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On the correspondence between arithmetic theories and propositional proof systems - a survey

Beyersdorff, O (2009) On the correspondence between arithmetic theories and propositional proof systems - a survey. Mathamatical Logic Quarterly, 55 (2). 116 - 137 . ISSN 0942-5616

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Abstract

The purpose of this paper is to survey the correspondence between bounded arithmetic and propositional proof systems. In addition, it also contains some new results which have appeared as an extended abstract in the proceedings of the conference TAMC 2008 [11]. Bounded arithmetic is closely related to propositional proof systems; this relation has found many fruitful applications. The aim of this paper is to explain and develop the general correspondence between propositional proof systems and arithmetic theories, as introduced by Krajíček and Pudlák [46]. Instead of focusing on the relation between particular proof systems and theories, we favour a general axiomatic approach to this correspondence. In the course of the development we particularly highlight the role played by logical closure properties of propositional proof systems, thereby obtaining a characterization of extensions of EF in terms of a simple combination of these closure properties.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009, Wiley-VCH-Verlag. This is an author produced version of a paper published in Mathamatical Logic Quarterly. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Bounded arithmetic, propositional proof systems, extended Frege systems, propositional translations, logical closure properties
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 13 Aug 2012 09:00
Last Modified: 08 Feb 2013 17:39
Published Version: http://dx.doi.org/10.1002/malq.200710069
Status: Published
Publisher: Wiley-VCH Berlin
Identification Number: 10.1002/malq.200710069
URI: http://eprints.whiterose.ac.uk/id/eprint/74440

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