Quantales and Temporal Logics

  • Bernhard Möller
  • Peter Höfner
  • Georg Struth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4019)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernhard Möller
    • 1
  • Peter Höfner
    • 1
  • Georg Struth
    • 2
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany
  2. 2.Department of Computer ScienceUniversity of SheffieldSheffieldUK

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