Counting and Reasoning with Plans

TL;DR

This paper explores quantitative and qualitative reasoning about plan spaces in classical planning, introducing new methods for counting and understanding plans, with practical implementation using knowledge compilation.

Contribution

It presents the first study on reasoning about plan spaces, introduces facets for easier counting, and implements scalable quantitative reasoning in planning.

Findings

Counting plans is computationally hard in general.

Facets help understand operator significance.

Practical framework scales well to large plan spaces.

Abstract

Classical planning asks for a sequence of operators reaching 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. Since counting 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 compilation to count different plans. This framework scales well to large plan spaces, while enabling rich reasoning capabilities such as learning pruning functions and explainable planning.