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Studia Logica

, Volume 50, Issue 2, pp 173–179 | Cite as

On decision procedures for sentential logics

  • Tomasz Skura
Article

Abstract

In Section 2 I give a criterion of decidability that can be applied to logics (i.e. Tarski consequence operators) without the finite model property. In Section 3 I study Łukasiewicz-style refutation procedures as a method of obtaining decidability results.This method also proves to be more general than Harrop's criterion.

Keywords

Mathematical Logic Decision Procedure Computational Linguistic Model Property Consequence Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    W.J. Blok, 179-01 varieties of Heyting algebras not generated by their finite members, Algebra Universalis 7(1977), 115–117.Google Scholar
  2. [2]
    D.M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic, D. Reidel, Dordrecht 1981.Google Scholar
  3. [3]
    R. Harrop, On the existence of finite models and decision procedures for propositional calculi, Proceedings of the Cambridge Philosophical Society 54(158), 1–13.Google Scholar
  4. [4]
    A.V. Kuznetsov and V.Y. Gerchiu, On superintuitionistic logics and finite approximability (in Russian), Doklady AN SSSR 195 (1970), 1029–1032.Google Scholar
  5. [5]
    J. Łukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, Clarendon Press, Oxford 1951.Google Scholar
  6. [6]
    T. Prucnal and A. Wroński, An algebraic characterization of the notion of structural completeness, Bulletin of the Section of Logic 3(1974), 30–33.Google Scholar
  7. [7]
    M.O. Rabin, Computable algebra, general theory and theory of computable fields, Transactions of the American Mathematical Society 95(1960), 341–360.Google Scholar
  8. [8]
    J. Słupecki et al, Theory of rejected propositions I, Studia Logica 29(1971), 75–123.Google Scholar
  9. [9]
    A. Wroński, On cardinalities of matrices strongly adequate for the intuitionistic propositional logic, Reports on Mathematical Logic 3(1974), 67–72.Google Scholar
  10. [10]
    V.A. Yankov, On the relationship between deducibility in the intuitionistic propositional calculus and finite implicational structures (in Russian), Doklady AN SSSR 151 (1963), 1203–1204.Google Scholar
  11. [11]
    J. Zygmunt, Notes on decidability and finite approximability of sentential logics Acta Universitatis Wratislaviensis, Logika 8(1983), 69–81.Google Scholar

Copyright information

© Polish Academy of Sciences 1991

Authors and Affiliations

  • Tomasz Skura
    • 1
  1. 1.Department of LogicWrocław UniversityWrocławPoland

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