Counting and Reasoning with Plans

2025-01-31

AI Summary

This work addresses the quantitative analysis of finite-horizon plan spaces in classical planning, initiating the first systematic study of scalable counting and statistical inference for polynomially bounded plans. We propose a quantitative reasoning framework grounded in propositional logic compilation and knowledge compilation (specifically, deterministic Decomposable Negation Normal Form, d-DNNF), which replaces exact counting with efficient “facet”-based significance modeling. The framework supports conditional probability estimation, operator importance quantification, and causality-driven, interpretable plan generation. Theoretically rigorous and computationally tractable, our approach significantly improves counting efficiency, importance assessment accuracy, and explanation generation capability on standard benchmarks—particularly for large-scale plan spaces. By unifying statistical reasoning with symbolic compilation, it establishes a novel paradigm for trustworthy planning.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Classical Planning
• Plan Enumeration
• Statistical Probability

Innovation

• Qualitative and Quantitative Analysis
• Plan Enumeration via Knowledge Compilation
• Explainable Planning