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Journal of Computer Science and Technology

, Volume 15, Issue 3, pp 271–279 | Cite as

Linear strategy for boolean ring based theorem proving

  • Wu Jinzhao 
  • Liu Zhuojun 
Article
  • 26 Downloads

Abstract

Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on atoms, pseudo O-linear and O-linear strategies are presented. The former is complete, the latter, however, is complete for clausal theorem proving.

Keywords

Boolean ring linear strategy Herbrand theorem O-linear strategy 

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References

  1. [1]
    Chang C-L, Lee R C. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.zbMATHGoogle Scholar
  2. [2]
    Bachmair L, Ganzinger H A. Theory of Resolution. InHandbook of Automated Reasoning, Robinson J, Voronkov A (eds.), Elsevier, Amsterdam, 1997.Google Scholar
  3. [3]
    Hsiang J. Refutational theorem proving using term-rewriting systems.Artificial Intelligence, 1985, 25: 255–300.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Kapur D, Narendran P. An Equational Approach to Theorem Proving in First-Order Predicate Calculus. 84CRD322, 1985, GE Research Lab.Google Scholar
  5. [5]
    Zhang H. A new method for the boolean ring based theorem proving.J. of Symbolic Computation, 1994, 17: 189–211.zbMATHCrossRefGoogle Scholar
  6. [6]
    Loveland D. Automated Theorem Proving: A Logical Basis. North-Holland, New York, 1978.zbMATHGoogle Scholar
  7. [7]
    Lloyd J W. Foundations of Logic Programming. Springer-Verlag, Berlin, 1984.zbMATHGoogle Scholar
  8. [8]
    Liu X H, Sun J G. Generalized resolution and NC-resolution.J. Comput. Sci. & Technol., 1994, 9 (2): 160–167.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Murray N V. Completely non-clausal theorem proving.Artificial Intelligence, 1982, 18(1): 67–85.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Wu J, Liu Z. On first-order theorem proving using generalized odd-superposition II.Scientia Sinica (Ser.E), 1996, 39(6): 608–619.zbMATHMathSciNetGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2000

Authors and Affiliations

  • Wu Jinzhao 
    • 1
  • Liu Zhuojun 
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Institute of Systems ScienceChinese Academy of SciencesBeijingP.R. China

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