Proof theory for admissible rules

Annals of Pure and Applied Logic 159 (1-2):171-186 (2009)
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Abstract

Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic objects, for admissibility, the basic objects are sequent rules. Proof systems are defined here for admissible rules of classes of modal logics, including K4, S4, and GL, and also Intuitionistic Logic IPC. With minor restrictions, proof search in these systems terminates, giving decision procedures for admissibility in the logics.

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Rosalie Iemhoff
Utrecht University

Citations of this work

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References found in this work

Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
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Best solving modal equations.Silvio Ghilardi - 2000 - Annals of Pure and Applied Logic 102 (3):183-198.
Complexity of admissible rules.Emil Jeřábek - 2007 - Archive for Mathematical Logic 46 (2):73-92.

View all 11 references / Add more references