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Logical Closure Properties of Propositional Proof Systems

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Book cover Theory and Applications of Models of Computation (TAMC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4978))

Abstract

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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Authors and Affiliations

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

    Olaf Beyersdorff

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  1. Olaf Beyersdorff
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Manindra Agrawal Dingzhu Du Zhenhua Duan Angsheng Li

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Beyersdorff, O. (2008). Logical Closure Properties of Propositional Proof Systems. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_28

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  • DOI: https://doi.org/10.1007/978-3-540-79228-4_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79227-7

  • Online ISBN: 978-3-540-79228-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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