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The Deduction Theorem for Strong Propositional Proof Systems

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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 \(\mathsf{NP}\) -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 \(\mathsf{NP}\) -pairs.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, Leibniz Universität Hannover, Hannover, Germany

    Olaf Beyersdorff

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  1. Olaf Beyersdorff
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Correspondence to Olaf Beyersdorff.

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An extended abstract of this paper appeared in the proceedings of the conference FSTTCS 2007 [2]. Part of this work was done while at Humboldt-University Berlin, where the author was supported by DFG grant KO 1053/5-1.

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Beyersdorff, O. The Deduction Theorem for Strong Propositional Proof Systems. Theory Comput Syst 47, 162–178 (2010). https://doi.org/10.1007/s00224-008-9146-6

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  • DOI: https://doi.org/10.1007/s00224-008-9146-6

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