# Counting and Reasoning with Plans

arXiv: https://arxiv.org/abs/2502.00145 · HTML: https://mlsanity.com/paper/2502.00145/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 79 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 9 of 9)

- [Clingo = ASP + Control: Preliminary Report](https://mlsanity.com/paper/1405.3694/) (2014)
- [Learning Domain-Independent Planning Heuristics with Hypergraph Networks](https://mlsanity.com/paper/1911.13101/) (2019)
- [Learning Domain-Independent Heuristics for Grounded and Lifted Planning](https://mlsanity.com/paper/2312.11143/) (2023)
- [The Model Counting Competition 2020](https://mlsanity.com/paper/2012.01323/) (2020)
- [Contrastive Explanations of Plans Through Model Restrictions](https://mlsanity.com/paper/2103.15575/) (2021)
- [Answer Set Solving with Bounded Treewidth Revisited](https://mlsanity.com/paper/1702.02890/) (2017)
- [Rushing and Strolling among Answer Sets -- Navigation Made Easy](https://mlsanity.com/paper/2112.07596/) (2021)
- [Stable Model Counting and Its Application in Probabilistic Logic Programming](https://mlsanity.com/paper/1411.5410/) (2014)
- [Disjoint Partial Enumeration without Blocking Clauses](https://mlsanity.com/paper/2306.00461/) (2023)

## Built on by (most cited first, 2 of 2)

- [Facets in Argumentation: A Formal Approach to Argument Significance](https://mlsanity.com/paper/2505.10982/) (2025)
- [Complexity of Faceted Explanations in Propositional Abduction](https://mlsanity.com/paper/2507.14962/) (2025)

## Abstract (arXiv)

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.