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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/4988

Title: Algebraic aspects of cut elimination
Authors: Belardinelli, Francesco
Jipsen, Peter
Ono, Hiroakira
Keywords: Algebraic Gentzen systems
cut elimination
substructural logics
residuated lattices
finite model property
Issue Date: 2004-07
Publisher: Springer
Magazine name: Studia Logica
Volume: 77
Number: 2
Start page: 209
End page: 240
DOI: 10.1023/B:STUD.0000037127.15182.2a
Abstract: We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17].
Rights: This is the author-created version of Springer, Francesco Belardinelli, Peter Jipsen and Hiroakira Ono, Studia Logica, 77(2), 2004, 209-240. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1023/B:STUD.0000037127.15182.2a
URI: http://hdl.handle.net/10119/4988
Material Type: author
Appears in Collections:i10-1. 雑誌掲載論文 (Journal Articles)

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