Implicit Proofs

Journal of Symbolic Logic 69 (2):387 - 397 (2004)
We describe a general method how to construct from a propositional proof system P a possibly much stronger proof system iP. The system iP operates with exponentially long P-proofs described "implicitly" by polynomial size circuits. As an example we prove that proof system iEF, implicit EF, corresponds to bounded arithmetic theory $V_{2}^{1}$ and hence, in particular, polynomially simulates the quantified propositional calculus G and the $\pi_{1}^{b}-consequences$ of $S_{2}^{1}$ proved with one use of exponentiation. Furthermore, the soundness of iEF is not provable in $S_{2}^{1}$ . An iteration of the construction yields a proof system corresponding to $T_{2} + Exp$ and, in principle, to much stronger theories
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/30041732
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,774
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Nathan Segerlind (2007). The Complexity of Propositional Proofs. Bulletin of Symbolic Logic 13 (4):417-481.
A. Carbone (2002). The Cost of a Cycle is a Square. Journal of Symbolic Logic 67 (1):35-60.
Melvin Fitting (2008). A Quantified Logic of Evidence. Annals of Pure and Applied Logic 152 (1):67-83.

Monthly downloads

Added to index


Total downloads

9 ( #254,415 of 1,728,009 )

Recent downloads (6 months)

4 ( #183,615 of 1,728,009 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.