Temporal Logic with Recursion

Authors Florian Bruse, Martin Lange

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Florian Bruse
  • School of Electrical Engineering and Computer Science, University of Kassel, Germany
Martin Lange
  • School of Electrical Engineering and Computer Science, University of Kassel, Germany

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Florian Bruse and Martin Lange. Temporal Logic with Recursion. In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We introduce extensions of the standard temporal logics CTL and LTL with a recursion operator that takes propositional arguments. Unlike other proposals for modal fixpoint logics of high expressive power, we obtain logics that retain some of the appealing pragmatic advantages of CTL and LTL, yet have expressive power beyond that of the modal μ-calculus or MSO. We advocate these logics by showing how the recursion operator can be used to express interesting non-regular properties. We also study decidability and complexity issues of the standard decision problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Program specifications
  • formal specification
  • temporal logic
  • expressive power


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