Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as a class of ternary relations with both group-like and category-like properties. A hierarchy of subclasses is explored, each with better algebraic behavior than the preceding, culminating in a direct efficient conversion-by-rewriting algorithm.

翻译：本文采用范畴群论为带前缀的度量单位及转换规则构建了形式语义模型，定义了基本结构以及自然与偶然两类语义运算。转换规则被表示为兼具群性与范畴性的一类三元关系。本文探讨了一个子类层级结构，每个子类相较于前驱均展现出更优的代数性质，最终导出了一个基于重写机制的直接高效转换算法。