Real-world data are often inconsistent. Although a substantial amount of research has been done on measuring inconsistency, this research concentrated on knowledge bases formalized in propositional logic. Recently, inconsistency measures have been introduced for relational databases. However, nowadays, real-world information is always more frequently represented by graph-based structures which offer a more intuitive conceptualization than relational ones. In this paper, we explore inconsistency measures for graph databases with regular path constraints, a class of integrity constraints based on a well-known navigational language for graph data. In this context, we define several inconsistency measures dealing with specific elements contributing to inconsistency in graph databases. We also define some rationality postulates that are desirable properties for an inconsistency measure for graph databases. We analyze the compliance of each measure with each postulate and find various degrees of satisfaction; in fact, one of the measures satisfies all the postulates. Finally, we investigate the data and combined complexity of the calculation of all the measures as well as the complexity of deciding whether a measure is lower than, equal to, or greater than a given threshold. It turns out that for a majority of the measures these problems are tractable, while for the other different levels of intractability are exhibited.

中文翻译：

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关于测量具有常规路径约束的图数据库中的不一致性


现实世界的数据常常不一致。尽管在测量不一致性方面已经进行了大量研究，但本研究集中在命题逻辑形式化的知识库上。最近，针对关系数据库引入了不一致措施。然而，如今，现实世界的信息总是更频繁地由基于图形的结构表示，这提供了比关系结构更直观的概念化。在本文中，我们探索了具有常规路径约束的图数据库的不一致度量，这是一类基于众所周知的图数据导航语言的完整性约束。在这种情况下，我们定义了几种不一致措施，用于处理导致图数据库不一致的特定元素。我们还定义了一些合理性假设，这些假设是图数据库不一致性度量的理想属性。我们分析每项措施与每项假设的符合程度，并发现不同程度的满意度；事实上，其中一项措施满足所有假设。最后，我们研究所有度量计算的数据和组合复杂性，以及决定度量是否低于、等于或大于给定阈值的复杂性。事实证明，对于大多数措施来说，这些问题都是可以解决的，而对于其他措施来说，则表现出不同程度的棘手性。