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Combining the Temporal and Epistemic Dimensions for MTL Monitoring

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Formal Modeling and Analysis of Timed Systems (FORMATS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10419))

Abstract

We define a new notion of satisfaction of a temporal logic formula \(\varphi \) by a behavior w. This notion, denoted by \((w,t,t')\,\models \, \varphi \), is characterized by two time parameters: the position t from which satisfaction is considered, and the end of the (finite) behavior \(t'\) which indicates how much do we know about the behavior. We define this notion in dense time where \(\varphi \) is a formula in the future fragment of metric temporal logic (MTL) and w is a Boolean signal of bounded variability. We show that the set of all pairs \((t,t')\) such that \((w,t,t')\,\models \, \varphi \) can be expressed as a finite union of two-dimensional zones and give an effective procedure to compute it.

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Notes

  1. 1.

    In the context of reactive systems, finite behaviors are sometimes even considered anomalous, representing deadlocks.

  2. 2.

    By a slight abuse of notation we use the same symbol for a formula and its satisfaction signal.

  3. 3.

    It means that if a constraint \(f(t,t')\le c\) is implied by other constraints, the constraint \(f(t,t')\le c-\varepsilon \) is not implied by them for any \(\varepsilon >0\).

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Author information

Authors and Affiliations

  1. IRIF, Paris Diderot University, Paris, France

    Eugene Asarin

  2. Verimag, CNRS/University of Grenoble-Alpes, Grenoble, France

    Oded Maler & Dogan Ulus

  3. Austrian Institute of Technology, Vienna, Austria

    Dejan Nickovic

Authors
  1. Eugene Asarin
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  2. Oded Maler
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  3. Dejan Nickovic
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  4. Dogan Ulus
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Corresponding author

Correspondence to Dogan Ulus .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, United Kingdom

    Alessandro Abate

  2. Dept. d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Gilles Geeraerts

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Asarin, E., Maler, O., Nickovic, D., Ulus, D. (2017). Combining the Temporal and Epistemic Dimensions for MTL Monitoring. In: Abate, A., Geeraerts, G. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2017. Lecture Notes in Computer Science(), vol 10419. Springer, Cham. https://doi.org/10.1007/978-3-319-65765-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-65765-3_12

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