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Formalized Proof Systems for Propositional Logic

Authors: Julius Michaelis and Tobias Nipkow

Published in: LIPIcs, Volume 104, 23rd International Conference on Types for Proofs and Programs (TYPES 2017)


Abstract
We have formalized a range of proof systems for classical propositional logic (sequent calculus, natural deduction, Hilbert systems, resolution) in Isabelle/HOL and have proved the most important meta-theoretic results about semantics and proofs: compactness, soundness, completeness, translations between proof systems, cut-elimination, interpolation and model existence.

Cite as

Julius Michaelis and Tobias Nipkow. Formalized Proof Systems for Propositional Logic. In 23rd International Conference on Types for Proofs and Programs (TYPES 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 104, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{michaelis_et_al:LIPIcs.TYPES.2017.5,
  author =	{Michaelis, Julius and Nipkow, Tobias},
  title =	{{Formalized Proof Systems for Propositional Logic}},
  booktitle =	{23rd International Conference on Types for Proofs and Programs (TYPES 2017)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-071-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{104},
  editor =	{Abel, Andreas and Nordvall Forsberg, Fredrik and Kaposi, Ambrus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2017.5},
  URN =		{urn:nbn:de:0030-drops-100537},
  doi =		{10.4230/LIPIcs.TYPES.2017.5},
  annote =	{Keywords: formalization of logic, proof systems, sequent calculus, natural deduction, resolution}
}
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