In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of premisses as absolute truths as is done in predicate logic. Viewing the set of premisses as a set of assumptions, however, it is possible to deduce useful conclusions from an inconsistent set of premisses. In this paper a logic for reasoning with inconsistent knowledge is described. This logic is a generalization of the work of N. Rescher [15]. In the logic a reliability relation is used to choose between incompatible assumptions. These choices are only made when a contradiction is derived. As long as no contradiction is derived, the knowledge is assumed to be consistent. This makes it possible to define an argumentation-based deduction process for the logic. For the logic a semantics based on the ideas of Y. Shoham [22, 23], is defined. It turns out that the semantics for the logic is a preferential semantics according to the definition S. Kraus, D. Lehmann and M. Magidor [12]. Therefore the logic is a logic of system P and possesses all the properties of an ideal non-monotonic logic.

翻译：在许多情况下，人类必须基于不一致的知识进行推理。这些不一致性可能源于信息源并非完全可靠。为了处理不一致知识的推理，不能像谓词逻辑那样将前提集视为绝对真理。然而，若将前提集视为一组假设，则有可能从不一致的前提集中推导出有用的结论。本文描述了一种用于推理不一致知识的逻辑。该逻辑是对 N. Rescher [15] 工作的推广。在此逻辑中，通过可靠性关系在不相容的假设之间进行选择。这些选择仅在推导出矛盾时进行。只要未推导出矛盾，就假定知识是一致的。这使得为该逻辑定义基于论证的演绎过程成为可能。针对该逻辑，基于 Y. Shoham [22, 23] 的思想定义了语义学。结果表明，该逻辑的语义符合 S. Kraus、D. Lehmann 和 M. Magidor [12] 的定义，是一种优先语义。因此，该逻辑属于系统 P 的逻辑，并具备理想非单调逻辑的所有性质。