More than a name? On implications of preconditions and effects of compound HTN planning tasks

There are several formalizations for hierarchical planning. Many of them allow to specify preconditions and effects for compound tasks. They can be used, e.g., to assist during the modeling process by ensuring that the decomposition methods' plans "implement" the compound tasks' intended meaning. This is done based on so-called legality criteria that relate these preconditions and effects to the method's plans and pose further restrictions. Despite the variety of expressive hierarchical planning formalisms, most theoretical investigations are only known for standard HTN planning, where compound tasks are just names, i.e., no preconditions or effects can be specified. Thus, up to know, a direct comparison to other hierarchical planning formalisms is hardly possible and fundamental theoretical properties are yet unknown. To enable a better comparison between such formalisms (in particular with respect to their computational expressivity), we first provide a survey on the different legality criteria known from the literature. Then, we investigate the theoretical impact of these criteria for two fundamental problems to planning: plan verification and plan existence. We prove that the plan verification problem is at most NP-complete, while the plan existence problem is in the general case both semi-decidable and undecidable, independent of the demanded criteria. Finally, we discuss our theoretical findings and practical implications.