Skip to main content

Semantic Selection for Resolution in Clause Graphs

  • Conference paper
  • First Online:
AI 2002: Advances in Artificial Intelligence (AI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2557))

Included in the following conference series:

  • 1127 Accesses

Abstract

In this contribution we present a variant of a resolution theorem prover which selects resolution steps based on the proportion of models a newly generated clause satisfies compared to all models given in a reference class. This reference class is generated from a subset of the initial clause set. Since the empty clause does not satisfy any models, preference is given to such clauses which satisfy few models only. Because computing the number of models is computationally expensive on the one hand, but will remain almost unchanged after the application of one single resolution step on the other hand, we adapt Kowalski’s connection graph method to store the number of models at each link.

The second author likes to thank Norman Foo and the Knowledge Systems Group at the AIDepartmen t of the University of New South Wales for their hospitality.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Bundy, editor. Proceedings of the 12th CADE, LNAI 814. Springer-Verlag, 1994.

    Google Scholar 

  2. R. Caferra and N. Peltier. Disinference rules, model building and abduction. In E. OrElowska, editor, Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa, chapter 20, pages 331–353. Physica-Verlag, 1999.

    Google Scholar 

  3. S. Choi. Towards semantic goal-directed forward reasoning in resolution. In D. Scott, editor, Proceedings of the AIMSA’2002, LNAI 2443, pages 243–252, 2002.

    Google Scholar 

  4. H. Chu and D. A. Plaisted. Semantically guided first-order theorem proving using hyper-linking. In Bundy [1], pages 192–206.

    Google Scholar 

  5. N. Eisinger. Completeness, Confluence, and Related Properties of Clause Graph Resolution. Research Notes in Artificial Intelligence. Pitman, London, 1991.

    Google Scholar 

  6. N. Eisinger and H. J. Ohlbach. The Markgraf Karl Refutation Procedure (MKRP). In J. Siekmann, editor, Proceedings of the 8th CADE, LNAI 230, pages 681–682. Springer-Verlag, 1986.

    Google Scholar 

  7. K. Hodgson and J. Slaney. Development of a semantically guided theorem prover. In Goré et al. Proceedings of the IJCAR 2001, LNAI 2083, pages 443–447. Springer-Verlag, 2001.

    Google Scholar 

  8. X. Huang, M. Kerber, M. Kohlhase, E. Melis, D. Nesmith, J. Richts, and J. Siekmann. KEIM: A toolkit for automated deduction. In Bundy [1], pages 807–810.

    Google Scholar 

  9. R. Kowalski. A proof procedure using connection graphs. Journal of the Association for Computing Machinery, 22(4):572–595, 1975.

    MATH  MathSciNet  Google Scholar 

  10. S. J. Lee and D. A. Plaisted. Eliminating duplication with the hyper-linking strategy. Journal of Automated Reasoning, 9(1):25–42, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. McCune. OTTER 3.0 Reference Manual and Guide. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, USA, 1994.

    Google Scholar 

  12. W. McCune. Solution of the Robbins problem. Journal of Automated Reasoning, 19:263–276, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  13. F. J. Pelletier. Seventy-five problems for testing automatic theorem provers. Journal of Automated Reasoning, 2(2):191–216, 1986.

    Google Scholar 

  14. D. A. Plaisted and Y. Zhu. Ordered semantic hyper-linking. Journal of Automated Reasoning, 25(3):167–217, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Riazanov and A. Voronkov. Vampire 1.1. In Goré et al. Proceedings of the IJCAR 2001, LNAI 2083, pages 376–380. Springer-Verlag, 2001.

    Google Scholar 

  16. J. A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the Association for Computing Machinery, 12(1):23–41, 1965.

    MATH  MathSciNet  Google Scholar 

  17. J. Siekmann and G. Wrightson. An open research problem: Strong completeness of R. Kowalski’s connection graph proof procedure. Logic Journal of the IGPL, 10(1):85–103, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Slaney. FINDER: Finite Domain Enumerator. In Bundy [1], pages 798–801.

    Google Scholar 

  19. J. Slaney, E. Lusk, and W. McCune. SCOTT: Semantically Constrained Otter. In Bundy [1], pages 764–768.

    Google Scholar 

  20. C. Weidenbach, B. Gaede, and G. Rock. SPASS & FLOTTER, Version 0.42. In M. A. McRobbie and J. K. Slaney, editors, Proceedings of the 13th CADE, LNAI 1104, pages 141–145. Springer-Verlag, 1996.

    Google Scholar 

  21. L. Wos, G. A. Robinson, and D. F. Carson. Efficiency and completeness of the set of support strategy in theorem proving. Journal of the Association for Computing Machinery, 12(4):536–541, 1965.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Choi, S., Kerber, M. (2002). Semantic Selection for Resolution in Clause Graphs. In: McKay, B., Slaney, J. (eds) AI 2002: Advances in Artificial Intelligence. AI 2002. Lecture Notes in Computer Science(), vol 2557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36187-1_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-36187-1_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00197-3

  • Online ISBN: 978-3-540-36187-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics