A representation of temporal extent in an HTN is important not only for modeling concurrently executing agents but also for performing abstract reasoning with summary information. If an agent is scheduling abstract actions and can only sequentially order them, it will be severely restricted in the kinds of solutions it can find. For example, the agent may prefer solutions with shorter makespans, and should seek plans with subthreads that can be carried out concurrently.
In this section we define concurrent hierarchical plans (CHiPs), how the state changes over time based on their executions, and concepts of success and failure of executions in a possible world, or history. Because we later define summary information and abstract plan interactions in terms of the definitions and semantics given in this section, the treatment here is fairly detailed (though for an even more comprehensive treatment, see [Clement, 2002]). However, we begin by summarizing the main concepts and notation introduced, to give the reader the basic gist.