisation of the original conjecture and we examine two proof critics which can be used to create this generalisation. Using these critics we believe we have produced the first automatic proofs of this challenge problem.

We use this example to motivate a comparison of the two critics and propose that there is a place for specialist critics as well as powerful general critics. In particular we advocate the development of critics that do not use meta-variables.


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  1. 1.
    D. Basin and T. Walsh. A calculus for and termination of rippling. Journal of Automated Reasoning, 16(1–2):147–180, 1996.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Bundy. The use of explicit plans to guide inductive proofs. In R. Lusk and R. Overbeek, editors, 9th Conference on Automated Deduction, pages 111–120. Springer-Verlag, 1988. Longer version available from Edinburgh as DAI Research Paper No. 349.Google Scholar
  3. 3.
    A. Bundy. The automation of proof by mathematical induction. In A Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, Volume 1. Elsevier, 2001.Google Scholar
  4. 4.
    A. Bundy, A. Stevens, F. van Harmelen, A. Ireland, and A. Smaill. Rippling: A heuristic for guiding inductive proofs. Artificial Intelligence, 62:185–253, 1993. Also available from Edinburgh as DAI Research Paper No. 567.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. Bundy, F. van Harmelen, C. Horn, and A. Smaill. The Oyster-Clam system. In M.E. Stickel, editor, 10th International Conference on Automated Deduction, pages 647–648. Springer-Verlag, 1990. Lecture Notes in Artificial Intelligence No. 449. Also available from Edinburgh as DAI Research Paper 507.Google Scholar
  6. 6.
    C. Castellini and A. Smaill. Tactic-based theorem proving in first-order modal and temporal logics. In IJCAR 2001, workshop t10, 2001.Google Scholar
  7. 7.
    A. Degtyarev and M. Fisher. Towards first-order temporal resolution. In F. Baader, G. Brewka, and T. Eiter, editors, KI 2001: Advances in Artificial Intelligence, Joint German/Austrian Conference on AI, Vienna, Austria, September 19–21, 2001, Proceedings, volume 2174 of Lecture Notes in Computer Science. Springer, 2001.Google Scholar
  8. 8.
    L. A. Dennis, A. Bundy, and I. Green. Making a productive use of failure to generate witness for coinduction from divergent proof attempts. Annals of Mathematics and Artificial Intelligence, 29:99–138, 2000. Also available from Edinburgh as Informatics Report RR0004.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    M. Fisher, C. Dixon, and M. Peim. Clausal temporal resolution. ACM Transactions on Computational Logic, 1(4), 2001.Google Scholar
  10. 10.
    D.M. Gabbay, I. Hodkinson, and M. Reynolds. Temporal Logic: Mathematical Foundations and Computational Aspects. Oxford University Press, 1994.Google Scholar
  11. 11.
    A. Ireland and A. Bundy. Productive use of failure in inductive proof. Journal of Automated Reasoning, 16(1–2):79–111, 1996. Also available as DAI Research Paper No 716, Dept. of Artificial Intelligence, Edinburgh.Google Scholar
  12. 12.
    C. B. Jones. Software Development: A Rigorous Approach. Prentice-Hall international series in Computer Science. Prentice-Hall, 1980.Google Scholar
  13. 13.
    J. Richardson and A. Smaill. Continuations of proof strategies. In M.P. Bonacina and B. Gramlich, editors, Proc. 4th International Workshop on Strategies in Automated Deduction (STRATEGIES 2001), Siena, Italy, june 2001. Available from http://www.logic.at/strategies/strategies01/.
  14. 14.
    J.D.C. Richardson, A. Smaill, and I. Green. System description: Proof planning in higher-order logic with lambda-clam. In C. Kirchner and H. Kirchner, editors, Conference on Automated Deduction (CADE’98), volume 1421 of Lecture Notes in Computer Science, pages 129–133. Springer-Verlag, 1998.CrossRefGoogle Scholar
  15. 15.
    A. Smaill and I. Green. Higher-order annotated terms for proof search. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics: 9th International Conference, TPHOLs’96, volume 1275 of Lecture Notes in Computer Science, pages 399–414, Turku, Finland, 1996. Springer-Verlag. Also available from Edinburgh as DAI Research Paper 799.Google Scholar
  16. 16.
    T. Walsh. A divergence critic for inductive proof. Journal of Artificial Intelligence Research, 4:209–235, 1996.MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Louise A. Dennis
    • 1
  • Alan Bundy
    • 2
  1. 1.School of Computer Science and Information TechnologyUniversity of NottinghamNottingham
  2. 2.Division of InformaticsUniversity of EdinburghEdinburgh

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