On word problems in Horn theories

  • Emmanuel Kounalis
  • Michael Rusinowitch
Part 1 Research Articles
Part of the Lecture Notes in Computer Science book series (LNCS, volume 308)


We interpret Horn clauses as conditional rewrite rules. Then we give sufficient conditions so that the word problem can be decided by conditional normalization in some Horn theory. We also show how to prove theorems in the initial models of Horn theories.


Horn clause resolution term-rewriting system word problems initial model inductionless induction 


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  1. CLARK K.L. Negation as failure in "Logic and databases. eds Gallaire H., MInker J. Plenum Press, New York 3–32(1978).Google Scholar
  2. FRIBOURG L. SLOG: A logic programming language interpreter based on clausal superposition and rewriting. Proc. of the 1985 Symposium on Logic Programming. Boston, MA pp. 172–184, july 1985.Google Scholar
  3. DERSHOWITZ. N Termination. In: Rewriting Techniques and Applications, J.P. Jouannaud, ed., Lect. Notes in Comp. Sci., vol.202, Springer, 180–224, 1985Google Scholar
  4. GANZINGER. H Ground Term Confluence in Parametric Conditional Equational Specifications, Proceeding of 4th Symposium on Theoretical Aspects of Computer Science Passau, RFA, February 1987Google Scholar
  5. GOGUEN J., MESEGUER J. Eqlog: Equality, Types, and Generic Modules for Logic Programming. J. of Logic Programming, Vol.1, Number 2, pages 179–210, 1984.Google Scholar
  6. HSIANG. J., RUSINOWITCH M. On word problems in equational theories. ICALP 1987Google Scholar
  7. JOUANNAUD J. P., KOUNALIS E. Automatic proofs by induction in equational theories without constructors. Proc. of the Symposium on Logic in Computer Science, Cambridge, MA, pp 358–366, June 1986.Google Scholar
  8. JOUANNAUD, J.P, WALDMANN. B Reductive Conditional Term Rewriting Systems, Proc. 3rd IFIP Conf. on Formal Description of Programming Concepts Lyngby, Danemark, 1986Google Scholar
  9. HUET G., Confluent reduction: abstract properties and applications to term-rewriting systems. JACM 27, 797–821. (1980).CrossRefGoogle Scholar
  10. KAPLAN S. Simplifying Conditional Term Rewriting Systems: Unification, Termination Confluence, to appear in J. of Symb Comp.Google Scholar
  11. KNUTH. D, BENDIX. P Simple Word Problems in Abstract Algebra, Leech J.ed, Pergamon Press, pp. 263–297, 1970Google Scholar
  12. KUCHLIN, W. A confluence criterion based on the generalised Newman lemma. proc. of EUROCAL, B.Caviness, LNCS 204, (1985) pp. 390–399.Google Scholar
  13. LANKFORD D. S. Canonical inference. Memo ATP-32, Dept. of Math. Comp. Sc., University of Texas, Austin, Texas, 1975.Google Scholar
  14. PADAWITZ P. Horn Clause specifications: a uniform framework for abstract data types and logic programming. Universitat Passau, MIP-8516 December 1985.Google Scholar
  15. PAUL E. On solving the equality problem in theories defined by Horn clauses. Th. Comp. Sc. 44, pp.127–153.Google Scholar
  16. PLOTKIN, G. Building-in equational theories, Machine Intelligence 7, B. Meltzer and D. Mitchie,eds, American Elsevier, New-York (1972) pp. 73–90.Google Scholar
  17. REITER R. On closed world databases, In "Logic and databases. eds Gallaire H., Minker J. Plenum Press, New York 55–76(1978).Google Scholar
  18. REMY. J.L Etude des syste'mes de re'e'criture conditionnelle et applications aux types abstraits alge'briques, The'se d'Etat, I.N.P.L, Nancy, 1982Google Scholar
  19. RUSINOWITCH. M, Demonstration automatique par des techniques de Re'e'criture. Thesis, Universite' de Nancy 1, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Emmanuel Kounalis
    • 1
  • Michael Rusinowitch
    • 2
  1. 1.LRI Universite de Paris-SudOrsay CedexFrance
  2. 2.CRIN Campus ScientifiqueVandoeuvre les NancyFrance

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