Notre Dame Journal of Formal Logic 51 (4):485-502 (2010)

Abstract
With each superintuitionistic propositional logic L with a disjunction property we associate a set of modal logics the assertoric fragment of which is L . Each formula of these modal logics is interdeducible with a formula representing a set of rules admissible in L . The smallest of these logics contains only formulas representing derivable in L rules while the greatest one contains formulas corresponding to all admissible in L rules. The algebraic semantic for these logics is described
Keywords intuitionistic logic   modal logic   admissible rule   Heyting algebra   monadic algebra   intermediate logic
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DOI 10.1215/00294527-2010-031
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References found in this work BETA

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.
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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