Metalogic of Intuitionistic Propositional Calculus

Notre Dame Journal of Formal Logic 51 (4):485-502 (2010)
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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Kosta Došen (1992). Modal Logic as Metalogic. Journal of Logic, Language and Information 1 (3):173-201.

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