Using weakest application conditions to rank graph transformations for graph repair

Abstract

When using graphs and graph transformations to model systems, consistency is an important concern. While consistency has primarily been viewed as a binary property, i.e., a graph is consistent or inconsistent with respect to a set of constraints, recent work has presented an approach to consistency as a graduated property. This allows living with inconsistencies for a while and repairing them when necessary. For repairing inconsistencies in a graph, we use graph transformation rules with so-called {\em impairment-indicating and repair-indicating application conditions} to understand how much repair gain certain rule applications would bring. Both types of conditions can be derived from given graph constraints. Our main theorem shows that the difference between the number of actual constraint violations before and after a graph transformation step can be characterised by the difference between the numbers of violated impairment-indicating and repair-indicating application conditions. This theory forms the basis for algorithms with look-ahead that rank graph transformations according to their potential for graph repair. An evaluation shows that graph repair can be well-supported by rules with these new types of application conditions in terms of effectiveness and scalability.