It has been increasingly recognized that identifying roles of formulas of a knowledge base in the inconsistency of that base can help us better look inside the inconsistency. However, there are few approaches to identifying such roles of formulas from a perspective of models in some paraconsistent logic, one of typical tools used to characterize inconsistency in semantics. In this paper, we characterize the role of each formula in the inconsistency arising in a knowledge base from informational as well as causal aspects in the framework of Priest's minimally inconsistent logic of paradox. At first, we identify the causal responsibility of a formula for the inconsistency based on the counterfactual dependence of the inconsistency on the formula under some contingency in semantics. Then we incorporate the change on semantic information in the framework of causal responsibility to develop the informational responsibility of a formula for the inconsistency to capture the contribution made by the formula for the inconsistent information. This incorporation makes the informational responsibility interpretable from the point of view of causality, and capable of catching the role of a formula in inconsistent information concisely. In addition, we propose notions of naive and quasi naive responsibilities as two auxiliaries to describe special relations between inconsistency and formulas in semantic sense. Some intuitive and interesting properties of the two kinds of responsibilities are also discussed.

中文翻译：

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在Priest的最小不一致悖论逻辑下识别公式在不一致中的作用


人们越来越认识到，识别知识库公式在知识库不一致中的作用可以帮助我们更好地了解不一致的内部。然而，在一些次一致逻辑（用于表征语义不一致的典型工具之一）中，从模型的角度来识别公式的这种作用的方法很少。在本文中，我们在 Priest 的最小不一致逻辑悖论框架下，从信息和因果方面描述了知识库中出现的不一致中每个公式的作用。首先，我们根据在语义上的某些偶然情况下不一致对公式的反事实依赖来确定公式对不一致的因果责任。然后，我们将语义信息的变化纳入因果责任的框架中，以开发不一致信息公式的信息责任，以捕获不一致信息公式所做出的贡献。这种合并使得信息责任可以从因果关系的角度进行解释，并且能够简洁地捕捉公式在不一致信息中的作用。此外，我们提出了朴素责任和准朴素责任的概念作为两个辅助手段来描述语义意义上的不一致和公式之间的特殊关系。还讨论了这两种职责的一些直观且有趣的属性。