Refinement of Kripke Models for Dynamics

Abstract

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 static models assures us to safely reason about any dynamic properties 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.

To know or not to know: epistemic approaches to security protocol verification

“…Engelhardt et al (2002)). Moreover, some model checking techniques such as abstraction and symmetry reduction that are specific to ETL or DEL can be found in (Dechesne et al, 2008;Cohen et al, 2009a;Cohen et al, 2009b). Due to the space limitations we will not go into the details.…”