How exactly is a tag-based system not a DAG, regardless of whether tags can imply other tags or not? > It's got a root, it propagates from the root to leaf nod

How exactly is a tag-based system not a DAG, regardless of whether tags can imply other tags or not? > It's got a root, it propagates from the root to leaf nodes, and there is no recursion. A network of instances and tags satisfies the same properties. Do you have any counterexample? If not, I have to dismiss a notion that "tag-based systems" stand in opposition to "hierarchical systems" since every network of objects and tags is a DAG.