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.
KeywordsMathematical Logic Decision Procedure Computational Linguistic Model Property Consequence Operator
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- W.J. Blok, 179-01 varieties of Heyting algebras not generated by their finite members, Algebra Universalis 7(1977), 115–117.Google Scholar
- D.M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic, D. Reidel, Dordrecht 1981.Google Scholar
- 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
- A.V. Kuznetsov and V.Y. Gerchiu, On superintuitionistic logics and finite approximability (in Russian), Doklady AN SSSR 195 (1970), 1029–1032.Google Scholar
- J. Łukasiewicz, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, Clarendon Press, Oxford 1951.Google Scholar
- 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
- M.O. Rabin, Computable algebra, general theory and theory of computable fields, Transactions of the American Mathematical Society 95(1960), 341–360.Google Scholar
- J. Słupecki et al, Theory of rejected propositions I, Studia Logica 29(1971), 75–123.Google Scholar
- A. Wroński, On cardinalities of matrices strongly adequate for the intuitionistic propositional logic, Reports on Mathematical Logic 3(1974), 67–72.Google Scholar
- 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
- J. Zygmunt, Notes on decidability and finite approximability of sentential logics Acta Universitatis Wratislaviensis, Logika 8(1983), 69–81.Google Scholar