On Purported Gentzen Formulations of Two Positive Relevant Logics

[10] offers two (cut-free) subscripted Gentzen systems, G₂T₊ and G₂R₊, which are claimed to be equivalent in an appropriate sense to the positive relevant logics T₊ and R₊, respectively. In this paper we show that that claim is false. We also show that the argument in [10] for the further claim that...

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Bibliographic Details
Published inStudia logica Vol. 44; no. 3; pp. 233 - 236
Main Author Giambrone, Steve
Format Journal Article
LanguageEnglish
Published Ossolineum and D. Reidel 01.01.1985
Subjects
Abstract logic
Decision making
Logical theorems
Mathematical logic
Relevance logic
Sequents
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Summary:[10] offers two (cut-free) subscripted Gentzen systems, G₂T₊ and G₂R₊, which are claimed to be equivalent in an appropriate sense to the positive relevant logics T₊ and R₊, respectively. In this paper we show that that claim is false. We also show that the argument in [10] for the further claim that cut and/or modus ponens is admissible in two other subscripted Gentzen systems, G₁T₊ and G₁R₊, is unsound.
ISSN:0039-3215
1572-8730