HTN Plan Verification by Qualitative Temporal Reasoning

Plan verification is the task of checking whether a proposed plan correctly solves a given planning problem. In Hierarchical Task Network (HTN) planning, this verification problem is known to be NP-hard. Existing approaches to HTN plan verification range from SAT encodings to parser-based techniques. However, existing methods do not explicitly exploit the temporal structure inherent in hierarchical decomposition. In this paper, we establish a formal connection between HTN planning and temporal reasoning by showing how decomposition structures can be naturally represented using qualitative constraint networks. Building on this insight, we present a new top-down encoding that transforms the verification of partially ordered task networks into a temporal reasoning problem. We prove the correctness of this encoding and explain how it accounts for both the hierarchical and temporal aspects of HTN plans. By linking HTN plan verification with qualitative temporal reasoning, our approach introduces a principled formal framework for reasoning about complex temporal relationships in hierarchical plans. This connection offers new perspectives for knowledge representation in structured planning domains.