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TRANSLATIONS BETWEEN LINEAR AND TREE NATURAL DEDUCTION SYSTEMS FOR RELEVANT LOGICS

Published online by Cambridge University Press:  08 April 2021

SHAWN STANDEFER*
Affiliation:
SCHOOL OF HISTORICAL AND PHILOSOPHICAL STUDIES THE UNIVERSITY OF MELBOURNE PARKVILLE, VIC 3010, AUSTRALIA E-mail: standefer@gmail.com URL: http://www.standefer.net

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.

Type
Research Article
Copyright
© Association for Symbolic Logic, 2021

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TRANSLATIONS BETWEEN LINEAR AND TREE NATURAL DEDUCTION SYSTEMS FOR RELEVANT LOGICS
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