PPDDL Semantics

For completeness, we present a formal semantics for PPDDL planning problems in terms of a mapping to a probabilistic transition system with rewards. A planning problem defines a set of state variables V, possibly containing both Boolean and numeric state variables, although we only consider planning problems without any numeric state variables in this section. An assignment of values to state variables defines a state, and the state space S of the planning problem is the set of states representing all possible assignments of values to variables. In addition to V, a planning problem defines an initial-state distribution p₀ : S → [0, 1] with $\sum_{{s\in S}}^{}$p₀(s) = 1 (that is, p₀ is a probability distribution over states), a formula φ_G over V characterizing a set of goal states G = {s | s $\models$ φ_G}, a one-time reward r_G associated with entering a goal state, and a set of actions A instantiated from PPDDL action schemata. For goal-directed planning problems, without explicit rewards, we use r_G = 1.