We propose two classes of doxastic extensions of fuzzy \L ukasiewicz logic that are sound and complete with respect to some appropriate classes of Kripke-based models in which both atomic propositions and accessibility relations are fuzzy. One class of these extensions is equipped with pseudo-classical belief that has properties similar to the classical belief, and the other class is based on a new notion of belief that we call it \textit{skeptical} belief. We model a fuzzy version of the muddy children problem using pseudo-classical belief and a CPA-security experiment using skeptical belief, then by showing that the pseudo-classical belief is not appropriate for modeling the belief of an adversary in a CPA-experiment we justify proposing the notion of skeptical belief. Furthermore, we prove the soundness and completeness theorems for some of the proposed doxastic extensions.

翻译：我们提出了两类模糊卢卡西维奇逻辑的信念扩展，这些扩展相对于适当的克里普克模型类而言是可靠且完备的，其中原子命题和可达性关系均为模糊的。第一类扩展配备了具有类似于经典信念特性的伪经典信念，而第二类扩展基于一种我们称之为“怀疑信念”的新信念概念。我们使用伪经典信念建模了泥巴儿童问题的模糊版本，并使用怀疑信念建模了CPA安全性实验，通过证明伪经典信念不适用于建模CPA实验中对手的信念，我们论证了提出怀疑信念概念的必要性。此外，我们还证明了所提出的部分信念扩展的可靠性与完备性定理。