Notre Dame Journal of Formal Logic

Metalogic of Intuitionistic Propositional Calculus

Alex Citkin


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.

Article information

Notre Dame J. Formal Logic Volume 51, Number 4 (2010), 485-502.

First available in Project Euclid: 29 September 2010

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Zentralblatt MATH identifier

Primary: 03B55: Intermediate logics 03F45: Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
Secondary: 06D20: Heyting algebras [See also 03G25]

intuitionistic logic modal logic admissible rule Heyting algebra monadic algebra intermediate logic


Citkin, Alex. Metalogic of Intuitionistic Propositional Calculus. Notre Dame J. Formal Logic 51 (2010), no. 4, 485--502. doi:10.1215/00294527-2010-031.

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