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A propositional logic with explicit fixed points
Studia Logica 40 (2):155 - 175 (1981)
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.Author's Profile
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Citations of this work
Collection Frames for Distributive Substructural Logics.Greg Restall & Shawn Standefer - 2023 - Review of Symbolic Logic 16 (4):1120-1157.
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.
References found in this work
Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
The unprovability of consistency: an essay in modal logic.George Boolos - 1979 - New York: Cambridge University Press.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Arithmetical necessity, provability and intuitionistic logic.Rob Goldblatt - 1978 - Theoria 44 (1):38-46.
Provability, truth, and modal logic.George Boolos - 1980 - Journal of Philosophical Logic 9 (1):1 - 7.
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