A simple cut-free system for a paraconsistent logic equivalent to S5

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Abstract

NS5 is a paraconsistent logic in the classical language, which is equivalent to the well-known modal logic S5. We provide a particularly simple hypersequential system for the propositional NS5, and prove a strong cut-admissibility theorem for it. Our system is obtained from the standard hypersequential system for classical logic by just weakening its two rules for negation, and without introducing any new structural rule. We also explain how to extend the results to the natural first-order extension of NS5. The latter is equivalent to the Constant Domain first-order S5.

Original languageEnglish
Title of host publication12th Conference on "Advances in Modal Logic", AiML 2018
EditorsGuram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer
PublisherCollege Publications
Pages29-42
Number of pages14
ISBN (Print)1904987206
StatePublished - 2018
Event12th Conference on "Advances in Modal Logic", AiML 2018 - Bern, Switzerland
Duration: 27 Aug 201831 Aug 2018

Publication series

NameAdvances in Modal Logic
Volume12

Conference

Conference12th Conference on "Advances in Modal Logic", AiML 2018
Country/TerritorySwitzerland
CityBern
Period27/08/1831/08/18

Keywords

  • Cut-elimination
  • Hypersequents
  • Modal logic
  • Paraconsistent logic
  • S5

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