In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures, finitely additive probability measures, plausibilty measures (and their duals, belief functions), and possibility measures. We give axioms and inference rules for the associated system of coalgebraic modal logic, and construct the canonical coalgebras to prove a completeness result.

翻译：本文定义了一类适用于构建余代数的多项式函子，该类余代数可表征不确定性起重要作用的进程。在这些多项式函子中，我们引入了上、下概率测度、有限可加概率测度、似然测度（及其对偶信度函数）与可能性测度。我们给出了相应余代数模态逻辑系统的公理与推理规则，并通过构造典范余代数证明了完备性结果。