Refinement of Kripke Models for Dynamics

  • Authors:
  • Francien Dechesne;Simona Orzan;Yanjing Wang

  • Affiliations:
  • Department of Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands NL-5600MB;Department of Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands NL-5600MB;Centrum voor Wiskunde en Informatica, GB Amsterdam, The Netherlands NL-1090

  • Venue:
  • Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
  • Year:
  • 2008

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Abstract

We propose a property-preserving refinement/abstraction theory for Kripke Modal Labelled Transition Systems incorporating not only state mapping but also label and proposition lumping, in order to have a compact but informative abstraction. We develop a 3-valued version of Public Announcement Logic (PAL) which has a dynamic operator that changes the model in the spirit of public broadcasting. We prove that the refinement relation on staticmodels assures us to safely reason about any dynamicproperties in terms of PAL-formulas on the abstraction of a model. The theory is in particular interesting and applicable for an epistemic setting as the example of the Muddy Children puzzle shows, especially in the view of the growing interest for epistemic modelling and (automatic) verification of communication protocols.