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TRANSLATIONS BETWEEN LINEAR AND TREE NATURAL DEDUCTION SYSTEMS FOR RELEVANT LOGICS

Part of: Proof theory and constructive mathematics General logic

Published online by Cambridge University Press:  08 April 2021

SHAWN STANDEFER
SHAWN STANDEFER*
Affiliation:
SCHOOL OF HISTORICAL AND PHILOSOPHICAL STUDIES THE UNIVERSITY OF MELBOURNEPARKVILLE, VIC3010, AUSTRALIAE-mail: standefer@gmail.comURL: http://www.standefer.net
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Abstract

Anderson and Belnap presented indexed Fitch-style natural deduction systems for the relevant logics R, E, and T. This work was extended by Brady to cover a range of relevant logics. In this paper I present indexed tree natural deduction systems for the Anderson–Belnap–Brady systems and show how to translate proofs in one format into proofs in the other, which establishes the adequacy of the tree systems.

Keywords

relevant logicsnatural deductiontranslations

MSC classification

Primary: 03F52: Linear logic and other substructural logics
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 2 , June 2021 , pp. 285 - 306
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Copyright
© Association for Symbolic Logic, 2021

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