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A Tableau Calculus for a Temporal Logic with Temporal Connectives

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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

The paper presents a tableau calculus for a linear time temporal logic for reasoning about processes and events in concurrent systems. The logic is based on temporal connectives in the style of Transaction Logic [BK94] and explicit quantification over states. The language extends first-order logic with sequential and parallel conjunction, parallel disjunction, and temporal implication. Explicit quantification over states via state variables allows to express temporal properties which cannot be formulated in modal logics.

Using the tableau representation of temporal Kripke structures presented for CTL in [MS96] which represents states by prefix terms, explicit quantification over states is integrated into the tableau calculus by an adaptation of the δ-rule from first-order tableau calculi to the linear ordering of the universe of states.

Complementing the CTL calculus, the paper shows that this tableau representation is both suitable for modal temporal logics and for logics using temporal connectives.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Germany

    Wolfgang May

Authors
  1. Wolfgang May
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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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May, W. (1999). A Tableau Calculus for a Temporal Logic with Temporal Connectives. 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_21

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  • DOI: https://doi.org/10.1007/3-540-48754-9_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66086-6

  • Online ISBN: 978-3-540-48754-8

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