An inference system for horn clause logic with equality

A foundation for conditional E-unification and for logic programming in the presence of equality
  • Wayne Snyder
  • Christopher Lynch
Chapter 7 Extension Of Unification And Narrowing Techniques
Part of the Lecture Notes in Computer Science book series (LNCS, volume 516)


In this extended abstract of a full paper we present an inference system for Horn clause logic with equality which is complete not only refutationally but also with respect to the answer substitutions returned, without using functional reflexivity axioms or paramodulating at variable positions. It is goal directed in the sense that—as in SLD resolution—inference rules are only applied to the goal statement. We present the inference system (which subsumes those used for SLD-resolution and for general E-unification), prove its soundness and completeness, and then suggest how this approach forms the appropriate foundation for the study of inference systems (like logic programming interpreters) which return answer substitutions.


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5 Bibliography

  1. [1]
    Dougherty, D., and P. Johann, “An Improved General E-Unification Method,” CADE90, Kaiserlautern, Germany.Google Scholar
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    Gallier, J.H., Raatz, S., “Extending SLD-Resolution to Equational Horn Clauses Using E-unification”, to appear in Journal of Logic Programming (1987).Google Scholar
  3. [3]
    “Complete Sets of Transformations for General E-Unification,” Jean Gallier and Wayne Snyder, TCS 67 (1989) 203–260.Google Scholar
  4. [4]
    “An Inference System for Horn Clause Logic with Equality: A foundation for conditional E-unification and Horn clause logic with equality,” Wayne Snyder and Christopher Lynch, Boston University Technical Report No. BU-TR90-014.Google Scholar
  5. [5]
    “Conditional Equational Theories and Complete Sets of Transformations,” Steffen Hölldobler, Proceedings of International Conference of Fifth Generation Computer Systems (1988).Google Scholar
  6. [6]
    Padawitz, P., Computing in Horn Theories, EATCS Monographs on Theoretical Computer Science, Vol. 16, Springer-Verlag, Berlin (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Wayne Snyder
    • 1
  • Christopher Lynch
    • 1
  1. 1.Boston University Department of Computer ScienceBoston

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