A propositional logic with explicit fixed points

Studia Logica 40 (2):155 - 175 (1981)
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Abstract

This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.

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Citations of this work

Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - 2024 - Studia Logica 112 (3):611-660.
Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
A Closer Look at Some Subintuitionistic Logics.Sergio Celani & Ramon Jansana - 2001 - Notre Dame Journal of Formal Logic 42 (4):225-255.
Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.

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References found in this work

Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Provability, truth, and modal logic.George Boolos - 1980 - Journal of Philosophical Logic 9 (1):1 - 7.

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