Checking the consistency of a metamodel involves finding a valid metamodel instance that provably meets the set of constraints that are defined over the metamodel. These constraints are often specified in Object Constraint Language. Often, a metamodel is inconsistent due to conflicts among the constraints. Existing approaches and tools are typically incapable of pinpointing the conflicting constraints, and this makes it difficult for users to debug and fix their metamodels. In this paper, we present a formal approach for locating conflicting constraints in inconsistent metamodels. Our approach has four distinct features: (1) users can rank individual metamodel features using their own domain-specific knowledge, (2) we transform these ranked features to a weighted maximum satisfiability modulo theories problem and solve it to compute the set of maximum achievable features, (3) we pinpoint the conflicting constraints by solving the set cover problem using a novel algorithm, and (4) we have implemented our approach into a fully automated tool called MaxUSE. Our evaluation results, using our assembled set of benchmarks, demonstrate the scalability of our work and that it is capable of efficiently finding conflicting constraints.

检查元模型的一致性涉及找到一个有效的元模型实例，该实例可证明满足在元模型上定义的约束集。这些约束通常在对象约束语言中指定。通常，由于约束之间的冲突，元模型是不一致的。现有的方法和工具通常无法指出冲突的约束，这使用户难以调试和修复其元模型。在本文中，我们提出了一种在不一致的元模型中定位冲突约束的正式方法。我们的方法具有四个独特的功能：（1）用户可以使用自己的特定领域知识对单个元模型功能进行排名，（2）将这些排序后的特征转换为加权最大可满足性模理论问题，并对其进行求解以计算最大可实现特征的集合；（3）通过使用一种新颖的算法解决集合覆盖问题，找出冲突约束；以及（4 ），我们已将我们的方法实施到称为MaxUSE的全自动工具中。我们使用组合的基准测试套件评估结果证明了我们工作的可扩展性，并且能够有效地发现冲突的约束。