PDDL Axioms Are Equivalent to Least Fixed Point Logic

Abstract

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. We show that both variants can express exactly the same queries as least fixed point logic. They are thus strictly more expressive than stratified Datalog, which aligns with another restriction on axioms occasionally considered in the planning literature. Complementing this theoretical analysis, we also present a compilation that eliminates negative occurrences of derived predicates from PDDL axioms.