We propose a doxastic \L ukasiewicz logic \textbf{B\L} that is sound and complete with respect to the class of Kripke-based models in which atomic propositions and accessibility relations are both infinitely valued in the standard MV-algebra [0,1]. We also introduce some extensions of \textbf{B\L} corresponding to axioms \textbf{D}, \textbf{4}, and \textbf{T} of classical epistemic logic. Furthermore, completeness of these extensions are established corresponding to the appropriate classes of models.

翻译：我们提出一种信念 Łukasiewicz 逻辑 \textbf{B\L}，该逻辑相对于一类基于 Kripke 的模型是可靠且完备的，其中原子命题和可达关系均在标准 MV-代数 [0,1] 中取无限值。我们还引入了 \textbf{B\L} 的若干扩展，对应经典认知逻辑的公理 \textbf{D}、\textbf{4} 和 \textbf{T}。此外，这些扩展相对于相应的模型类建立了完备性。