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On decision procedures for sentential logics

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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.

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References

  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. D.M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic, D. Reidel, Dordrecht 1981.

    Google Scholar 

  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.

  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. J. Łukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, Clarendon Press, Oxford 1951.

    Google Scholar 

  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. 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. J. Słupecki et al, Theory of rejected propositions I, Studia Logica 29(1971), 75–123.

    Google Scholar 

  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. 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. J. Zygmunt, Notes on decidability and finite approximability of sentential logics Acta Universitatis Wratislaviensis, Logika 8(1983), 69–81.

    Google Scholar 

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  1. Department of Logic, Wrocław University, Szewska 36, 50-139, Wrocław, Poland

    Tomasz Skura

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  1. Tomasz Skura
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Skura, T. On decision procedures for sentential logics. Stud Logica 50, 173–179 (1991). https://doi.org/10.1007/BF00370180

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  • DOI: https://doi.org/10.1007/BF00370180

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