Abstract We address the issue of quantitatively assessing the severity of inconsistencies in non-monotonic frameworks. While measuring inconsistency in classical logics has been investigated for some time now, taking the non-monotonicity into account poses new challenges. In order to tackle them, we focus on the structure of minimal strongly K -inconsistent subsets of a knowledge base K —a sound generalization of minimal inconsistent subsets to arbitrary, possibly non-monotonic, frameworks which induces a generalization of Reiter's famous hitting set duality between minimal inconsistent and maximal consistent subsets of a knowledge base. We propose measures based on this notion and investigate their behavior in a non-monotonic setting by revisiting existing rationality postulates, analyzing the compliance of the proposed measures with these postulates, and by investigating their computational complexity. Motivated by the observation that a knowledge base of a non-monotonic logic can also be repaired by adding formulas – whereas Reiter's duality is only concerned about removing –, we also investigate situations where we are given potential additional assumptions to repair a knowledge base. For this, we characterize the minimal modifications to a knowledge base in terms of a hitting set duality

中文翻译：

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处理和测量非单调逻辑中的不一致性

摘要 我们解决了定量评估非单调框架中不一致的严重程度的问题。虽然测量经典逻辑中的不一致性已经研究了一段时间，但考虑到非单调性带来了新的挑战。为了解决这些问题，我们专注于知识库 K 的最小强 K 不一致子集的结构——最小不一致子集到任意、可能非单调的框架的合理推广，这导致了 Reiter 著名的命中集二元性的推广知识库的最小不一致子集和最大一致子集之间。我们提出基于这一概念的措施，并通过重新审视现有的理性假设来研究他们在非单调环境中的行为，分析提议的措施与这些假设的合规性，并通过调查它们的计算复杂性。由于观察到非单调逻辑的知识库也可以通过添加公式来修复——而 Reiter 的对偶性只关心删除——的动机，我们还研究了给我们潜在的额外假设来修复知识库的情况。为此，我们根据命中集二元性来表征对知识库的最小修改 我们还调查了给我们潜在的额外假设来修复知识库的情况。为此，我们根据命中集二元性来表征对知识库的最小修改 我们还调查了给我们潜在的额外假设来修复知识库的情况。为此，我们根据命中集二元性来表征对知识库的最小修改