Sesqui-Pushout Rewriting with Type Refinements

Sesqui-pushout rewriting is an algebraic graph transformation approach that provides mechanisms for vertex cloning. If a vertex gets cloned, the original and the copy obtain the same context, i.e. all incoming and outgoing edges of the original are copied as well. This behaviour is not satisfactory in practical examples which require more control over the context cloning process. In this paper, we provide such a control mechanism by allowing each transformation rule to refine the underlying type graph. We discuss the relation to the existing approaches to controlled sesqui-pushout vertex cloning, elaborate a basic theoretical framework, and demonstrate its applicability by a practical example.