Near-Horn Prolog and the ancestry family of procedures

  • David W. Reed
  • Donald W. Loveland


The near-Horn Prolog procedures have been proposed as effective procedures in the area of disjunctive logic programming, an extension of logic programming to the (first-order) non-Horn clause domain. In this paper, we show that these case-analysis based procedures may be viewed as members of a class of procedures called the “ancestry family”, which also includes Model Elimination (and its variants), the Positive Refinement of Model Elimination, and SLWV-resolution. The common feature which binds these procedures is the extension of SLD-resolution to full first-order logic with the addition of an ancestor cancellation rule. Procedures in the ancestry family are all sound and complete first-order procedures that can be seen to vary along three parameters: (1) the number of clause contrapositives required, (2) the amount of ancestor checking that must occur, and (3) the use (if any) of a Restart rule. Using a sequent-style presentation format for all procedures, we highlight the close relationships among these procedures and compare their relative advantage.


Neural Network Artificial Intelligence Complex System Nonlinear Dynamics Presentation Format 
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.


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  1. [1]
    O.L. Astrachan and D.W. Loveland, METEORs: High performance theorem provers for Model Elimination, in:Automated Reasoning: Essays in Honor of Woody Bledsoe, ed. R.S. Boyer (Kluwer, Dordrecht, 1991).Google Scholar
  2. [2]
    R. Caferra, E. Eder, B. Fronhöfer and W. Bibel, Extension of Prolog through matrix reduction,6th European Conf. on Artificial Intelligence, Pisa, Italy (1984).Google Scholar
  3. [3]
    S. Fleisig, D. Loveland, A. Smiley and D. Yarmash, An implementation of the Model Elimination proof procedure, J. ACM 21(1974)124–139.Google Scholar
  4. [4]
    D.M. Gabbay, N-Prolog: An extension of Prolog with hypothetical implication, Part 2, J. Logic Program. 4(1985)251–283.Google Scholar
  5. [5]
    D.M. Gabbay and U. Reyle, N-Prolog: An extension of Prolog with hypothetical implication, Part 1, J. Logic Program. 4(1984)319–355.Google Scholar
  6. [6]
    R. Hill, LUSH resolution and its completeness, Technical Report DCL Memo 78, Department of Artificial Intelligence, University of Edinburgh (1974).Google Scholar
  7. [7]
    R. Kowalski and D. Kuehner, Linear resolution with selection function, Artificial Intelligence 2(1971)227–260.Google Scholar
  8. [8]
    R. Kowalski, Predicate calculus as a programming language,Proc. 6th IFIP Congress (North-Holland, 1974) pp. 569–574.Google Scholar
  9. [9]
    R. Letz, S. Bayerl, J. Schumann and W. Bibel, SETHEO — a high-performance theorm prover, J. Autom. Reasoning 8(1992)183–212.Google Scholar
  10. [10]
    D.W. Loveland, Mechanical theorem proving by model elimination, J. ACM 15(1968)236–251.Google Scholar
  11. [11]
    D.W. Loveland, A simplified format for the Model Elimination procedure, J. ACM 16(1969)349–363.Google Scholar
  12. [12]
    D.W. Loveland,Automated Theorem Proving: A Logical Basis (North-Holland, Amsterdam, 1978).Google Scholar
  13. [13]
    D.W. Loveland, Near-Horn Prolog, in:Logic Programming: Proc. 4th Int. Conf., ed. J. Lassez (MIT Press, 1987) pp. 456–469.Google Scholar
  14. [14]
    D.W. Loveland, Near-Horn Prolog and beyond, J. Autom. Reasoning 7(1991)1–26.Google Scholar
  15. [15]
    D.W. Loveland and D.W. Reed, A near-Horn Prolog for compilation, in:Computational Logic: Essays in Honor of Alan Robinso, ed. J. Lassez (MIT Press, 1991).Google Scholar
  16. [16]
    J. Minker and G. Zanon, An extension to linear resolution with selection function, Inf. Proces. Lett. 14(1982)191–194.Google Scholar
  17. [17]
    L.M. Pereira, L. Caires and J. Alferes, Classical negation for normal logic programs,Proc. 7th “Seminário Brasileiro de Inteligência Artificial”, (1990).Google Scholar
  18. [18]
    L.M. Pereira, L. Caires and J. Alferes, SLWV — a theorem prover for logic programming,Proc. 3rd Workshop on Extensions of Logic Programming (ELP '92), Lecture Notes in Artificial Intelligence 660 (Springer, Berlin, 1993) pp. 1–23.Google Scholar
  19. [19]
    D. Plaisted, A simplified problem reduction format, Artificial Intelligence 18(1982)227–261.Google Scholar
  20. [20]
    D. Plaisted, Non-Horn clause logic programming without contrapositives, J. Autom. Reasoning 4(1988)287–325.Google Scholar
  21. [21]
    D. Plaisted, A sequent style Model Elimination strategy and a positive refinement, J. Autom. Reasoning 6(1990)389–402.Google Scholar
  22. [22]
    D.W. Reed, A case-analysis approach to disjunctive logic programming, Ph.D. Thesis, Duke University (1992).Google Scholar
  23. [23]
    D.W. Reed and D.W. Loveland, A comparison of three Prolog extensions, J. Logic Program. 12(1) (1992).Google Scholar
  24. [24]
    D.W. Reed, D.W. Loveland and B.T. Smith, A near-Horn approach to disjunctive logic programming,Proc. 2nd Workshop on Extensions of Logic Programming (ELP '91), Lecture Notes in Artificial Intelligence 596 (Springer, Berlin, 1992) pp. 345–369.Google Scholar
  25. [25]
    M.E. Stickel and D.W. Loveland, A hole in goal trees: Some guidance from Resolution theory,Proc. 3rd Int. Joint Conf. on Artificial Intelligence (1973) pp. 153–161. Also in IEEE Trans. Comp. C-25 (April 1976).Google Scholar
  26. [26]
    J. Schumann and R. Letz, PARTHEO — a high performance parallel theorem prover,Proc. 10th Int. Conf. on Automated Deduction (1990) pp. 40–56.Google Scholar
  27. [27]
    M.E. Stickel, A Prolog technology theorem prover, New Generation Comp. 2(1984)371–383.Google Scholar
  28. [28]
    T. Wakayama, Indefinite query answers in deductive knowledge bases,Proc. 3rd IASTED Int. Symp. on Expert Systems Theory and Applications (1988).Google Scholar
  29. [29]
    T. Wakayama, Reasoning with indefinite information in Resolution-based languages, Ph.D. Thesis, Syracuse University (1989).Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • David W. Reed
    • 1
  • Donald W. Loveland
    • 1
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA

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