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

Arnon Avron; Ori Lahav

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

Arnon Avron, Ori Lahav

School of Computer Science

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	12th Conference on "Advances in Modal Logic", AiML 2018
Editors	Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer
Pages	29-42
Number of pages	14
State	Published - 2018
Event	12th Conference on "Advances in Modal Logic", AiML 2018 - Bern, Switzerland Duration: 27 Aug 2018 → 31 Aug 2018

Publication series

Name	Advances in Modal Logic
Volume	12

Conference

Conference	12th Conference on "Advances in Modal Logic", AiML 2018
Country/Territory	Switzerland
City	Bern
Period	27/08/18 → 31/08/18

Keywords

Cut-elimination
Hypersequents
Modal logic
Paraconsistent logic
S5

All Science Journal Classification (ASJC) codes

Logic
Computational Theory and Mathematics
Computational Mathematics

Cite this

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title = "A simple cut-free system for a paraconsistent logic equivalent to S5",

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.",

keywords = "Cut-elimination, Hypersequents, Modal logic, Paraconsistent logic, S5",

author = "Arnon Avron and Ori Lahav",

note = "Publisher Copyright: {\textcopyright} 2018 College Publications. All rights reserved.; 12th Conference on {"}Advances in Modal Logic{"}, AiML 2018 ; Conference date: 27-08-2018 Through 31-08-2018",

year = "2018",

language = "الإنجليزيّة",

isbn = "1904987206",

series = "Advances in Modal Logic",

pages = "29--42",

editor = "Guram Bezhanishvili and Giovanna D'Agostino and George Metcalfe and Thomas Studer",

booktitle = "12th Conference on {"}Advances in Modal Logic{"}, AiML 2018",

}

A simple cut-free system for a paraconsistent logic equivalent to S5. / Avron, Arnon; Lahav, Ori.
12th Conference on "Advances in Modal Logic", AiML 2018. ed. / Guram Bezhanishvili; Giovanna D'Agostino; George Metcalfe; Thomas Studer. 2018. p. 29-42 (Advances in Modal Logic; Vol. 12).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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ER -

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

Abstract

Publication series

Conference

Keywords

All Science Journal Classification (ASJC) codes

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Cite this