Skip to main content
SpringerLink
Log in
Book cover

Annual Conference on Artificial Intelligence

KI 2001: KI 2001: Advances in Artificial Intelligence pp 320–334Cite as

Learning Search Control Knowledge for Equational Theorem Proving

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2174))

Abstract

One of the major problems in clausal theorem proving is the control of the proof search. In the presence of equality, this problem is particularly hard, since nearly all state-of-the-art systems perform the proof search by saturating a mostly unstructured set of clauses. We describe an approach that enables a superposition-based prover to pick good clauses for generating inferences based on experiences from previous successful proof searches for other problems. Information about good and bad search decisions (useful and superfluous clauses) is automatically collected from search protocols and represented in the form of annotated clause patterns. At run time, new clauses are compared with stored patterns and evaluated according to the associated information found. We describe our implementation of the system. Experimental results demonstrate that a learned heuristic significantly outperforms the conventional base strategy, especially in domains where enough training examples are available.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. L. Bachmair and H. Ganzinger. Rewrite-Based Equational Theorem Proving with Selection and Simplification. Journal of Logic and Computation, 3(4):217–247, 1994.

    Article  MathSciNet  Google Scholar 

  2. L. Bachmair and H. Ganzinger. Equational Reasoning in Saturation-Based Theorem Proving. In W. Bibel and P.H. Schmitt, editors, Automated Deduction-A Basis for Applications, volume 9 (1) of Applied Logic Series, chapter 11, pages 353–397. Kluwer Academic Publishers, 1998.

    Google Scholar 

  3. J. Van Baalen, P. Robinson, M. Lowry, and T. Pressburger. Explaining Synthesized Software. In Proc. of the 13th IEEE Conference on Automated Software Engineering, Honolulu. IEEE, 1998.

    Google Scholar 

  4. J. Denzinger, M. Fuchs, C. Goller, and S. Schulz. Learning from Previous Proof Experience. Technical Report AR99-4, Institut für Informatik, Technische Universität München, 1999. (also to be published as a SEKI report).

    Google Scholar 

  5. B.I. Dahn, J. Gehne, T. Honigmann, and A. Wolf. Integration of Automated and Interactive Theorem Proving in ILF. In W.W. McCune, editor, Proc. of the 14th CADE, Townsville, number 1249 in LNAI, pages 57–60. Springer, 1997.

    Google Scholar 

  6. J. Denzinger and S. Schulz. Learning Domain Knowledge to Improve Theorem Proving. In M.A. McRobbie and J.K. Slaney, editors, Proc. of the 13th CADE, New Brunswick, number 1104 in LNAI, pages 62–76. Springer, 1996.

    Google Scholar 

  7. J. Denzinger and S. Schulz. Automatic Acquisition of Search Control Knowledge from Multiple Proof Attempts. Journal of Information and Computation, 162:59–79, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  8. B.I. Dahn and C. Wernhard. First Order Proof Problems Extracted from an Article in the MIZAR Mathematical Library. In Proceedings of the 1st FTP, Linz, pages 58–62. RISC Linz, Austria, 1997.

    Google Scholar 

  9. B. Fischer and J. Schumann. SETHEO Goes Software-Engineering: Application of ATP to Software Reuse. In W.W. McCune, editor, Proc. of the 14th CADE, Townsville, number 1249 in LNAI, pages 65–68. Springer, 1997.

    Google Scholar 

  10. M. Fuchs. Experiments in the Heuristic Use of Past Proof Experience. In M.A. McRobbie and J.K. Slaney, editors, Proc. of the 13th CADE, New Brunswick, number 1104 in LNAI, pages 523–537. Springer, 1996.

    Google Scholar 

  11. M. Fuchs. Learning Search Heuristics for Automated Deduction. Number 34 in Forschungsergebnisse zur Informatik. Verlag Dr. Kovač, 1997. Accepted as a Ph.D. Thesis at the Fachbereich Informatik, Universität Kaiserslautern.

    Google Scholar 

  12. C. Goller and A. Küchler. Learning Task-Dependent Distributed Representations by Backpropagation Through Structure. In Proc. of the ICNN-96, volume 1, pages 347–352. IEEE, 1996.

    Google Scholar 

  13. S. Gürdens and René Peralta. Validation of Cryptographic Protocols by Efficient Automatic Testing. In J. Etheredge and B. Manaris, editors, Proc. of the 13th FLAIRS, Orlando, pages 7–12. AAAI Press, 2000.

    Google Scholar 

  14. D. Hutter, B. Langenstein, C. Sengler, J.H. Siekmann, W. Stephan, and A. Wolpers. Verication support environment (VSE). Journal of High Integrity Systems, 1(6):523–531, 1996.

