The Deduction Theorem for Strong Propositional Proof Systems

Beyersdorff, O (2010) The Deduction Theorem for Strong Propositional Proof Systems. Theory of Computing Systems, 47 (1). 162 - 178 . ISSN 1432-4350

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Abstract

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NPUnknown control sequence '\mathsf' -pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NPUnknown control sequence '\mathsf' -pairs.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2010, Springer Verlag. This is an author produced version of a paper published in Theory of Computing Systems. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com
Keywords:	Deduction theorem, Optimal propositional proof systems, Disjoint NP-pairs, Frege systems
Academic Units:	The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	07 Aug 2012 12:53
Last Modified:	08 Feb 2013 17:39
Published Version:	http://dx.doi.org/10.1007/s00224-008-9146-6
Status:	Published
Publisher:	Springer Verlag
Identification Number:	10.1007/s00224-008-9146-6
URI:	http://eprints.whiterose.ac.uk/id/eprint/74443

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