In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various classes of neighborhood frames. Most importantly, by adopting the intersection semantics and the subset semantics in the literature, we extend the results to the case of public announcements, which gives us the desired reduction axioms and has good applications related to Moore sentences, successful formulas and self-refuting formulas. Also, we can say something about the comparative merits of the intersection semantics and the subset semantics.

在本文中，我们研究了邻域语义下未知真理和错误信念的逻辑。我们比较了两种逻辑的相对表达能力。事实证明，它们在各类邻域模型上是无与伦比的，并且这两种逻辑的组合在任何类别的邻域模型上都具有与标准模态逻辑一样的表现力。我们为每个逻辑提出态射，这可以帮助我们探索框架可定义性问题，展示一般的健全性和完整性结果，并概括文献中的一些结果。我们在各类邻域框架上公理化了这两种逻辑。最重要的是，通过采用文献中的交集语义和子集语义，我们将结果扩展到公告的情况，这给了我们想要的归约公理，并且在摩尔句子、成功公式和自我反驳公式方面有很好的应用。此外，我们可以谈谈交叉语义和子集语义的比较优点。