Skip to main content

On word problems in Horn theories

  • Part 1 Research Articles
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 308))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • CLARK K.L. Negation as failure in "Logic and databases. eds Gallaire H., MInker J. Plenum Press, New York 3–32(1978).

    Google Scholar 

  • 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 

  • DERSHOWITZ. N Termination. In: Rewriting Techniques and Applications, J.P. Jouannaud, ed., Lect. Notes in Comp. Sci., vol.202, Springer, 180–224, 1985

    Google Scholar 

  • GANZINGER. H Ground Term Confluence in Parametric Conditional Equational Specifications, Proceeding of 4th Symposium on Theoretical Aspects of Computer Science Passau, RFA, February 1987

    Google Scholar 

  • 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 

  • HSIANG. J., RUSINOWITCH M. On word problems in equational theories. ICALP 1987

    Google Scholar 

  • 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 

  • JOUANNAUD, J.P, WALDMANN. B Reductive Conditional Term Rewriting Systems, Proc. 3rd IFIP Conf. on Formal Description of Programming Concepts Lyngby, Danemark, 1986

    Google Scholar 

  • HUET G., Confluent reduction: abstract properties and applications to term-rewriting systems. JACM 27, 797–821. (1980).

    Article  Google Scholar 

  • KAPLAN S. Simplifying Conditional Term Rewriting Systems: Unification, Termination Confluence, to appear in J. of Symb Comp.

    Google Scholar 

  • KNUTH. D, BENDIX. P Simple Word Problems in Abstract Algebra, Leech J.ed, Pergamon Press, pp. 263–297, 1970

    Google Scholar 

  • KUCHLIN, W. A confluence criterion based on the generalised Newman lemma. proc. of EUROCAL, B.Caviness, LNCS 204, (1985) pp. 390–399.

    Google Scholar 

  • LANKFORD D. S. Canonical inference. Memo ATP-32, Dept. of Math. Comp. Sc., University of Texas, Austin, Texas, 1975.

    Google Scholar 

  • PADAWITZ P. Horn Clause specifications: a uniform framework for abstract data types and logic programming. Universitat Passau, MIP-8516 December 1985.

    Google Scholar 

  • PAUL E. On solving the equality problem in theories defined by Horn clauses. Th. Comp. Sc. 44, pp.127–153.

    Google Scholar 

  • 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 

  • REITER R. On closed world databases, In "Logic and databases. eds Gallaire H., Minker J. Plenum Press, New York 55–76(1978).

    Google Scholar 

  • 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, 1982

    Google Scholar 

  • RUSINOWITCH. M, Demonstration automatique par des techniques de Re'e'criture. Thesis, Universite' de Nancy 1, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

S. Kaplan J. -P. Jouannaud

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kounalis, E., Rusinowitch, M. (1988). On word problems in Horn theories. In: Kaplan, S., Jouannaud, J.P. (eds) Conditional Term Rewriting Systems. CTRS 1987. Lecture Notes in Computer Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19242-5_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-19242-5_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19242-8

  • Online ISBN: 978-3-540-39166-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics