When defining the requirements of a system, specification units typically are partial or incomplete descriptions of a system
component. In this context, providing a complete description of a component means integrating all the existing partial views
for that component. However, in many cases defining the semantics of this integration operation is not an easy task. In particular,
this is the case when the framework used at the specification level is, in some sense, an “operational” one (e.g. a Petri
net or a statechart). Moreover, this problem may also apply to the definition of compositional semantics for modular constructs
for this kind of frameworks.
In this paper, we study this problem, at a general level. First, we define a general notion of framework whose semantics is
defined in terms of transformations over states represented as algebras and characterize axiomatically the standard tight semantics. Then, inspired in the double-pullback approach defined for graph transformation, we axiomatically present a loose semantics for this class of transformation systems, exploring
their compositional properties. In addition, we see how this approach may be applied to a number of formalisms.