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 satisfying stronger useful algebraic properties than the preceding, culminating in a direct efficient conversion-by-rewriting algorithm.

翻译：本文基于范畴群论为带前缀的度量单位及其转换规则构建了形式化语义模型。文中定义了基本结构、自然语义运算与条件语义运算，将转换规则表征为一类兼具群特性与范畴特性的三元关系。研究探索了该关系的子类层次结构，其中每一子类均满足比前一类更强的实用代数性质，最终推导出可直接通过重写实现的高效转换算法。