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Normalisation for Some Quite Interesting Many-Valued Logics

Kürbis, N; Petrukhin, Y; (2021) Normalisation for Some Quite Interesting Many-Valued Logics. Logic and Logical Philosophy , 30 (3) pp. 493-534. 10.12775/llp.2021.009. Green open access

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Abstract

In this paper, we consider a set of quite interesting three- and four-valued logics and prove the normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3⊃. Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation.

Type: Article
Title: Normalisation for Some Quite Interesting Many-Valued Logics
Open access status: An open access version is available from UCL Discovery
DOI: 10.12775/llp.2021.009
Publisher version: https://doi.org/10.12775/llp.2021.009
Language: English
Additional information: This is an Open Access article published under a Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/).
Keywords: natural deduction; normalisation; three-valued logic; four-valued logic; logic of paradox; Nelson logic
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10130910
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