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Cut-Free Display Calculi for Nominal Tense Logics

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1617))

Abstract

We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL≠) which is known to be properly displayable by application of Kracht’s results. The rules of the display calculus δMNTL for MNTL mimic those of the display calculus δMTL≠ for MTL≠. Since δMNTL does not satisfy Belnap’s condition (C8), we extend Wansing’s strong normalisation theorem to get a similar theorem for any extension of δMNTL by addition of structural rules satisfying Belnap’s conditions (C2)–(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht’s techniques, deduce that these Sahlqvist extensions of δMNTL also admit cut-free display calculi.

Visit to ARP supported by an Australian Research Council International Fellowship.

Supported by an Australian Research Council Queen Elizabeth II Fellowship.

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Author information

Authors and Affiliations

  1. Laboratoire LEIBNIZ - C.N.R.S., 46 av. Félix Viallet, 38000, Grenoble, France

    Stéphane Demri

  2. Automated Reasoning Project and Dept. of Computer Science, Australian National University, ACT, 0200, Canberra, Australia

    Rajeev Goré

Authors
  1. Stéphane Demri
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  2. Rajeev Goré
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Institute for Programming and Logics, University at Albany - SUNY, Albany, NY, 12222, USA

    Neil V. Murray

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© 1999 Springer-Verlag Berlin Heidelberg

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Demri, S., Goré, R. (1999). Cut-Free Display Calculi for Nominal Tense Logics. In: Murray, N.V. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1999. Lecture Notes in Computer Science(), vol 1617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48754-9_16

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  • DOI: https://doi.org/10.1007/3-540-48754-9_16

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  • Print ISBN: 978-3-540-66086-6

  • Online ISBN: 978-3-540-48754-8

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