The use of expressive logical axioms to specify derived predicates often allows planning domains to be formulated more compactly and naturally. We consider axioms in the form of a logic program with recursively defined predicates and negation-as-failure, as in PDDL 2.2. We show that problem formulations with axioms are not only more elegant, but can also be easier to solve, because specifying indirect action effects via axioms removes unnecessary choices from the search space of the planner. Despite their potential, however, axioms are not widely supported, particularly by cost-optimal planners. We draw on the connection between planning axioms and answer set programming to derive a consistency-based relaxation, from which we obtain axiom-aware versions of several admissible planning heuristics, such as hmax and pattern database heuristics.

We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning context.