A formal approach to aspect-oriented modelling of scenarios

The article deals with formalizing the aspect-oriented approach to software design. We prove that, from the viewpoint of AOP, the best transformations are those that allow the tracing of component embedding into systems. The formalization of AOP is based on the category theory construction of a formal design discipline. In order to describe the traced transformations we introduce the concept of $M$-initial morphism. By way of application, we consider a formalization of aspect-oriented models for scenarios of system behavior as labeled posets. We describe a general method for formal transformation of aspect-oriented models for dynamical systems into labeled event structures.