A Note on Gödel-Dummet Logic LC

Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n-1}\rightarrow A_{n})\vee (A_{n}\rightarrow A_{0})\) is equivalent to Gödel-Dummett log...

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Bibliographic Details
Published inBulletin of the Section of Logic Vol. 50; no. 3; pp. 325 - 335
Main Authors Robles , Gemma, Méndez, José M
Format Journal Article
LanguageEnglish
Published Warsaw Wydawnictwo Uniwersytetu Łódzkiego 2021
Lodz University Press
University of Łódź
Subjects
gödel-dummet logic lc
intermediate logics
Logic
GödelDummet logic LC
Intermediate logics
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Summary:Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n-1}\rightarrow A_{n})\vee (A_{n}\rightarrow A_{0})\) is equivalent to Gödel-Dummett logic LC. However, if \(n\) is an even number equal to or greater than 2, IPC plus the said axiom is a sublogic of LC.
ISSN:0138-0680
2449-836X
DOI:10.18778/0138-0680.2021.15