Advertisement

Proof Planning with Multiple Strategies

  • Erica Melis
  • Andreas Meier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)

Abstract

Humans have different problem solving strategies at their disposal and they can flexibly employ several strategies when solving a complex problem, whereas previous theorem proving and planning systems typically employ a single strategy or a hard coded combination of a few strategies. We introduce multi-strategy proof planning that allows for combining a number of strategies and for switching flexibly between strategies in a proof planning process. Thereby proof planning becomes more robust since it does not necessarily fail if one problem solving mechanism fails. Rather it can reason about preference of strategies and about failures. Moreover, our strategies provide a means for structuring the vast amount of knowledge such that the planner can cope with the otherwise overwhelming knowledge in mathematics.

Keywords

Open Goal Control Rule Multiple Strategy Constraint Solver Partial Plan 
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. 1.
    Gandalf. In CASC-14 http://www.cs.jcu.edu.au/~tptp/casc-14/, 1997.
  2. 2.
    R.G. Bartle and D.R. Sherbert. Introduction to Real Analysis. John Wiley & Sons, New York, 1982.zbMATHGoogle Scholar
  3. 3.
    C. Benzmüller, L. Cheikhrouhou, D. Fehrer, A. Fiedler, X. Huang, M. Kerber, M. Kohlhase, K. Konrad, A. Meier, E. Melis, W. Schaarschmidt, J. Siekmann, and V. Sorge. OMEGA: Towards a mathematical assistant. In Proc. CADE-14, pages 252–255. Springer-Verlag, 1997.Google Scholar
  4. 4.
    C. Benzmüller, M. Jamnik, M. Kerber, and V. Sorge. Agent Based Mathematical Reasoning? In 7th CALCULEMUS Workshop, pages 21–32, 1999.Google Scholar
  5. 5.
    W.W. Bledsoe, R.S. Boyer, and W.H. Henneman. Computer proofs of limit theorems. Artificial Intelligence, 3(1):27–60, 1972.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    A. Bundy. The use of explicit plans to guide inductive proofs. In Proc. of CADE-9, pages 111–120, 1988.Google Scholar
  7. 7.
    A. Bundy, A. Stevens, F. Van Harmelen, A. Ireland, and A. Smaill. A heuristic for guiding inductive proofs. Artificial Intelligence, 63:185–253, 1993.CrossRefGoogle Scholar
  8. 8.
    A. Bundy, F. van Harmelen, J. Hesketh, and A. Smaill. Experiments with proof plans for induction. Journal of Automated Reasoning, 7:303–324, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Denzinger and M. Fuchs. Cooperation of heterogeneous provers. In Proc. of IJCAI, pages 10–15. Morgan Kaufmann, 1999.Google Scholar
  10. 10.
    B. Hayes-Roth. A blackboard architecture for control. Artificial Intelligence, pages 251–321, 1985.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.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    W.W. McCune. Otter 2.0 users guide. Technical Report ANL-90/9, Argonne National Laboratory, 1990.Google Scholar
  13. 13.
    E. Melis. AI-techniques in proof planning. In Proc. of European Conference on Artificial Intelligence, pages 494–498. Kluwer, 1998.Google Scholar
  14. 14.
    E. Melis. Combining proof planning with constraint solving. In Proc. of Calculemus and Types’98, 1998.Google Scholar
  15. 15.
    E. Melis. The“limit” domain. In Proc. of the Fourth International Conference on Artificial Intelligence in Planning Systems (AIPS’98), pages 199–206, 1998.Google Scholar
  16. 16.
    E. Melis and A. Meier. Proof planning with multiple strategies. Seki report SR-99-06, Universität des Saarlandes, FB Informatik, 1999.Google Scholar
  17. 17.
    E. Melis and A. Meier. Proof planning with multiple strategies II. In FLoC’99 workshop on Strategies in Automated Deduction, pages 61–72, 1999.Google Scholar
  18. 18.
    E. Melis and J.H. Siekmann. Knowledge-based proof planning. Artificial Intelligence, 1999.Google Scholar
  19. 19.
    E. Melis and C. Ullrich. Flexibly interleaving processes. In K.-D. Althoff and R. Bergmann, editors, International Conference on Case-Based Reasoning, volume 1650 of Lecture Notes in Artificial Intelligence, pages 263–275. Springer, 1999.Google Scholar
  20. 20.
    G. Polya. How to Solve it. Princeton University Press, Princeton, 1945.zbMATHGoogle Scholar
  21. 21.
    A.H. Schoenfeld. Mathematical Problem Solving. Academic Press, New York, 1985.zbMATHGoogle Scholar
  22. 22.
    D.S. Weld. An introduction to least committment planning. AI magazine, 15(4):27–61, 1994.Google Scholar
  23. 23.
    D.E. Wilkins and K.L. Myers. A multiagent planning architecture. In Proc. of the Fourth International Conference on AI Planning Systems (AIPS’98), pages 154–162, 1998.Google Scholar
  24. 24.
    A. Wolf. Strategy selection for automated theorem proving. In Proc. of AIMSA’ 98, pages 452–465, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Erica Melis
    • 1
  • Andreas Meier
    • 1
  1. 1.Fachbereich InformatikUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations