Admissible rules in the implication–negation fragment of intuitionistic logic

Annals of Pure and Applied Logic 162 (2):162-171 (2010)

Abstract

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis

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References found in this work

One Hundred and Two Problems in Mathematical Logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.
Unification in Intuitionistic Logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
Complexity of Admissible Rules.Emil Jeřábek - 2007 - Archive for Mathematical Logic 46 (2):73-92.
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.

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Citations of this work

Admissible Rules and the Leibniz Hierarchy.James G. Raftery - 2016 - Notre Dame Journal of Formal Logic 57 (4):569-606.
KD is Nullary.Philippe Balbiani & Çiğdem Gencer - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):196-205.
A Syntactic Approach to Unification in Transitive Reflexive Modal Logics.Rosalie Iemhoff - 2016 - Notre Dame Journal of Formal Logic 57 (2):233-247.
On Rules.Rosalie Iemhoff - 2015 - Journal of Philosophical Logic 44 (6):697-711.
Hereditarily Structurally Complete Positive Logics.Alex Citkin - 2020 - Review of Symbolic Logic 13 (3):483-502.

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