重新定义无知逻辑，让罗姆斯菲尔德式无知不再可被简化。
Axiomatizing Rumsfeld Ignorance
- 区分两种不同访问关系，打破原有定义依赖
- 在多种双框架类上给出完备公理化体系
- 适用于形式逻辑与认知推理研究者
Kit Fine 在近期论文中揭示了（一阶）无知、二阶无知及罗姆斯菲尔德无知的逻辑性质。然而，罗姆斯菲尔德无知可由无知定义，导致部分结果与公理化问题变得平凡。主要原因是无知与罗姆斯菲尔德无知所包含的隐式知识算子的可达关系相同。本文假设这两个可达关系不同，其中一个为另一个的任意子集，从而避免可定义性问题，并保留大部分原有有效公式。主要成果是在若干适当的双框架类上建立公理化体系。最后，将该框架应用于分析 Fine 的原始结果。
原文摘要 · Abstract (English)
In a recent paper, Kit Fine presents some striking results concerning the logical properties of (first-order) ignorance, second-order ignorance and Rumsfeld ignorance. However, Rumsfeld ignorance is definable in terms of ignorance, which makes some existing results and the axiomatization problem trivial. A main reason is that the accessibility relations for the implicit knowledge operator contained in the packaged operators of ignorance and Rumsfeld ignorance are the same. In this work, we assume the two accessibility relations to be different so that one of them is an arbitrary subset of the other. This will avoid the definability issue and retain most of the previous validities. The main results are axiomatizations over various proper bi-frame classes. Finally we apply our framework to analyze Fine's results.
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