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The deduction theorem for strong propositional proof systems

Beyersdorff, O (2007) The deduction theorem for strong propositional proof systems. In: Arvind, V and Prasad, S, (eds.) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Foundations of software technology and theoretical computer science, 12-14 December 2007, New Delhi, India. Lecture Notes in Computer Science, 4855 . Springer Verlag , 241 - 252 .

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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 NP-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 NP-pairs.

Item Type: Proceedings Paper
Copyright, Publisher and Additional Information: © 2007, Springer Verlag. This is an author produced version of a paper published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 10 Dec 2012 12:48
Last Modified: 08 Jun 2014 20:15
Published Version: http://dx.doi.org/10.1007/978-3-540-77050-3_20
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/978-3-540-77050-3_20
URI: http://eprints.whiterose.ac.uk/id/eprint/74801

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