Abstract

Minimal inconsistent subsets of knowledge bases in monotonic logics play an important role when investigating the reasons for conflicts and trying to handle them. In the context of non-monotonic reasoning this notion is not as meaningful due to the possibility of resolving conflicts by adding information. In this paper we investigate inconsistency in non-monotonic logics while taking this issue into account. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics even if we allow adding novel information to a given knowledge base. We illustrate the versatility of the main theorems by covering more sophisticated situations and demonstrate how to utilize our results to analyze inconsistency in abstract argumentation.

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