Linear Temporal Logic and Z Refinement

  • John Derrick
  • Graeme Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3116)


Since Z, being a state-based language, describes a system in terms of its state and potential state changes, it is natural to want to describe properties of a specified system also in terms of its state. One means of doing this is to use Linear Temporal Logic (LTL) in which properties about the state of a system over time can be captured. This, however, raises the question of whether these properties are preserved under refinement. Refinement is observation preserving and the state of a specified system is regarded as internal and, hence, non-observable.

In this paper, we investigate this issue by addressing the following questions. Given that a Z specification A is refined by a Z specification C, and that P is a temporal logic property which holds for A, what temporal logic property Q can we deduce holds for C? Furthermore, under what circumstances does the property Q preserve the intended meaning of the property P? The paper answers these questions for LTL, but the approach could also be applied to other temporal logics over states such as CTL and the μ-calculus.


refinement temporal logic LTL 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • John Derrick
    • 1
  • Graeme Smith
    • 2
  1. 1.Computing LaboratoryUniversity of KentCanterburyUK
  2. 2.School of Information Technology and Electrical EngineeringThe University of QueenslandAustralia

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