Equivalences of logic programs

Extended abstract
  • M. J. Maher
Session 4b: Theory And Higher-Order Functions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 225)


For applications such as deductive databases employing the Open World Assumption, failed derivations have a lesser importance. In this case, use of the identical equivalences based upon the functional semantics [P] and the logical consequences of P allows the application of two different and powerful tools to reason about programs. In particular, these equivalences seem ideal for discussing the deductive structure of such deductive databases, independent of any particular state of the database of facts.

When negation-as-failure is used in evaluating queries, the equivalence of completed programs is more appropriate. This equivalence is only slightly stronger than (high level) operational equivalence and the well-developed formalism of logic is available to facilitate reasoning about programs.


Logic Program Function Symbol Predicate Symbol Horn Clause Ground Atom 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. K.L. Clark, Negation as Failure, in: Logic and Databases, H. Gallaire, J. Minker (eds.), Plenum Press, 1978.Google Scholar
  2. M.H. Van Emden and R.A. Kowalski, The Semantics of Predicate Logic as a Programming Language, Journal of the ACM 23, 4 (1976), 733–742.CrossRefGoogle Scholar
  3. G. Gottlob and A. Leitsch, On the Efficiency of Subsumption Algorithms, Journal of the ACM 32, 2 (1985), 280–295.Google Scholar
  4. M. Fitting, A Kripke-Kleene Semantics for Logic Programs, Journal of Logic Programming 2, 4 (1985), 295–312.CrossRefGoogle Scholar
  5. A. Hansson and S.A. Tarnlund, Program Transformation by a Function that Maps Simple Lists into D-Lists, Proc. Workshop on Logic Programming, S.A. Tarnlund (ed.), Debrecen, Hungary, July 1980.Google Scholar
  6. C. J. Hogger, Derivation of Logic Programs, Journal of the ACM 28, 2 (1981), 372–392.Google Scholar
  7. J. Jaffar, J-L. Lassez and M.J. Maher, A Theory of Complete Logic Programs With Equality, Proc. Conference on Fifth Generation Computer Systems, Tokyo, November 1984, 175–184.Google Scholar
  8. J. Jaffar, J-L. Lassez and M.J. Maher, A logic Programming Language Scheme, in: Logic Programming: Relations, Functions and Equations, D. DeGroot, G. Lindstrom (eds.), Prentice Hall, 1986. Also TR84/12 Dept. of Computer Science, University of Melbourne, 1984.Google Scholar
  9. J-L. Lassez and M.J. Maher, The Denotational Semantics of Horn Clauses as a Production System, Proc. AAAI-83, Washington D.C., August 1983, 229–231.Google Scholar
  10. J-L. Lassez and M.J. Maher, Closures and Fairness in the Semantics of Programming Logic, Theoretical Computer Science 29, (1984), 167–184.CrossRefGoogle Scholar
  11. J.W. Lloyd, Foundations of Logic Programming, Springer-Verlag, 1984.Google Scholar
  12. M.J. Maher, Semantics of Logic Programs, Ph.D. dissertation, University of Melbourne, 1985.Google Scholar
  13. A. Mycroft and R.A. O'Keefe, A Polymorphic Type System for Prolog, Artificial Intelligence 23, 3 (1984), 295–307.MathSciNetGoogle Scholar
  14. N.J. Nilsson, Principles of Artificial Intelligence, Springer-Verlag, 1982.Google Scholar
  15. R.A. O'Keefe, Towards an Algebra for Constructing Logic Programs, Proc. Symposium on Logic Programming, Boston, 1985.Google Scholar
  16. G.D. Plotkin, A Note on Inductive Generalization, in: Machine Intelligence 5, B. Meltzer, D. Michie (eds.), Edinburgh University Press, 1969, 153–165.Google Scholar
  17. J. Sebelik and P. Stepanek, Horn Clause Programs Suggested by Recursive Function, Proc. Workshop on Logic Programming, S.A. Tarnlund (ed.), Debrecen, Hungary, July 1980.Google Scholar
  18. J.R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, Mass., 1967.Google Scholar
  19. H. Tamaki and T. Sato, Unfold/Fold Transformation of Logic Programs, Proc. 2nd. Logic Programming Conference, Sweden, July 1984, 127–138.Google Scholar
  20. S.A. Tarnlund, Horn Clause Computability, BIT 17, 2 (1977), 215–226.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • M. J. Maher
    • 1
  1. 1.Dept. of Computer ScienceUniversity of MelbourneUSA

Personalised recommendations