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Quantales and Temporal Logics

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Algebraic Methodology and Software Technology (AMAST 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4019))

Abstract

We propose an algebraic semantics for the temporal logic CTL * and simplify it for its sublogics CTL and LTL. We abstractly represent state and path formulas over transition systems in Boolean left quantales. These are complete lattices with a multiplication that preserves arbitrary joins in its left argument and is isotone in its right argument. Over these quantales, the semantics of CTL * formulas can be encoded via finite and infinite iteration operators; the CTL and LTL operators can be related to domain operators. This yields interesting new connections between representations as known from the modal μ-calculus and Kleene/ω-algebra.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Augsburg, D-86135, Augsburg, Germany

    Bernhard Möller & Peter Höfner

  2. Department of Computer Science, University of Sheffield, Sheffield, S1 4DP, UK

    Georg Struth

Authors
  1. Bernhard Möller
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  2. Peter Höfner
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  3. Georg Struth
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Macquarie University,  

    Michael Johnson

  2. Dept. of Computer Science, Univ. of Tartu, J. Liivi 2, P.O. Box, EE-50409, Tartu, Estonia

    Varmo Vene

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© 2006 Springer-Verlag Berlin Heidelberg

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Möller, B., Höfner, P., Struth, G. (2006). Quantales and Temporal Logics. In: Johnson, M., Vene, V. (eds) Algebraic Methodology and Software Technology. AMAST 2006. Lecture Notes in Computer Science, vol 4019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784180_21

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  • DOI: https://doi.org/10.1007/11784180_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35633-2

  • Online ISBN: 978-3-540-35636-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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