Abstract
The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued Łukasiewicz logic C ∞) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).
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The content of this paper was presented in a talk at the Bulgarian-Polish Conference of Logic held at Sofia, Bulgaria, in September 1985 and in a talk given at the XXXI Conference of the History of Logic, Cracow, October 1985.
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Czelakowski, J. Local deductions theorems. Stud Logica 45, 377–391 (1986). https://doi.org/10.1007/BF00370271
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DOI: https://doi.org/10.1007/BF00370271