    Google Scholar 

  15. W.W. McCune. Solution of the Robbins Problem. Journal of Automated Reasoning, 3(19):263–276, 1997.

    Article  MathSciNet  Google Scholar 

  16. W.W. McCune and L. Wos. Otter: The CADE-13 Competition Incarnations. Journal of Automated Reasoning, 18(2):211–220, 1997. Special Issue on the CADE 13 ATP System Competition.

    Article  Google Scholar 

  17. W. Reif, G. Schellhorn, and K. Stenzel. Interactive Correctness Proofs for Software Modules Using KIV. In Proc. of the 10th Annual Conference on Computer Assurance, Gaithersburg. IEEE Press, 1995.

    Google Scholar 

  18. A. Riazanov and A. Voronkov. Vampire. In H. Ganzinger, editor, Proc. of the 16th CADE, Trento, number 1632 in LNAI, pages 292–2296. Springer, 1999.

    Google Scholar 

  19. J. Schumann. Automatic Verification of Cryptographic Protocols with SETHEO. In W. McCune, editor, Proc. of the 14th CADE, Townsville, number 1249 in LNAI, pages 87-11. Springer, 1997.

    Google Scholar 

  20. S. Schulz. System Abstract: E 0.3. In H. Ganzinger, editor, Proc. of the 16th CADE, Trento, number 1632 in LNAI, pages 297–391. Springer, 1999.

    Google Scholar 

  21. S. Schulz. Learning Search Control Knowledge for Equational Deduction. Number 230 in DISKI. Akademische Verlagsgesellschaft Aka GmbH Berlin, 2000. Ph.D. Thesis, Fakultät für Informatik, Technische Universit ät München.

    Google Scholar 

  22. S. Schulz. System Abstract: E 0.61. In R. Goré, A. Leitsch, and T. Nipkow, editors, Proc. of the 1st IJCAR, Siena, number 2083 in LNAI, pages 370–375. Springer, 2001.

    Google Scholar 

  23. S. Schulz, A. Küchler, and C. Goller. Some Experiments on the Applicability of Folding Architecture Networks to Guide Theorem Proving. In D.D. Dankel II, editor, Proc. of the 10th FLAIRS, Daytona Beach, pages 377–381. Florida AI Research Society, 1997.

    Google Scholar 

  24. C.B. Suttner and G. Sutcliffe. The TPTP Problem Library (TPTP v2.1.0). Technical Report AR-97-01 (TUM), 97/04 (JCU), Institut für Informatik, Technische Universität München, Munich, Germany/ Department of Computer Science, James Cook University, Townsville, Australia, 1997. Jointly published.

    Google Scholar 

  25. G. Sutcliffe, C.B. Suttner, and T. Yemenis. The TPTP Problem Library. In A. Bundy, editor, Proc. of the 12th CADE, Nancy, number 814 in LNAI, pages 252–266. Springer, 1994.

    Google Scholar 

  26. D.D. Sleator and R.E. Tarjan. Self-Adjusting Binary Search Trees. Journal of the ACM, 32(3):652–686, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  27. M. Stickel, R. Waldinger, M. Lowry, T. Pressburger, and I. Underwood. Deductive Composition of Astronomical Software from Subroutine Libraries. In A. Bundy, editor, Proc. of the 12th CADE, Nancy, number 814 in LNAI, pages 341–355. Springer, 1994.

    Google Scholar 

  28. C. Weidenbach, B. Afshordel, U. Brahm, C. Cohrs, T. Engel, G. Jung, E. Keen, C. Theobalt, and D. Topic. System Abstract: SPASS Version 1.0.0. In H. Ganzinger, editor, Proc. of the 16th CADE, Trento, number 1632 in LNAI, pages 378–382. Springer, 1999.

    Google Scholar 

  29. C. Weidenbach. Toward an Automatic Analysis of Security Protocols in First-Order Logic. In H. Ganzinger, editor, Proc. of the 16th CADE, Trento, number 1632 in LNAI, pages 314–328. Springer, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, D-80290, München, Germany

    Stephan Schulz

Authors
  1. Stephan Schulz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RWTH Aachen, Theoretical Computer Science, Ahornstrasse 55, 52074, Aachen, Germany

    Franz Baader

  2. Intelligent Systems Department, University of Leipzig, Computer Science Institute, Augustusplatz 10-11, 04109, Leipzig, Germany

    Gerhard Brewka

  3. Institute of Information Systems Knowledge-Based Systems Group, Vienna University of Technology, Favoritenstrasse 11, 1040, Wien, Austria

    Thomas Eiter

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schulz, S. (2001). Learning Search Control Knowledge for Equational Theorem Proving. In: Baader, F., Brewka, G., Eiter, T. (eds) KI 2001: Advances in Artificial Intelligence. KI 2001. Lecture Notes in Computer Science(), vol 2174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45422-5_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-45422-5_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42612-7

  • Online ISBN: 978-3-540-45422-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation