On the Complexity and Expressiveness of Automated Planning Languages Supporting Temporal Reasoning

Automated planning is an important area of Artificial Intelligence, which has been thoroughly developed in the last decades. In recent years, a significant amount of research has focused on planning languages and systems supporting temporal reasoning, recognizing its importance in modeling and solving real-world complex tasks. Many such languages are action-based, i.e., they model planning problems by specifying which actions can be executed at any given time to affect the environment. Timeline-based planning, a different paradigm originally introduced to support planning and scheduling of space operations, models planning domains as systems composed of a set of independent, but interacting, components, whose behavior over time, the timelines, is governed by a set of temporal constraints. A thorough theoretical study of timeline-based planning languages, and a rigorous comparison with action-based languages, are still missing. We outline recent results and future directions on this front. Automated planning has always been an important area of Artificial Intelligence, which has undertaken great developments during the last decades. In the action-based approach of classical planning, the task of the planner is to find a sequence of actions that, applied from an initial state, allow an executor to achieve a given goal. Modern domain description languages (e.g., PDDL [Gerevini et al., 2009]), usually adopt this point of view. Even in its simple form, classical planning is still a very hard problem, as it is PSPACE-complete, although complex classical planning problems can be solved very efficiently in practice by modern planners, thanks to the development of many effective search heuristics and steady progress of related areas such as boolean satisfiability checking, satisfiability modulo theories, and constraint satisfaction. Some problem domains, however, require a more explicit form of temporal reasoning, which does not fit well into classical planning where actions have discrete and instantaneous effects. Thus, temporal planning an extension of classical planning which models and reasons about time more explicitly, has been studied in the literature (among many others). Action-based temporal planning, in its general form, is computationally much more complex than classical planning, since it is EXPSPACE-complete [Rintanen, 2007]. A different paradigm, which instead has always been tightly related to temporal reasoning aspects, is timelinebased planning, which was introduced at NASA to support planning and scheduling of space operations [Muscettola, 1994]. In timeline-based planning languages, problem domains are modeled as systems composed of a set of independent, but interacting, components, whose behavior over time, the timelines, is governed by a set of temporal constraints. This point of view is different than the one of actionbased planning, as a single executor is generally not present, and the solution plan globally governs the behavior of the whole system. This approach, implemented in many planning and scheduling systems (e.g., EUROPA [Barreiro et al., 2012], ASPEN [Chien et al., 2000] and APSI-TRF [Cesta et al., 2009]), allows a greater modularity in the modeling of the behavior of systems composed of a high number of independent components, which has been proven useful in many complex use cases [Muscettola, 1994; Jónsson et al., 2000; Cesta et al., 2007]. The formalism supported by most of these systems, which has recently been thoroughly formalized by [Cialdea Mayer et al., 2016], allows one to model a kind of nondeterminism that affect the exact scheduling of activities (flexible timelines), and to model the behavior of the environment by specifying uncontrollable components. Despite its applicability, general theoretical properties of this formalism have not been deeply studied, yet. In particular, a characterization of the computational complexity of the different levels of timeline-based planning problems is missing, as well as a comprehensive comparison of the expressive power of timeline-based languages, with respect to action-based counterparts. The goal of our work is twofold: (1) to progress towards a solid theoretical understanding of the fundamental issues regarding the timeline-based planning paradigm, and (2) to compare the expressiveness of timeline-based and action-based planning languages. The results obtained so far explore both directions. In [Gigante et al., 2016] we provide a first expressiveness comparison between temporal action-based planning, in the form of the simple PDDL-equivalent planning language introduced by Rintanen [2007], and non-flexible timeline-based planning. Building upon the formalization of timelines provided in [Cialdea Mayer et al., 2016], we identify a syntactically Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI-17)