On Verifying Linear Execution Strategies in Planning Against Nature

While planning and acting in environments in which nature can trigger non-deterministic events, the agent has to consider that the state of the environment might change without its consent. Practically, it means that the agent has to make sure that it eventually achieves its goal (if possible) despite the acts of nature. In this paper, we first formalize the semantics of such problems in Alternating-time Temporal Logic, which allows us to prove some theoretical properties of different types of solutions. Then, we focus on linear execution strategies, which resemble classical plans in that they follow a fixed sequence of actions. We show that any problem that can be solved by a linear execution strategy can be solved by a particular form of linear execution strategy which assigns wait-for preconditions to each action in the plan that specifies when to execute that action. Then, we propose a sound algorithm that verifies a sequence of actions and assigns wait-for preconditions to them by leveraging abstraction.