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PROOF-THEORETIC ANALYSIS OF THE QUANTIFIED ARGUMENT CALCULUS

Published online by Cambridge University Press:  10 June 2019

EDI PAVLOVIĆ  and
NORBERT GRATZL
EDI PAVLOVIĆ*
Affiliation:
Department of Philosophy, History and Art Studies, University of Helsinki
NORBERT GRATZL*
Affiliation:
Fakultät Für Philosophie, Wissenschaftstheorie Und Religionswissenschaft, Munich Center for Mathematical Philosophy (MCMP), Ludwig-Maximilians-Universität München
*
*DEPARTMENT OF PHILOSOPHY, HISTORY AND ART STUDIES UNIVERSITY OF HELSINKI P.O. BOX 24 FI-00014 HELSINKI, FINLAND E-mail: Edi.Pavlovic@helsinki.fi
†FAKULTÄT FÜR PHILOSOPHIE WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFT MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY (MCMP) LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN GESCHWISTER-SCHOLL-PLATZ 1, D-80539 MÜNCHEN, GERMANY E-mail: N.Gratzl@lmu.de
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Abstract

This article investigates the proof theory of the Quantified Argument Calculus (Quarc) as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction (Suppes-Lemmon style), we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries (including subformula property and thus consistency).

Keywords

03F0303F0503B1003B65Quantified Argument Calculusproof theorysequent calculusnatural deduction
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 4 , December 2019 , pp. 607 - 636
Copyright
Copyright © Association for Symbolic Logic 2019 

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