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A Dose of Timed Logic, in Guarded Measure

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4202))

Abstract

We consider interval measurement logic IML, a sublogic of Zhou and Hansen’s interval logic, with measurement functions which provide real-valued measurement of some aspect of system behaviour in a given time interval. We interpret IML over a variety of time domains (continuous, sampled, integer) and show that it can provide a unified treatment of many diverse temporal logics including duration calculus (DC), interval duration logic (IDL) and metric temporal logic (MTL). We introduce a fragment GIML with restricted measurement modalities which subsumes most of the decidable timed logics considered in the literature.

Next, we introduce a guarded first-order logic with measurements MGF. As a generalisation of Kamp’s theorem, we show that over arbitrary time domains, the measurement logic GIML is expressively complete for it. We also show that MGF has the 3-variable property.

In addition, we have a preliminary result showing the decidability of a subset of GIML when interpreted over timed words.

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Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, Chennai, 600113, India

    Kamal Lodaya

  2. Tata Institute of Fundamental Research, Colaba, Mumbai, 400005, India

    Paritosh K. Pandya

Authors
  1. Kamal Lodaya
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  2. Paritosh K. Pandya
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Editor information

Editors and Affiliations

  1. LIAFA, CNRS and University Paris Diderot,  

    Eugene Asarin

  2. LSV, CNRS & ENS de Cachan, France

    Patricia Bouyer

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© 2006 Springer-Verlag Berlin Heidelberg

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Lodaya, K., Pandya, P.K. (2006). A Dose of Timed Logic, in Guarded Measure. In: Asarin, E., Bouyer, P. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2006. Lecture Notes in Computer Science, vol 4202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867340_19

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  • DOI: https://doi.org/10.1007/11867340_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45026-9

  • Online ISBN: 978-3-540-45031-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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