On the Nature of Modal Truth in Plans

Chapman’s paper, “Planning for Conjunctive Goals,” has been widely acknowledged as a major step towards understanding the nature of nonlinear planning, and it has been one of the bases of later work by others—but it is not free of problems. This paper discusses the following problems with modal truth and the modal truth criterion. 1. It is NP-hard to tell, given a plan P and a ground atom p, whether P is possibly true in P ’s final situation. This is true despite the fact that modal truth criterion can be computed in polynomial time. 2. The reason for this discrepancy is that the “possible truth” version of the modal truth criterion is incorrect. It tells whether ¬p is not necessarily true—but this is different from telling whether p is possibly true. Possible truth is not the dual of necessary truth, as Chapman had thought it was. 3. Instead, possible truth is the dual of another problem, which is co-NP-hard: the problem of determining whether p is true over all executable completions of a plan. Despite the above problems, the “necessary truth” version of the modal truth criterion (and hence the tweak planner) are still correct. ∗This work was supported in part by NSF Grants IRI-8907890 and NSFD CDR-88003012.