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：带有前缀和转换规则的度量单位通过范畴群论给出形式语义模型。定义了基本结构以及自然与偶然语义运算。转换规则被表示为具有类群和类范畴性质的三元关系类。我们探讨了一个子类层次结构，每个子类相比前一类具有更好的代数性质，最终得到一个直接高效的基于重写的转换算法。