Eliminating Negative Occurrences of Derived Predicates from PDDL Axioms

Axioms are a feature of the Planning Domain Definition Language PDDL that can be considered as a generalization of database query languages such as Datalog. The PDDL standard restricts negative occurrences of predicates in axiom bodies to predicates that are directly set by actions and not derived by axioms. In the literature, authors often deviate from this limitation and only require that the set of axioms is stratifiable. Both variants can express exactly the same queries as least fixed-point logic, indicating that negative occurrences of derived predicates can be eliminated. We present the corresponding transformation.

Pseudo-Boolean Proof Logging for Optimal Classical Planning

We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general framework for generating lower-bound certificates based on pseudo-Boolean constraints, which is agnostic to the planning algorithm used. As a case study, we show how to modify the $A^{*}$ algorithm to produce proofs of optimality with modest overhead, using pattern database heuristics and $h^\textit{max}$ as concrete examples. The same proof logging approach works for any heuristic whose inferences can be efficiently expressed as reasoning over pseudo-Boolean constraints.