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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: [email protected]
†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: [email protected]
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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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References

BIBLIOGRAPHY

Baaz, M. & Leitsch, A. (2011). Methods of Cut-Elimination. Trends in Logic, Vol. 34. Dordrecht: Springer.Google Scholar
Bencivenga, E. (2002). Free logics. In Gabbay, D. and Guenthner, F., editors. Handbook of Philosophical Logic, Second Edition, Vol. 5. Dordrecht: Springer, pp. 147–196.CrossRefGoogle Scholar
Ben-Yami, H. (2014). The Quantified Argument Calculus. The Review of Symbolic Logic, 7, 120–146.CrossRefGoogle Scholar
Ben-Yami, H. (2004). Logic and Natural Language. Aldershot: Ashgate.Google Scholar
Ben-Yami, H. & Pavlovic, E. (2015). Completeness of the Quantified Argument Calculus, manuscript.Google Scholar
Buss, S. (1998). An introduction to proof theory. In Buss, S., editor. Handbook of Proof Theory. Amsterdam: Elsevier, pp. 1–78.Google Scholar
Gentzen, G. (1969). An introduction to proof theory. In Szabo, M., editor. The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland, pp. 68–131.Google Scholar
Gratzl, N. (2010). A sequent calculus for a negative free logic. Studia Logica, 96, 331–348.CrossRefGoogle Scholar
Kleene, S. C. (2000). Introduction to Metamathematics (thirteenth edition). Groningen: Wolters-Noordhoff Publishing.Google Scholar
Lambert, K. (1997). Free Logics: Their Foundations, Character, and Some Applications Thereof. Sankt Augustin: Academia Verlag.Google Scholar
Lambert, K. (2001). Free logics. In Goble, L., editor. The Blackwell Guide to Philosophical Logic. Malden, MA: Blackwell Publishers, pp. 258–279.Google Scholar
Lanzet, R. & Ben-Yami, H. (2006). Logical inquiries into a new formal system with plural reference. In Hendriks, V. F., editor. First-Order Logic Revisited. Logische Philosophie, Vol. 12. Berlin: Logos Verlag, pp. 173–223.Google Scholar
Negri, S. & von Plato, J. (2001). Structural Proof Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Schütte, K. (1960). Beweistheorie. Berlin: Springer.Google Scholar
Takeuti, G. (1987). Proof Theory (second edition). Amsterdam: North-Holland.Google Scholar