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

Authors
Sergei Artemov
CUNY Graduate Center
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
Keywords Realism-essay
Categories (categorize this paper)
DOI 10.2307/2687821
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 52,956
Through your library

References found in this work BETA

Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16 (1963):83-94.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
Basic Proof Theory.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.

View all 30 references / Add more references

Citations of this work BETA

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.

View all 84 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
284 ( #26,384 of 2,343,995 )

Recent downloads (6 months)
2 ( #332,401 of 2,343,995 )

How can I increase my downloads?

Downloads

My notes