Studia Logica 65 (1):53-89 (2000)

Abstract
In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1005243108996
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Correspondences Between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
Representations of Structural Closure Operators.José Gil-Férez - 2011 - Archive for Mathematical Logic 50 (1-2):45-73.

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