Interacting agents that interleave planning, plan coordination, and plan execution for hierarchical plans (e.g. HTNs or procedures for PRS) should reason about abstract plans and their concurrent execution before they are fully refined. Poor decisions made at abstract levels can lead to costly backtracking or even failure. We claim that better decisions require information at abstract levels that summarizes the preconditions and effects that must or may apply when a plan is refined. Here we formally characterize concurrent hierarchical plans and a method for deriving summary information for them, and we illustrate how summary conditions can be used to coordinate the concurrent interactions of plans at different levels of abstraction. The properties of summary conditions and rules determining what interactions can or might hold among asynchronously executing plans are proven to support the construction of sound and complete coordination mechanisms for concurrent hierarchical planning agents.
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