Disentangling crosscutting in AOSD: formalization based on a crosscutting pattern

Crosscutting is usually described in terms of scattering and tangling. However, the distinction between these concepts is vague, which could lead to ambiguous statements. Sometimes, precise definitions are required, e.g., for the formal identification of crosscutting concerns. We propose a conceptual framework for formalizing these concepts based on a crosscutting pattern that shows the mapping between elements at two levels, e.g., concerns and representations of concerns. The definitions of the concepts are formalized in terms of linear algebra, and visualized with matrices and matrix operations. In this way, crosscutting can be clearly distinguished from scattering and tangling. The usability of dependency matrices is illustrated in the analysis of crosscutting across several refinement levels, which can be formalized through the cascading of the crosscutting pattern.