Recent years witness a growing interest in nonstandard epistemic logics of "knowing whether", "knowing what", "knowing how", and so on. These logics are usually not normal, i.e., the standard axioms and reasoning rules for modal logic may be invalid. In this paper, we show that the conditional "knowing value" logic proposed by Wang and Fan \cite{WF13} can be viewed as a disguised normal modal logic by treating the negation of the Kv operator as a special diamond. Under this perspective, it turns out that the original first-order Kripke semantics can be greatly simplified by introducing a ternary relation $R_i^c$ in standard Kripke models, which associates one world with two $i$-accessible worlds that do not agree on the value of constant $c$. Under intuitive constraints, the modal logic based on such Kripke models is exactly the one studied by Wang and Fan (2013,2014}. Moreover, there is a very natural binary generalization of the "knowing value" diamond, which, surprisingly, does not increase the expressive power of the logic. The resulting logic with the binary diamond has a transparent normal modal system, which sharpens our understanding of the "knowing value" logic and simplifies some previously hard problems.
近年来，非标准认知逻辑（knowingwhether，knowinghow，knowingwhat，knowingwhy等）引起了人们越来越大的兴趣，这些逻辑中引入的新的认知模态在语义上都共享$\exists x \Box ϕ$的一般模式，例如，知道如何实现$ϕ$大致意味着存在一种方法，这样你就知道它是一种方法，以确保$ϕ$。此外，由此产生的逻辑是可判定的。受这些特定逻辑的启发，在这项工作中，我们提出了一个非常通用和强大的框架的基础上，量词自由谓词语言扩展了一个新的模态$\Box^x$，它包完全$\exists x \Box$在一起。我们表明，所得到的语言，虽然更有表现力，共享许多良好的性质的基本命题模态逻辑在任意模型，如有限树模型属性和van Bentham的特征w.r.t.一阶模态逻辑我们公理化的逻辑在S5框架与直观的公理捕捉之间的相互作用$\Box^x$和知道，运营商在认知设置。
