Building on early work by Girard (1987) and using closely related techniques from the proof theory of many-valued logics, we propose a sequent calculus capturing a hierarchy of notions of satisfaction based on the Strong Kleene matrices introduced by Barrio et al. (Journal of Philosophical Logic 49:93–120, 2020) and others. The calculus allows one to establish and generalize in a very natural manner several recent results, such as the coincidence of some of these notions with their classical counterparts, and the possibility of expressing some notions of satisfaction for higher-level inferences using notions of satisfaction for inferences of lower level. We also show that at each level all notions of satisfaction considered are pairwise distinct and we address some remarks on the possible significance of this (huge) number of notions of consequence.

基于 Girard (1987) 的早期工作，并使用多值逻辑证明理论中的密切相关技术，我们提出了一种基于 Barrio 等人引入的 Strong Kleene 矩阵的连续演算来捕捉满足感的层次结构。(Journal of Philosophical Logic 49:93–120, 2020) 等。微积分允许人们以一种非常自然的方式建立和概括几个最近的结果，例如这些概念中的一些与其经典对应物的重合，以及使用满意度概念表达更高层次推理的某些满意度概念的可能性低层次的推论。