Logical Closure Properties of Propositional Proof Systems

(Extended Abstract)
  • Olaf Beyersdorff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4978)


In this paper we define and investigate basic logical closure properties of propositional proof systems such as closure of arbitrary proof systems under modus ponens or substitutions. As our main result we obtain a purely logical characterization of the degrees of schematic extensions of \({\mathit{EF}}\) in terms of a simple combination of these properties. This result underlines the empirical evidence that \({\mathit{EF}}\) and its extensions admit a robust definition which rests on only a few central concepts from propositional logic.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Olaf Beyersdorff
    • 1
  1. 1.Institut für Theoretische InformatikLeibniz Universität HannoverGermany

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