The sharpness property of justification models is essential for formal analysis of epistemic scenarios like Russell’s prime minister example. The problem to axiomatize this property in the prepositional justification language was left open. We propose a solution and provide complete axiomatizations for the class of all sharp basic justification models and also for the class of all sharp justification models in the case of extended language with an additional operation “plus” (the union of justifications).

中文翻译：

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证明逻辑的清晰度属性

证明模型的敏锐性对于形式分析认知情景（如罗素总理的例子）至关重要。用介词对齐语言公理化此属性的问题仍然没有解决。我们提出了一个解决方案，并为所有尖锐的基本证明模型类别以及在扩展语言的情况下为所有尖锐的证明模型类别提供了完整的公理化，并带有附加的操作“加号”（理由的并集）。