Advertisement

Relating resolution and algebraic completion for Horn logic

  • Roland Dietrich
Term Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)

Abstract

Since first order logic and, especially, Horn logic is used as a programming language, the most common interpretation method for such programs is resolution. Algebraic completion and term rewriting techniques were recently proposed as an alternative to resolution oriented theorem provers. In this paper, the relation between resolution and algebraic completion (restricted to Horn logic) is closely analysed. It is shown, that both methods are equivalent in terms of inference steps and unifications, and, that using the completion method for interpreting (Horn) logic programs, no efficiency can be gained as compared with resolution.

Keywords

Logic Program Inference System Inference Rule Theorem Prove Atomic Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BKNa85.
    D. Benanav, D. Kapur, P. Narendran: Complexity of Matching Problems, 1st Int. Conf. on Term Rewriting Techniques and Applications, Dijon, France, Springer LNCS 202, 1985.Google Scholar
  2. ClMe81.
    W. F. Clocksin, C. S. Mellish: Programming in Prolog, Springer, 1981.Google Scholar
  3. DeJo84.
    N. Dershowitz, N. A. Josephson: Logic Programming by Completion, Proc. 2nd Int. Logic Programming Conf., Uppsala, 1985.Google Scholar
  4. Deus83.
    P. Deussen: Control of and Algorithms for Reduction systems, Unpublished report, University of Karlsruhe, Institut für Informatik I, 1983.Google Scholar
  5. Deus85.
    P. Deussen: Private Communication, 1985.Google Scholar
  6. Diet85.
    R. Dietrich: Relating Resolution and Algebraic Completion for Horn Logic, Arbeitspapiere der GMD Nr. 177, Gesellschaft für Mathematik und Datenverarbeitung mbH, Bonn, 1985.Google Scholar
  7. GoMe84.
    J. A. Goguen, J. Meseguer: Equality, Types, Modules and (Why not?) Generics for Logic Programming, J. Logic Programming 1984, 2: 179–210.CrossRefGoogle Scholar
  8. Hero83.
    A. Herold: Some Basic Notions of First-Order Unification Theory, Universität Karlsruhe, Fakultät für Informatik, Interner Bericht Nr. 15/83, 1983.Google Scholar
  9. HsDe83.
    J. Hsiang, N. Dershowitz: Rewrite Methods for Clausal and Non-Clausal Theorem Proving, Proc. 10th Int. Conf. on Automata, Languages and Programming, Springer LNCS 154, 1983.Google Scholar
  10. Hsia83.
    J. Hsiang: Topics in Automated Theorem Proving and Program Generation, Ph. D. Thesis, University of Illinois at Urbana-Champaign, 1983.Google Scholar
  11. Hsia85.
    J. Hsiang: Two Results in Term Rewriting Theorem Proving, 1st Int. Conf. on Term Rewriting Techniques and Applications, Dijon, France, Springer LNCS 202, 1985.Google Scholar
  12. Huet80.
    G. Huet: Confluent Reductions: Abstract Properties and Application to Term Rewriting Systems, JACM, Vol. 27, No. 4, October 1980.Google Scholar
  13. HuOp80.
    G. Huet, D. C. Oppen: Equations and Rewrite Rules: A survey, R. Book (Ed.): Formal Language Theory. Perspectives and Open Problems. Academic Press, 1980.Google Scholar
  14. Hull80.
    J.-M. Hullot: Canonical Forms and Unification, Proc. 5th Int. Conf. on Automated Deduction, Springer LNCS 87, 1980.Google Scholar
  15. KaNa85.
    D. Kapur, P. Narendran: An Equational Approach to Theorem Proving in First-Order Predicate Calculus, Proc. IJCAI 85, Los Angeles, 1985.Google Scholar
  16. KnBe70.
    D. E. Knuth, P. B. Bendix: Simple Word Problems in Universal Algebra, J. Leech (Ed.): Computational Problems in Universal Algebra, Pergamon Press, 1970.Google Scholar
  17. Lloyd84.
    J. W. Lloyd: Foundations of Logic Programming, Springer, 1984.Google Scholar
  18. Love78.
    D. W. Loveland: Automated Theorem Proving: A Logical Basis, North-Holland, 1978.Google Scholar
  19. Nils82.
    N. J. Nilsson: Principles of Artificial Intelligence, Springer, 1982.Google Scholar
  20. Patt78.
    D. A. Waterman, F. Hayes-Roth (Eds.): Pattern Directed Inference Systems, Academic Press, 1978.Google Scholar
  21. Paul84.
    E. Paul: A New Interpretation of the Resolution Principle, Proc. 7th Int. Conf. on Automated Deduction, Springer LNCS 170, 1984.Google Scholar
  22. Robi65.
    J. A. Robinson: A Machine Oriented Logic Based on the Resolution Principle, JACM, Vol 12, No. 1, January 1965, pp. 23–41.CrossRefGoogle Scholar
  23. Slag74.
    J. R. Slagle: Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity, JACM, Vol 21, No. 4, October 1974, pp. 622–642.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Roland Dietrich
    • 1
  1. 1.GMD Research Laboratory at the University of KarlsruheKarlsruhe 1Germany (West)

Personalised recommendations