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.

翻译：在使用图和图变换对系统建模时，一致性是一个重要问题。虽然一致性主要被视为二元属性（即图相对于一组约束条件要么一致要么不一致），但最近的研究提出了一种将一致性视为渐变属性的方法。这允许在一段时间内容忍不一致性，并在必要时进行修复。在修复图中的不一致性时，我们使用带有所谓"损害指示"和"修复指示"应用条件的图变换规则，以了解特定规则应用能带来多大的修复收益。这两种类型的条件均可从给定的图约束中推导得出。我们的主要定理表明：图变换步骤前后实际违反约束数量的差异，可通过违反损害指示应用条件和修复指示应用条件的数量之差来刻画。该理论构成了前瞻性算法的基础，这些算法根据图变换的修复潜力对其进行排序。初步评估表明，带有这些新型应用条件的规则能够有效支持图修复。