Notre Dame Journal of Formal Logic

Metalogic of Intuitionistic Propositional Calculus

Alex Citkin

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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.

Article information

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

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1285765801

Digital Object Identifier
doi:10.1215/00294527-2010-031

Zentralblatt MATH identifier
05822359

Mathematical Reviews number (MathSciNet)
MR2741839

Subjects
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]

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

Citation

Citkin, Alex. Metalogic of Intuitionistic Propositional Calculus. Notre Dame J. Formal Logic 51 (2010), no. 4, 485--502. doi:10.1215/00294527-2010-031. http://projecteuclid.org/euclid.ndjfl/1285765801.


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