Explicit provability and constructive semantics

Bulletin of Symbolic Logic 7 (1):1-36 (2001)
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
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 31,334
Through your library
References found in this work BETA
Logic of Proofs.Sergei Artëmov - 1994 - Annals of Pure and Applied Logic 67 (1-3):29-59.
On the Interpretation of Intuitionistic Number Theory.S. C. Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
Some Remarks on the Notion of Proof.John Myhill - 1960 - Journal of Philosophy 57 (14):461-471.

View all 14 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.

View all 53 citations / Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
273 ( #14,141 of 2,225,156 )

Recent downloads (6 months)
2 ( #249,976 of 2,225,156 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature