Skip to main content

Flexible proof-replay with heuristics

  • Automated Reasoning and Theorem Proving
  • Conference paper
  • First Online:
Progress in Artificial Intelligence (EPIA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1323))

Included in the following conference series:

Abstract

We present a general framework for developing search heuristics for automated theorem provers. This framework allows for the construction of heuristics that are on the one hand able to replay (parts of) a given proof found in the past but are on the other hand flexible enough to deviate from the given proof path in order to solve similar proof problems. We substantiate the abstract framework by the presentation of three distinct techniques for learning search heuristics based on so-called features. We demonstrate the usefulness of these techniques in the area of equational deduction. Comparisons with the renowned theorem prover OTTER validate the applicability and strength of our approach.

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. Avenhaus, J.; Denzinger, J.; Fuchs, Matt.: DISCOUNT: A system for distributed equational deduction, Proc. 6th RTA, Kaiserslautern, FRG, 1995, LNCS 914, pp. 397–402.

    Google Scholar 

  2. Brock, B.; Cooper, S.; Pierce, W.: Analogical reasoning and proof discovery, Proc. CADE 9, Argonne, IL, USA, 1988, LNCS 310, pp. 454–468.

    Google Scholar 

  3. Bachmair, L.; Dershowitz, N.; Plaisted, D.A.: Completion without Failure, Coll. on the Resolution of Equations in Algebraic Structures, Austin (1987), Academic Press, 1989.

    Google Scholar 

  4. Cover, T.M.; Hart P.E.: Nearest Neighbor pattern classification, IEEE, Transactions on Information Theory 13, pp. 21–27, 1967.

    Google Scholar 

  5. Fuchs, M.: Flexible Proof-Replay with Heuristics, LSA-Report, LSA-97-03E, University of Kaiserslautern, 1997.

    Google Scholar 

  6. Fuchs, Matt.: Experiments in the Heuristic Use of Past Proof Experience, Proc. CADE 13, New Brunswick, NJ, USA, 1996.

    Google Scholar 

  7. Goller, C.; Küchler, A.: Learning Task-Dependent Distributed Representations by Back-propagation Through Structure, Proc. ICNN-96, 1996.

    Google Scholar 

  8. Knuth, D.E.; Bendix, P.B.: Simple Word Problems in Universal Algebra, Computational Algebra, J. Leech, Pergamon Press, 1970, pp. 263–297.

    Google Scholar 

  9. Kolbe, T.; Walther, C.: Reusing proofs, Proc. 11th ECAI '94, Amsterdam, HOL, 1994, pp. 80–84.

    Google Scholar 

  10. McCune, W.W.: OTTER 3.0 reference manual and guide, Techn. report ANL-946, Argonne Natl. Laboratory, 1994.

    Google Scholar 

  11. Owen, S.: Analogy for automated reasoning, Academic Press, 1990.

    Google Scholar 

  12. Suttner, C.; Ertel, W.: Automatic acquisition of search-guiding heuristics, Proc. CADE 10, Kaiserslautern, FRG, 1990, LNAI 449, pp. 470–484.

    Google Scholar 

  13. Sutcliffe, G.; Suttner, C.B.; Yemenis, T.: The TPTP Problem Library, Proc. CADE 12, Nancy, Springer LNAI 814, pp. 252–266, 1994

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ernesto Coasta Amilcar Cardoso

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fuchs, M. (1997). Flexible proof-replay with heuristics. In: Coasta, E., Cardoso, A. (eds) Progress in Artificial Intelligence. EPIA 1997. Lecture Notes in Computer Science, vol 1323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023906

Download citation

  • DOI: https://doi.org/10.1007/BFb0023906

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63586-4

  • Online ISBN: 978-3-540-69605-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics