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 -