Impasse-Driven Reasoning in Proof Planning

  • Andreas Meier
  • Erica Melis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3863)


In a problem solving process, a step may not result in the expected progress or may not be applicable as expected. Hence, knowledge how to overcome and react to impasses and other failures is an important ingredient of successful mathematical problem solving. To employ such knowledge in a proving system requires a variety of behaviors and a flexible control. Multi-strategy proof planning is a knowledge-based theorem proving approach that provides a variety of strategies and knowledge-based guidance for search at different levels. This paper introduces reasoning about impasses as a natural ingredient of meta-reasoning at a strategic level and illustrates the use of knowledge about failure handling in the proof planner multi.


Theorem Prove Residue Class Control Rule Inductive Proof Automate Theorem 
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.


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  1. 1.
    Bartle, R.G., Sherbert, D.R.: Introduction to Real Analysis. John Wiley & Sons, New York (1982)zbMATHGoogle Scholar
  2. 2.
    Bläsius, K.H., Bürckert, H.J. (eds.): Deduktionssysteme, Oldenbourg (1992)Google Scholar
  3. 3.
    Bledsoe, W.W.: Challenge Problems in Elementary Analysis. Journal of Automated Reasoning 6, 341–359 (1990)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bundy, A.: The Use of Explicit Plans to Guide Inductive Proofs. In: Lusk, E.R., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, pp. 111–120. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  5. 5.
    Corkill, D.D., Lesser, V.R., Hudlicka, E.: Unifying Data-Directed and Goal-Directed Control. In: Proceedings of AAAI 1982, pp. 143–147. AAAI Press, Menlo Park (1982)Google Scholar
  6. 6.
    Durfee, E.H., Lesser, V.R.: Incremental Planning to Control a Blackboard-Based Problem Solver. In: PROC of AAAI 1986, pp. 58–64. AAAI Press, Menlo Park (1986)Google Scholar
  7. 7.
    Huet, G.P.: Constrained Resolution: A Complete Method for Higher Order Logic. PhD thesis, Case Western Reverse University (1972)Google Scholar
  8. 8.
    Ireland, A.: The Use of Planning Critics in Mechanizing Inductive Proofs. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, pp. 178–189. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  9. 9.
    Ireland, A., Bundy, A.: Productive Use of Failure in Inductive Proof. Journal of Automated Reasoning 16(1-2), 79–111 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Meier, A.: MULTI – Proof Planning with Multiple Strategies. PhD thesis, Fachbereich Informatik, Universität des Saarlandes, Saarbrücken (2004)Google Scholar
  11. 11.
    Meier, A., Melis, E.: MULTI: A Multi-Strategy Proof Planner. In: Proceedings CADE–20. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Meier, A., Pollet, M., Sorge, V.: Comparing Approaches to Explore the Domain of Residue Classes. Journal of Symbolic Computation 34(4), 287–306 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Melis, E., Meier, A.: Proof Planning with Multiple Strategies. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 644–659. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Melis, E., Siekmann, J.: Knowledge-Based Proof Planning. Artificial Intelligence 115(1), 65–105 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Schoenfeld, A.H.: Mathematical Problem Solving. Academic Press, New York (1985)zbMATHGoogle Scholar
  16. 16.
    Zimmer, J., Melis, E.: Constraint solving for proof planning. Journal of Automated Reasoning (2004) (accepted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andreas Meier
    • 1
  • Erica Melis
    • 1
  1. 1.German Research Center for Artificial Intelligence (DFKI)SaarbrückenGermany

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