An Extension of the Knuth-Bendix Ordering with LPO-Like Properties

  • Michel Ludwig
  • Uwe Waldmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4790)

Abstract

The Knuth-Bendix ordering is usually preferred over the lexicographic path ordering in successful implementations of resolution and superposition, but it is incompatible with certain requirements of hierarchic superposition calculi. Moreover, it does not allow non-linear definition equations to be oriented in a natural way. We present an extension of the Knuth-Bendix ordering that makes it possible to overcome these restrictions.

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References

  1. 1.
    Baader, F., Nipkow, T.: Term rewriting and all that. Cambridge University Press, New York (1998)Google Scholar
  2. 2.
    Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. Journal of Logic and Computation 4(3), 217–247 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bachmair, L., Ganzinger, H., Waldmann, U.: Refutational theorem proving for hierarchic first-order theories. Applicable Algebra in Engineering, Communication and Computing (AAECC) 5(3/4), 193–212 (1994)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dick, J., Kalmus, J., Martin, U.: Automating the Knuth-Bendix ordering. Acta Informatica 28(2), 95–119 (1990)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Fernández, M.-L., Godoy, G., Rubio, A.: Recursive path orderings can also be incremental. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 230–245. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Ganzinger, H., Sofronie-Stokkermans, V., Waldmann, U.: Modular proof systems for partial functions with Evans equality. Information and Computation 204, 1453–1492 (2006)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hessenberg, G.: Grundbegriffe der Mengenlehre. Vandenhoeck & Ruprecht, Göttingen (1906)Google Scholar
  8. 8.
    Hillenbrand, T., Weidenbach, C.: Superposition for finite domains. Research Report MPI-I-2007-RG1-002, Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany (April 2007)Google Scholar
  9. 9.
    Just, W., Weese, M.: Discovering modern set theory. I: The Basics, Graduate Studies in Mathematics, vol. 8. American Mathematical Society (1996)Google Scholar
  10. 10.
    Kamin, S., Lévy, J.-J.: Attempts for generalising the recursive path orderings. Manuscript Department of Computer Science, University of Illinois, Urbana-Champaign (1980), available at http://perso.ens-lyon.fr/pierre.lescanne/not_accessible.html
  11. 11.
    Knuth, D.E., Bendix, P.B.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)Google Scholar
  12. 12.
    Löchner, B.: Things to know when implementing KBO. Journal of Automated Reasoning 36, 289–310 (2006)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Ludwig, M.: Extensions of the Knuth-Bendix ordering with LPO-like properties. Diploma thesis, Universität des Saarlandes, Saarbrücken, Germany (July 2006)Google Scholar
  14. 14.
    McCune, W.: Otter 3.3 Reference Manual. Argonne National Laboratory, Argonne, IL, USA, Technical Memorandum No. 263 (August 2003)Google Scholar
  15. 15.
    Prevosto, V., Waldmann, U.: SPASS+T. In: Sutcliffe, G., Schmidt, R., Schulz, S. (eds.) ESCoR: FLoC 2006 Workshop on Empirically Successful Computerized Reasoning, Seattle, WA, USA. CEUR Workshop Proceedings, vol. 192, pp. 18–33 (August 2006)Google Scholar
  16. 16.
    Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Communications 15, 91–110 (2002)MATHGoogle Scholar
  17. 17.
    Weidenbach, C., Brahm, U., Hillenbrand, T., Keen, E., Theobalt, C., Topić, D.: SPASS version 2.0. In: Voronkov, A. (ed.) CADE-18. LNCS (LNAI), vol. 2392, pp. 275–279. Springer, Heidelberg (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Michel Ludwig
    • 1
  • Uwe Waldmann
    • 2
  1. 1.Department of Computer Science, University of Liverpool, Liverpool L69 3BXUnited Kingdom
  2. 2.Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 SaarbrückenGermany

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