Reduction of Hilbert-type proof systems to the if-then-else equational logic

Article

Abstract

We present a construction of the linear reduction of Hilbert type proof systems for propositional logic to if-then-else equational logic. This construction is an improvement over the same result found in [4] in the sense that the technique used in the construction can be extended to the linear reduction of first-order logic to if-then-else equational logic.

AMS Mathematics Subject Classification

03B22 03F99 

Key words and phrases

Proof systems reduction if-then-else equational logic 

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References

  1. 1.
    N. Arai,A proper hierarchy of propositional sequent calculi, Theoretical Computer Science159 (1996), 343–354MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    N. Arai,Relative efficiency of propositional proof systems: resolution vs. cut-free LK, Annals of Pure and Applied Logic104 (2000), 3–16MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Bloom and R. Tindell,Varieties of “if-then-else”, Siam J. Computing12 (1983), 677–707MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    S. Burris,Discriminator varieties and symbolic computation, J. Symbolic Computation13 (1992), 175–207MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    S. Burris, manuscript, 1993Google Scholar
  6. 6.
    S. Cook and R. Rechkow,The relative efficiency of propositional proof systems, J. of Symbolic Logic44 (1979), no. 1, 36–50MATHCrossRefGoogle Scholar
  7. 7.
    J. Jeong,Linear reduction of first-order logic to if-then-else equation logic, in preparationGoogle Scholar
  8. 8.
    J. Krajicek and P. Pudlak,Propositional proof systems, the consistency of first order theories and the complexity of computations, J. of Symbolic Logic54 (1989), no. 3, 1063–1079.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    R. McKenzie,On the spectra, and negative solution of the decision problem for identities having finite nontrivial model, J. Symbolic Logic40 (1975), 186–196MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    A. Mekler and E. Nelson,Equational Bases for if-then-else logic, Siam J. of Computing,18 (1989), 465–485MathSciNetGoogle Scholar
  11. 11.
    J. Messner and J. Torán,Optimal proof systems for propositional logic and complete sets, Lecture Notes in Computer Sci.1373, Springer, Berlin, 1998, STACS 98 (Paris), 477–487Google Scholar
  12. 12.
    A. Urquhart,The complexity of Gentzen systems for propositional logic, Theoretical Computer Science66 (1989), 87–97MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  1. 1.Department of Mathematics EducationKyungpook National UniversityDaeguKorea

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