Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the modal Łukasiewicz many-valued logic. These logics are shown to be capable of expressing nuanced probabilistic concepts, including upper and lower probabilities. Our main contribution is a PSPACE-completeness result for two variants of the local consequence problem, providing a precise computational characterisation.

翻译：模态概率逻辑为在模态语境中推理概率提供了框架，涉及知识、信念、时间和行动等概念。本文研究了此类逻辑的一个特定族系，它扩展了模态Łukasiewicz多值逻辑。这些逻辑被证明能够表达细致的概率概念，包括上概率和下概率。我们的主要贡献是针对局部推理问题的两个变体给出了PSPACE完全性结果，从而提供了精确的计算复杂性刻画。