As recognized by tsuneto:98, external conditions are important for reasoning about potential refinements of abstract plans. Although the basic idea is the same, we define them a little differently and call them external preconditions to differentiate them from other conditions that we call external postconditions. Intuitively, an external precondition of a group of partially ordered plans is a precondition of one of the plans that is not achieved by another in the group and must be met external to the group. External postconditions, similarly, are those that are not undone by plans in the group and are net effects of the group. Definition 6 states that is an external [pre, post]condition of an execution if is a [pre, post]condition of a subplan for which it is not [achieved, undone] by some other subplan.
For the example in Figure 2, is not an external precondition because, although G must exist to produce H, G is supplied by the execution of the plan. Thus, is met internally, making an internal condition. is an external precondition, an internal condition, and an external postcondition because it is needed externally and internally; it is an effect of which releases M1 when it is finished; and no other plan in the decomposition undoes this effect.