  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. When repairing inconsistencies in a graph, we
use graph transformation rules with so-called impairment- 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 characterized 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 initial evaluation shows that
graph repair can be well supported by rules with these new types of application
conditions.
