The Basic Intuitionistic Logic of Proofs

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Journal of Symbolic Logic 72 (2):439 - 451 (2007)
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Abstract

The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found

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10.2178/jsl/1185803617

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Author Profiles

Sergei Artemov
CUNY Graduate Center
Rosalie Iemhoff
Utrecht University

Citations of this work

A Substructural Approach to Explicit Modal Logic.Shawn Standefer - 2023 - Journal of Logic, Language and Information 32 (2):333–362.
On the Logical Philosophy of Assertive Graphs.Daniele Chiffi & Ahti-Veikko Pietarinen - 2020 - Journal of Logic, Language and Information 29 (4):375-397.
Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
Hypersequent calculi for intuitionistic logic with classical atoms.Hidenori Kurokawa - 2010 - Annals of Pure and Applied Logic 161 (3):427-446.

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References found in this work

Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
The logic of proofs, semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
Best solving modal equations.Silvio Ghilardi - 2000 - Annals of Pure and Applied Logic 102 (3):183-198.
Logic of proofs.Sergei Artëmov - 1994 - Annals of Pure and Applied Logic 67 (1-3):29-59.
Intermediate Logics and Visser's Rules.Rosalie Iemhoff - 2005 - Notre Dame Journal of Formal Logic 46 (1):65-81.

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