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CUT AND GAMMA I: PROPOSITIONAL AND CONSTANT DOMAIN R

Published online by Cambridge University Press:  29 August 2019

YALE WEISS
YALE WEISS*
Affiliation:
The Saul Kripke Center, The Graduate Center, CUNY
*
†THE SAUL KRIPKE CENTER THE GRADUATE CENTER, CUNY 365 FIFTH AVE., ROOM 7118 NEW YORK, NY 10016, USA E-mail: [email protected]
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Abstract

The main object of this article is to give two novel proofs of the admissibility of Ackermann’s rule (γ) for the propositional relevant logic R. The results are established as corollaries of cut elimination for systems of tableaux for R. Cut elimination, in turn, is established both nonconstructively (as a corollary of completeness) and constructively (using Gentzen-like methods). The extensibility of the techniques is demonstrated by showing that (γ) is admissible for RQ* (R with constant domain quantifiers). The status of the admissibility of (γ) for RQ* was, to the best of the author’s knowledge, an open problem. Further extensions of these results will be explored in the sequel(s).

Keywords

03F0303F0503B47propositional relevant logicconstant domain relevant logicgammacut
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 887 - 909
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Copyright
Copyright © Association for Symbolic Logic 2019 

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