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Formalized Proof Systems for Propositional Logic

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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.

BibTeX - Entry

@InProceedings{michaelis_et_al:LIPIcs:2018:10053,
  author =	{Julius Michaelis and Tobias Nipkow},
  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 =	{2018},
  volume =	{104},
  editor =	{Andreas Abel and Fredrik Nordvall Forsberg and Ambrus Kaposi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10053},
  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}
}

Keywords: formalization of logic, proof systems, sequent calculus, natural deduction, resolution
Seminar: 23rd International Conference on Types for Proofs and Programs (TYPES 2017)
Issue date: 2018
Date of publication: 2018


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