In many usage scenarios of AI Planning technology, users will want not just a plan π but an explanation of the space of possible plans, justifying π. In particular, in oversubscription planning where not all goals can be achieved, users may ask why a conjunction A of goals is not achieved by π. We propose to answer this kind of question with the goal conjunctions B excluded by A, i. e., that could not be achieved if A were to be enforced. We formalize this approach in terms of plan-property dependencies, where plan properties are propo-sitional formulas over the goals achieved by a plan, and dependencies are entailment relations in plan space. We focus on entailment relations of the form ∧_(g∈A) g => ∧_(g∈B) g, and devise analysis techniques globally identifying all such relations, or locally identifying the implications of a single given plan property (user question) ∧_(g∈A) g. We show how, via compilation, one can analyze dependencies between a richer form of plan properties, specifying formulas over action subsets touched by the plan. We run comprehensive experiments on adapted IPC benchmarks, and find that the suggested analyses are reasonably feasible at the global level, and become significantly more effective at the local level.
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