Explicit provability and constructive semantics

Bulletin of Symbolic Logic 7 (1):1-36 (2001)
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Abstract

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus

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2009-01-28

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Sergei Artemov
CUNY Graduate Center

Citations of this work

The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
The Logic of Proofs, Semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
Justification Logic.Sergei Artemov - forthcoming - Stanford Encyclopedia of Philosophy.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
A Logic of Knowing Why.Chao Xu, Yanjing Wang & Thomas Studer - 2021 - Synthese 198 (2):1259-1285.

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References found in this work

Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.

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