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In this paper we show that states, transitions and behavior of concurrentsystems can often be modeled as sheaves over a suitable topological space. Inthis context, geometric logic can be used to describe which local properties(i.e. properties of individual systems) are preserved, at a global level, wheninterconnecting the systems. The main area of application is to modularverification of complex systems. We illustrate the ideas by means of an exampleinvolving a family of interacting controllers for trains on a rail track.

Sheaves and geometric logic and applications to the modular verification of complex systems