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CUT ELIMINATION IN HYPERSEQUENT CALCULUS FOR SOME LOGICS OF LINEAR TIME

Published online by Cambridge University Press:  13 August 2019

ANDRZEJ INDRZEJCZAK
ANDRZEJ INDRZEJCZAK*
Affiliation:
Department of Logic, Institute of Philosophy, University of Lodz
*
*DEPARTMENT OF LOGIC INSTITUTE OF PHILOSOPHY UNIVERSITY OF LODZ LINDLEYA 3/5, 90–131 ŁÓDŹ POLAND E-mail: [email protected]
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Abstract

This is a sequel article to [10] where a hypersequent calculus (HC) for some temporal logics of linear frames including Kt4.3 and its extensions for dense and serial flow of time was investigated in detail. A distinctive feature of this approach is that hypersequents are noncommutative, i.e., they are finite lists of sequents in contrast to other hypersequent approaches using sets or multisets. Such a system in [10] was proved to be cut-free HC formalization of respective logics by means of semantical argument. In this article we present an equivalent variant of this calculus for which a constructive syntactical proof of cut elimination is provided.

Keywords

03B4403F0303F05temporal logichypersequent calculuscut elimination
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 4 , December 2019 , pp. 806 - 822
Copyright
Copyright © Association for Symbolic Logic 2019 

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