Logical Encodings With No Time Indexes for Defining and Computing Admissible Heuristics for Planning

A limitation of the SAT approach to planning and the more recent Weighted-SAT approach to planning with preferences is the use of logical encodings where every fluent and action must be tagged with a time index. The result is that the complexity of the encodings grows exponentially with the planning horizon, and for metrics other than makespan, the optimality achieved is conditional on the planning horizon used. In this work, we consider the use of logical encodings in planning but for defining and computing admissible heuristics only, for which no time indices or planning horizons are required. The basic logical formulation, following a recent proposal by Bonet and Geffner in KR-06, captures a generalization of the optimal delete-relaxation heuristic, which is then extended with implicit plan constraints for boosting their values by capturing information lost in the delete-relaxation, and with a structural relaxation scheme for CNF formulae recently proposed by Ramirez and Geffner in CP-07 that reduces the treewidth of the theory to any bound w, producing thus poly-time admissible heuristics h that are able to handle costs and rewards, and (some) delete information. The experimental results, although preliminary, show that in some domains, these heuristics are cost-effective and can be competitive with the best known heuristics.