It has been proved that it is impossible to combine in one semantics for reactive systems the notions of modularity, causality and synchronous hypothesis. This limits bottom-up development of speciications. In this paper we introduce the notion of projectability, which is weaker than modularity, we deene a non global consistent semantics for Statecharts that enforces projectability, causality a...

In previous work it was shown that there is an epireflection ψ of the category of all compact normal, joinfit frames, with skeletal maps, in the full subcategory of frames which are also strongly projectable, and that ψ restricts to the epicompletion ε, which is the absolute reflection on compact regular frames. In the first part of this paper it is shown that ψ is a monoreflection and that the...

Using the description of a fiber product preserving bundle functor F in terms of Weil algebras, we deduce several geometric properties of the Fprolongations of principal and associated bundles. Then we clarify that the flow prolongation with respect to F of a projectable vector field can be constructed by using a natural morphism.