On the Complexity of Planning Operator Subsumption

Patrick Eyerich, Michael Brenner, Bernhard Nebel

Formal action models play a central role in several subfields of AI because they are used to model application domains, e.g., in automated planning. However, there are hitherto no automated methods for relating such domain models to each other, in particular for checking whether one is a specialization or generalization of the other. In this paper, we introduce two kinds of subsumption relations between operators, both of which are suitable for modeling and verifying hierarchies between actions and operators: applicability subsumption considers an action to be more general than another if the latter can be replaced by the first at each point in each sound sequence of actions; abstraction subsumption exploits relations between actions from an ontological point of view. For both kinds of subsumption, we prove complexity results for verifying operator subsumption in three important subclasses: The problems are NP-complete when the expressiveness of the operators is restricted to the well-known basic STRIPS formalism, Σp2-complete when we admit boolean logical operators and undecidable when the full power of the planning language ADL is permitted.

Subjects: 1.11 Planning; 11. Knowledge Representation

Submitted: Jun 16, 2008

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