TY - GEN
T1 - A simple cut-free system for a paraconsistent logic equivalent to S5
AU - Avron, Arnon
AU - Lahav, Ori
N1 - Publisher Copyright:
© 2018 College Publications. All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Cut-elimination
KW - Hypersequents
KW - Modal logic
KW - Paraconsistent logic
KW - S5
UR - http://www.scopus.com/inward/record.url?scp=85071938514&partnerID=8YFLogxK
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AN - SCOPUS:85071938514
SN - 1904987206
T3 - Advances in Modal Logic
SP - 29
EP - 42
BT - 12th Conference on "Advances in Modal Logic", AiML 2018
A2 - Bezhanishvili, Guram
A2 - D'Agostino, Giovanna
A2 - Metcalfe, George
A2 - Studer, Thomas
PB - College Publications
T2 - 12th Conference on "Advances in Modal Logic", AiML 2018
Y2 - 27 August 2018 through 31 August 2018
ER -