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 .
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.
|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:||31 Oct 2016 08:26|