We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic category. Also, we show how an axiomatic presentation for the graded theory may be modularly obtained from one for the grading theory and one for the base category. The Para construction on monoidal actegories is a motivating example for our framework. As a case study, we show how to axiomatise a variant of the graded category ImP, recently introduced by Liell-Cock and Staton to model imprecise probability. This culminates in a representation, as string diagrams with grading wires, of programs with primitives for nondeterministic and probabilistic choices and conditioning.

翻译：本文介绍了分级对称幺半范畴的字符串图表示方法。我们的研究框架包含分级幺半理论的定义及其对应的自由生成语法范畴。同时，我们展示了如何通过分级理论与基础范畴的公理化表述，以模块化方式获得分级理论的公理体系。幺半作用范畴上的Para构造是本框架的典型应用案例。作为具体研究，我们展示了如何对Liell-Cock与Staton近期提出的不精确概率建模分级范畴ImP的变体进行公理化处理。最终实现了对包含非确定性选择、概率选择及条件判断原语的程序，采用带分级导线的字符串图进行形式化表征。