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Tableau Development for a Bi-intuitionistic Tense Logic

  • Conference paper
Relational and Algebraic Methods in Computer Science (RAMICS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8428))

Abstract

The paper introduces a bi-intuitionistic logic with two modal operators and their tense versions. The semantics is defined by Kripke models in which the set of worlds carries a pre-order relation as well as an accessibility relation, and the two relations are linked by a stability condition. A special case of these models arises from graphs in which the worlds are interpreted as nodes and edges of graphs, and formulae represent subgraphs. The pre-order is the incidence structure of the graphs. These examples provide an account of time including both time points and intervals, with the accessibility relation providing the order on the time structure. The logic we present is decidable and has the effective finite model property. We present a tableau calculus for the logic which is sound, complete and terminating. The MetTel system has been used to generate a prover from this tableau calculus.

This research was supported by UK EPSRC research grant EP/H043748/1.

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Author information

Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, UK

    John G. Stell

  2. School of Computer Science, University of Manchester, Manchester, UK

    Renate A. Schmidt & David Rydeheard

Authors
  1. John G. Stell
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  2. Renate A. Schmidt
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  3. David Rydeheard
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Editor information

Editors and Affiliations

  1. NICTA and UNSW, Anzac Parade 223, 2033, Kensington, NSW, Australia

    Peter Höfner

  2. School of Computational Sciences, Chapman University, One University Drive, 92866, Orange, CA, USA

    Peter Jipsen

  3. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  4. Department of Computer Science, University of Augsburg, Universitätsstraße 6a, 86159, Augsburg, Germany

    Martin Eric Müller

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Stell, J.G., Schmidt, R.A., Rydeheard, D. (2014). Tableau Development for a Bi-intuitionistic Tense Logic. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_25

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  • DOI: https://doi.org/10.1007/978-3-319-06251-8_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06250-1

  • Online ISBN: 978-3-319-06251-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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