Acquisition of useful lemma-knowledge in automated reasoning

  • Joachim Draeger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1480)


This paper presents a method for solving “hard” problems with automated theorem provers. Main principle is the support of a conventional brute-force search by lemma-knowledge, which is generated and elicitated by the prover system. The performance of the proposed method depends critically on the usefulness of the elicitated lemmata for the actual proof task. In this context an evaluation function called information measure is introduced, which relates the effort required for the production of a lemma f to the problem relevancy of f. Experiments show its high potential.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Astrachan, O., Stickel, M.: Caching and Lemmaizing in Model Elimination Theorem Provers, in Kapur, D.: 11th International Conference on Automated Deduction 1992, LNAI 607, Springer 1992Google Scholar
  2. 2.
    Bundy. A.: The use of explicit plans to guide induction proofs, in Lusk, E.: 9th International Conference on Automated Deduction 1988, LNCS 310, Springer 1988Google Scholar
  3. 3.
    Bundy, A.: A Science of Reasoning, in Stickel, M.: 10th International Conference on Automated Deduction 1990, LNAI 449, Springer 1990Google Scholar
  4. 4.
    Draeger, J.: Zur Konstruktion leistungsfähiger Beweiser, Report AR-95-08, Technische Universität München 1995Google Scholar
  5. 5.
    Fuchs, M.: Controlled Use of Clausel Lemmas in Connection Tableau Calculi, Report AR-98-02, Technische Universität München 1998Google Scholar
  6. 6.
    Goller, C.: A Connectionist Control Component for the Theorem Prover SETHEO, in Proceedings of the ECAI'94 Workshop W14: Combining Symbolic and Connectionist Processing 1994Google Scholar
  7. 7.
    Goller, C.: A Connectionist Approach for Learning Search-Control Heuristics for Automated Deduction Systems, Dissertation, TU München 1997Google Scholar
  8. 8.
    Goller, C., Letz, R., Mayr, K., Schumann, J.: SETHEO V3.2: Recent Developments, in Bundy, A.: 12th International Conference on Automated Deduction 1994, LNAI 814, Springer 1994Google Scholar
  9. 9.
    Kolbe, T., Walther, C.: Reusing proofs, in Cohn, A.: 11th European Conference on Artificial Intelligence 1994, Wiley 1994Google Scholar
  10. 10.
    Letz, R., Schumann, J., Bayerl, S., Bibel, W.: SETHEO: A High-Performance Theorem Prover, Journal of Automated Reasoning 8 (1992) 183MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Letz, R., Mayr, K., Goller, C.: Controlled Integration of the Cut Rule into Connection Tableau Calculi, Journal of Automated Reasoning 13 (1994) 297MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    McCune, W.: Solution of the Robbins Problem, Journal of Automated Reasoning 19 (1997) 263MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Paulson, L.: Isabelle: a generic theorem prover, LNCS 828, Springer 1994Google Scholar
  14. 14.
    Polya, G.: Mathematics and Plausible Reasoning, Princeton 1954Google Scholar
  15. 15.
    Reif, W.: The KIV Approach to Software Verification, in Broy, M., Jähnichen, S.: KORSO: Methods, Languages, and Tools for the Construction of Correct Software, LNCS 1009, Springer 1995Google Scholar
  16. 16.
    Schumann, J.: DELTA — A Bottom-up Preprocessor for Top-Down Theorem Provers, System Abstract, in Bundy, A.: 12th International Conference on Automated Deduction 1994, LNAI 814, Springer 1994Google Scholar
  17. 17.
    Stickel, M.: A prolog technology theorem prover: Implementation by an extended prolog compiler, Journal of Automated Reasoning 4 (1988) 353MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Stickel, M.: Upside-Down Meta-Interpretation of the Model Elimination Theorem-Proving Procedure for Deduction and Abduction, Journal of Automated Reasoning 13 (1994) 189MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Sutcliffe, G., Suttner, C., Yemenis, T.: The TPTP Problem Library, in Bundy, A.: 12th International Conference on Automated Deduction 1994, LNAI 814, Springer 1994Google Scholar
  20. 20.
    Wolf, A., Fuchs, M.: Cooperative Parallel Automated Theorem Proving, in Schnekenburger, T., Stellner, G.: Dynamic Load Distribution for Parallel Applications, Teubner 1997Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joachim Draeger
    • 1
  1. 1.Technische Universität MünchenMünchenGermany

Personalised recommendations