When both Grounding and not Grounding are Bad -- A Partially Grounded Encoding of Planning into SAT (Extended Version)

2026-03-19

AI Summary

This work addresses the exponential state-space blowup caused by full grounding in classical planning and the inefficiency of purely lifted representations. To bridge this gap, the paper proposes three partially grounded SAT encodings that selectively ground only predicates while preserving actions in lifted form. This approach achieves, for the first time, a SAT encoding whose size grows linearly with plan length, thereby overcoming the quadratic complexity bottleneck of prior methods. Experimental results demonstrate that the proposed encodings significantly outperform state-of-the-art optimal-length planners on domains where grounding is particularly challenging.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Multiagent Systems: Multiagent Planning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Classical planning problems are typically defined using lifted first-order representations, which offer compactness and generality. While most planners ground these representations to simplify reasoning, this can cause an exponential blowup in size. Recent approaches instead operate directly on the lifted level to avoid full grounding. We explore a middle ground between fully lifted and fully grounded planning by introducing three SAT encodings that keep actions lifted while partially grounding predicates. Unlike previous SAT encodings, which scale quadratically with plan length, our approach scales linearly, enabling better performance on longer plans. Empirically, our best encoding outperforms the state of the art in length-optimal planning on hard-to-ground domains.

Problem

• classical planning
• grounding
• lifted representation
• SAT encoding
• exponential blowup

Innovation

• partially grounded encoding
• lifted planning
• SAT encoding
• linear scaling
• length-optimal planning