Four Relevant Gentzen Systems

This paper is a study of four subscripted Gentzen systems$G^{u}R_{+}$,$G^{u}T_{+}$,$G^{u}RW_{+}$and$G^{u}TW_{+}$. [16] shows that the first three are equivalent to the semilattice relevant logics^{u}R_{+}$,^{w}T_{+}$and^{u}RW_{+}$and conjectures that$G^{u}TW_{+}$is equivalent to^{u}TW_{+}$. Here we...

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Bibliographic Details
Published inStudia logica Vol. 46; no. 1; pp. 55 - 71
Main Authors Giambrone, Steve, Kron, Aleksandar
Format Journal Article
LanguageEnglish
Published Wroclaw, Poland Ossolineum and D. Reidel 01.03.1987
Ossolineum
Subjects
Barometers
Gases
Inference
Logical proofs
Logical theorems
Mathematical logic
Modus ponens
Relevance logic
Sequents
Syntactical consequents
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Summary:This paper is a study of four subscripted Gentzen systems$G^{u}R_{+}$,$G^{u}T_{+}$,$G^{u}RW_{+}$and$G^{u}TW_{+}$. [16] shows that the first three are equivalent to the semilattice relevant logics^{u}R_{+}$,^{w}T_{+}$and^{u}RW_{+}$and conjectures that$G^{u}TW_{+}$is equivalent to^{u}TW_{+}$. Here we prove Cut Theorems for these systems, and then show that modus ponens is admissible -- which is not so trivial as one normally expects. Finally, we give decision procedures for the contractionless systems,$G^{u}TW_{+}$and$G^{u}RW_{+}$.
ISSN:0039-3215
1572-8730
DOI:10.1007/BF00396905