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Towards tractable reasoning on temporal projection problems

It is well known that reasoning with AI temporal projection problems is difficult. Determining the Possible Truth problem, a basic temporal projection decision problem, in the so-called Simple Event System remains NP-complete. In this paper, two types of constraints, on the graph-theoretic representation of the cause-and-effect relationships between events and on the partial orders of events, are further considered upon this boundary NP-complete Possible Truth problem, in an attempt to gain tractability. In particular, we show that the problem is still NP-complete even if the cause-and-effect graphs maintain a strongly restricted topology, whereas it is tractable if the graph is closely associated with the set of pairwise disjoint partial orders, which in addition is hierarchically structured.