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Cut-Elimination: Syntax and Semantics

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Abstract

In this paper we first give a survey of reductive cut-elimination methods in classical logic. In particular we describe the methods of Gentzen and Schütte-Tait from the abstract point of view of proof reduction. We also present the method CERES (cut-elimination by resolution) which we classify as a semi-semantic method. In a further section we describe the so-called semantic methods. In the second part of the paper we carry the proof analysis further by generalizing the CERES method to CERESD (this part contains new previously unpublished results). In the generalized version CERESD we admit general elimination rules which are based on the mere semantical truth of sentences. We construct complete cut-free LK-derivations originating from derivations potentially containing unproven lemmas. Finally we give a comparison of reductive methods and CERESD by presenting a general simulation result.

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Authors and Affiliations

  1. Institut für Algebra und Diskrete Mathematik, Vienna University of Technology, Wiednerhauptstraße 8-10, 1040, Vienna, Austria

    M. Baaz

  2. Institut für Computer Sprachen, Vienna University of Technology, Favoritenstraße 9, 1040, Vienna, Austria

    A. Leitsch

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  1. M. Baaz
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  2. A. Leitsch
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Correspondence to A. Leitsch.

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Baaz, M., Leitsch, A. Cut-Elimination: Syntax and Semantics. Stud Logica 102, 1217–1244 (2014). https://doi.org/10.1007/s11225-014-9563-2

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  • DOI: https://doi.org/10.1007/s11225-014-9563-2

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