The Logic of Reachability

David E. Smith and Ari K. Jónsson

In recent years, Graphplan style reachability analysis and mutual exclusion reasoning have been used in many high performance planning systems. While numerous refinements and extensions have been developed, the basic plan graph structure and reasoning mechanisms used in these systems are tied to the very simple STRIPS model of action. In 1999, Smith and Weld generalized the Graphplan methods for reachability and mutex reasoning to allow actions to have differing durations. However, the representation of actions still has some severe limitations that prevent the use of these techniques for many real-world planning systems. In this paper, we 1) develop a logical notion of reachability that is independent of the particular representation and inference methods used in Graphplan, and 2) extend the notions of reachability and mutual exclusion to more general notions of time and action. As it turns out, the general rules for mutual exclusion reasoning take on a remarkably clean and simple form. However, practical instantiations of them turn out to be messy, and require that we make representation and reasoning choices.

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