Classical planning asks for a sequence of operators reach-ing a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored. A fundamental problem is to count plans, which relates to the conditional probability on the plan space. Indeed, qualitative and quantitative approaches are well-established in various other areas of automated reasoning.

We present the first study to quantitative and qualitative reasoning on the plan space. In particular, we focus on polynomially bounded plans. On the theoretical side, we study its complexity, which gives rise to rich reasoning modes. Sincecounting is hard in general, we introduce the easier notion of facets, which enables understanding the significance of operators. On the practical side, we implement quantitative reasoning for planning. Thereby, we transform a planning task into a propositional formula and use knowledge compilationto count different plans. This framework scales well to largeplan spaces, while enabling rich reasoning capabilities suchas learning pruning functions and explainable planning.