  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.
