A Theory of Conversion Relations for Prefixed Units of Measure

TL;DR

This paper develops a formal semantic model for units of measure with prefixes and conversion rules using categorial group theory, enabling efficient conversion algorithms.

Contribution

It introduces a novel formal semantic framework for prefixed units of measure based on categorial group theory, with a hierarchy of algebraic properties for conversion relations.

Findings

Defines a formal semantic model for units of measure with prefixes.

Establishes a hierarchy of conversion relation subclasses.

Develops an efficient conversion-by-rewriting algorithm.

Abstract

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.