Skip to main content

Strategy selection for automated theorem proving

  • Conference paper
  • First Online:
Artificial Intelligence: Methodology, Systems, and Applications (AIMSA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1480))

Abstract

Automated theorem provers use search strategies. Unfortunately, no strategy is uniformly successful on all problems. This motivates us to spend the available resources in terms of processors and time on different strategies. In this paper, we develop the basic concept of the complementarity of strategy sets. The problems of the initial strategy selection are discussed in detail. The paper also contains a short description of an implementation of a strategy parallel theorem prover (p-SETHEO) and an experimental evaluation of the schedule selection algorithm.

This work is supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 342, subproject A5 (PARIS).

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. P. Bonacina. Distributed Automated Deduction. PhD thesis, State University of New York, 1992.

    Google Scholar 

  2. M. P. Bonacina and J. Hsiang. Distributed Deduction by Clause Diffusion: The Aquarius Prover. In Proc. DISCO-93, volume 722 of LNCS, pages 272–287. Springer, 1993.

    Google Scholar 

  3. CASC-14 Homepage. http://www.cs.jcu.edu.au/~tptp/casc-14/, 1997.

    Google Scholar 

  4. B. I. Dahn, J. Gehne, T. Honigmann, and A. Wolf. Integration of Automated and Interactive Theorem Proving in ILF. In Proc. CADE-14, volume 1249 of LNAI, pages 57–60. Springer, 1997.

    Google Scholar 

  5. J. Denzinger. Knowledge-Based Distributed Search Using Teamwork. In Proc. ICMAS-95, pages 81–88. AAAI-Press, 1995.

    Google Scholar 

  6. J. Denzinger, M. Kronenburg, and S. Schulz. DISCOUNT. A Distributed and Learning Equational Prover. JAR, 18(2):189–198, 1997.

    Article  Google Scholar 

  7. J. Denzinger and S. Schulz. Learning Domain Knowledge to Improve Theorem Proving. In Proc. CADE-13, volume 1104 of LNAI, pages 62–76. Springer, 1996.

    Google Scholar 

  8. B. Fischer and J. Schumann. SETHEO Goes Software Engineering: Application of ATP to Software Reuse. In Proc. CADE-14, volume 1249 of LNAI, pages 65–68. Springer, 1997.

    Google Scholar 

  9. Matthias Fuchs. Automatic Selection of Search-Guiding Heuristics. In Proc. of 10th Int. Florida AI Research Society Conference, pages 1–5. Florida AI Research Society, 1997.

    Google Scholar 

  10. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979.

    Google Scholar 

  11. A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM: Parallel Virtual Machine. A Users' Guide and Tutorial for Networked Parallel Computing. MIT Press, 1994.

    Google Scholar 

  12. T. Honigmann and A. Wolf. An Algorithm for Load Distribution in Interactive Theorem Proving. In Proc. ALV-98, pages 13–22. Munich Univ. of Technology, Computer Science Dept., 1998.

    Google Scholar 

  13. R. Letz, K. Mayr, and Ch. Goller. Controlled Integration of the Cut Rule into Connection Tableau Calculi. JAR, 13(3):297–338, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. W. Loveland. Automated Theorem Proving: a Logical Basis. North-Holland, 1978.

    Google Scholar 

  15. M. Moser, O. Ibens, R. Letz, J. Steinbach, C. Goller, J. Schumann, and K. Mayr. SETHEO and E-SETHEO. The CADE-13 Systems. JAR, 18(2):237–246, 1997.

    Article  Google Scholar 

  16. L. C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of LNCS. Springer, 1994.

    Google Scholar 

  17. W. Reif. The KIV System: Systematic Construction of Verified Software. In Proc. CADE-11, volume 607 of LNAI, pages 753–757. Springer, 1992.

    Google Scholar 

  18. J. S. Rosenschein, M. Ginsburg, M. R. Genesereth. Cooperation Without Communication. In Proc. AAAI-86, pages 51–57. AAAI-Press, 1986.

    Google Scholar 

  19. J. Schumann and R. Letz. PARTHEO: a High Performance Parallel Theorem Prover. In Proc. CADE-10, volume 449 of LNAI, pages 44–56. Springer, 1990.

    Google Scholar 

  20. D. B. Sturgill and A. M. Segre. A Novel Asynchronous Parallelism Scheme for First-Order Logic. In Proc. CADE-12, volume 814 of LNAI, pages 484–498. Springer, 1994.

    Google Scholar 

  21. C. Suttner and J. Schumann. Parallel Automated Theorem Proving. In Parallel Processing for Artificial Intelligence, pages 209–257. Elsevier, 1994.

    Google Scholar 

  22. A. Wolf and M. Fuchs. Cooperative Parallel Automated Theorem Proving. In T. Schnekenburger and G. Stellner, editors, Dynamic Load Distribution for Parallel Applications, volume 24 of Teubner-Texte zur Informatik, pages 129–145. Teubner, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Fausto Giunchiglia

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wolf, A. (1998). Strategy selection for automated theorem proving. In: Giunchiglia, F. (eds) Artificial Intelligence: Methodology, Systems, and Applications. AIMSA 1998. Lecture Notes in Computer Science, vol 1480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057466

Download citation

  • DOI: https://doi.org/10.1007/BFb0057466

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64993-9

  • Online ISBN: 978-3-540-49793-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics