 The missing ingredient is then the relational property of transitivity. ’Shorter than’ is an example of a transitive property: Let x be shorter than y, and let y be shorter than z. Then x must be shorter than z. So, given \(w_{1},w_{2}\) and \(w_{3}\), if the relation R holds between \(w_{1}\) and \(w_{2}\) and between \(w_{2}\) and \(w_{3}\), then the arrow between \(w_{1}\) and \(w_{3}\) is the consequence of requiring the relation to be transitive: