A Dose of Timed Logic, in Guarded Measure

  • Kamal Lodaya
  • Paritosh K. Pandya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4202)


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.


Linear Order Temporal Logic Free Variable Order Logic Winning Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kamal Lodaya
    • 1
  • Paritosh K. Pandya
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Tata Institute of Fundamental Research, ColabaMumbaiIndia

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