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Syntactic Cut-Elimination and Backward Proof-Search for Tense Logic via Linear Nested Sequents

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11714))

Abstract

We give a linear nested sequent calculus for the basic normal tense logic \(\mathsf {Kt}\). We show that the calculus enables backwards proof-search, counter-model construction and syntactic cut-elimination. Linear nested sequents thus provide the minimal amount of nesting necessary to provide an adequate proof-theory for modal logics containing converse. As a bonus, this yields a cut-free calculus for symmetric modal logic \(\mathsf {KB}\).

Supported by WWTF project MA16-28.

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Authors and Affiliations

  1. Research School of Computer Science, Australian National University, Canberra, Australia

    Rajeev Goré

  2. Faculty of Informatics, Technical University of Vienna, Vienna, Austria

    Björn Lellmann

Authors
  1. Rajeev Goré
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  2. Björn Lellmann
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Correspondence to Björn Lellmann .

Editor information

Editors and Affiliations

  1. IBISC, Univ. Evry, Université Paris-Saclay, Evry, France

    Serenella Cerrito

  2. Middlesex University London, London, UK

    Andrei Popescu

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Goré, R., Lellmann, B. (2019). Syntactic Cut-Elimination and Backward Proof-Search for Tense Logic via Linear Nested Sequents. In: Cerrito, S., Popescu, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2019. Lecture Notes in Computer Science(), vol 11714. Springer, Cham. https://doi.org/10.1007/978-3-030-29026-9_11

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  • DOI: https://doi.org/10.1007/978-3-030-29026-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29025-2

  • Online ISBN: 978-3-030-29026-9

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