First consider positive trees, those employing only intersection and union nodes. Then bounds can be computed as follows. In an upward pass, a union node is assigned a box to circumscribe the union of the boxes of its children, and an intersection node is assigned the intersection of its children's boxes. What is more surprising is that natural variants of this procedure fail in some regard. Using spheres as bounding functions does not lead to unique fixed points.
Convex hulls do converge to fixed points, but they are computationally expensive.
The authors classify bounding functions according to various useful properties, and they prove theorems that permit refining the bounds while preserving the properties. They discuss the complications introduced by trees that include set difference nodes. On the positive side, simple box-bounding exhibits rapid convergence in practice. The paper oscillates between lucid high-level discussion supported by clear examples and turgid notation that takes some perseverance to penetrate. Effort is amply rewarded, however.