Planning for temporally extended goals in pure-past linear temporal logic

Abstract

We study planning for temporally extended goals expressed in Pure-Past Linear Temporal Logic (ppltl) in the context of deterministic (i.e., classical) and fully observable nondeterministic (FOND) domains. ppltl is the variant of Linear-time Temporal Logic on finite traces (ltl_f) that refers to the past rather than the future. Although ppltl is as expressive as ltl_f, we show that it is computationally much more effective for planning. In particular, we show that checking the validity of a plan for a ppltl formula is Markovian. This is achieved by introducing a linear number of additional propositional variables that capture the validity of the entire formula in a modular fashion. The solution encoding introduces only a linear number of new fluents proportional to the size of the ppltl goal and does not require any additional spurious action. We implement our solution technique in a system called $\mathrm{Plan4Past}$, which can be used alongside state-of-the-art classical and FOND planners. Our empirical analysis demonstrates the practical effectiveness of $\mathrm{Plan4Past}$ in both classical and FOND problems, showing that the resulting planner performs overall better than other planning approaches for ltl_f goals.