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Goal-Directed Calculi for Gödel-Dummett Logics

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Computer Science Logic (CSL 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2803))

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Abstract

In this work we present goal-directed calculi for the Gödel-Dummett logic LC and its finite-valued counterparts, LC n (n ≥ 2). We introduce a terminating hypersequent calculus for the implicational fragment of LC with local rules and a single identity axiom. We also give a labelled goal-directed calculus with invertible rules and show that it is co-NP. Finally we derive labelled goal-directed calculi for LC n .

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Author information

Authors and Affiliations

  1. Department of Computer Science, King’s College London, Strand, London, WC2R 2LS, UK

    George Metcalfe & Dov Gabbay

  2. Department of Computer Science, University of Turin, Corso Svizzera 185, 10149, Turin, Italy

    Nicola Olivetti

Authors
  1. George Metcalfe
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  2. Nicola Olivetti
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  3. Dov Gabbay
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Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Matthias Baaz

  2. Members of EACSL Jury for the Ackermann Award,  

    Johann A. Makowsky

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© 2003 Springer-Verlag Berlin Heidelberg

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Metcalfe, G., Olivetti, N., Gabbay, D. (2003). Goal-Directed Calculi for Gödel-Dummett Logics. In: Baaz, M., Makowsky, J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45220-1_33

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  • DOI: https://doi.org/10.1007/978-3-540-45220-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40801-7

  • Online ISBN: 978-3-540-45220-1

  • eBook Packages: Springer Book Archive

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