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The Admissible Rules of ${{mathsf{BD}_{2}}}$ and ${mathsf{GSc}}$
Notre Dame Journal of Formal Logic 59 (3):325-353 (2018)
Abstract
The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and GSc.Other Versions
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Citations of this work
Decidability of admissibility: On a problem by Friedman and its solution by Rybakov.Jeroen P. Goudsmit - 2021 - Bulletin of Symbolic Logic 27 (1):1-38.
Decidability of Admissibility: On a Problem by Friedman and its Solution by Rybakov.Jeroen P. Goudsmit - 2021 - Bulletin of Symbolic Logic 27 (1):1-38.
References found in this work
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
On the admissible rules of intuitionistic propositional logic.Rosalie Iemhoff - 2001 - Journal of Symbolic Logic 66 (1):281-294.
Canonical formulas for k4. part I: Basic results.Michael Zakharyaschev - 1992 - Journal of Symbolic Logic 57 (4):1377-1402.
Concerning formulas of the types a →b ∨c, a →(ex)b(X).Ronald Harrop - 1960 - Journal of Symbolic Logic 25 (1):27-32.
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