In the literature, the question about how to axiomatize the transitive logic of false belief is thought of as hard and left as an open problem. In this paper, among other contributions, we deal with this problem. In more details, although the standard doxastic operator is undefinable with the operator of false belief, the former is {\em almost definable} with the latter. On one hand, the involved almost definability schema guides us to find the desired core axioms for the transitive logic and the Euclidean logic of false belief. On the other hand, inspired by the schema and other considerations, we propose a suitable canonical relation, which can uniformly handle the completeness proof of various logics of false belief, including the transitive logic. We also extend the results to the logic of radical ignorance, due to the interdefinability of the operators of false belief and radical ignorance.

翻译：文献中，如何公理化虚假信念的传递逻辑被认为是一个难题，并被搁置为开放问题。本文在诸多贡献中重点处理了该问题。具体而言，尽管标准信念算子无法用虚假信念算子定义，但前者可被后者"几乎定义"。一方面，这种几乎定义模式引导我们找到虚假信念传递逻辑与欧几里得逻辑所需的核心公理；另一方面，受该模式及其他考量启发，我们提出一种合适的规范关系，可统一处理包括传递逻辑在内的各类虚假信念逻辑的完备性证明。由于虚假信念算子与彻底无知算子可相互定义，我们还将相关结论推广至彻底无知逻辑。