Full Idea
The logic for potentiality corresponds to modal system T, the minimum for metaphysics. The S4 axiom ◊◊φ → ◊φ says iterated potentialities collapse, and the S5 ◊φ → □◊φ says potentialities can't be lost.
Gist of Idea
Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials
Source
Barbara Vetter (Potentiality [2015], 5.9)
Book Reference
Vetter,Barbara: 'Potentiality: from Dispositions to Modality' [OUP 2015], p.196
A Reaction
[compressed] This seems persuasive. I nice example of modern analytic metaphysics, that you have to find a logic that suits your theory. N.Salmon defends system T for all of metaphysics, though most people favour S5.