Court judgments reveal how legal rules have been interpreted and applied to facts, providing a foundation for understanding structured legal reasoning. However, existing automated approaches for capturing legal reasoning, including large language models, often fail to identify the relevant legal context, do not accurately trace how facts relate to legal norms, and may misrepresent the layered structure of judicial reasoning. These limitations hinder the ability to capture how courts apply the law to facts in practice. In this paper, we address these challenges by constructing a legal knowledge graph from 648 Japanese administrative court decisions. Our method extracts components of legal reasoning using prompt-based large language models, normalizes references to legal provisions, and links facts, norms, and legal applications through an ontology of legal inference. The resulting graph captures the full structure of legal reasoning as it appears in real court decisions, making implicit reasoning explicit and machine-readable. We evaluate our system using expert annotated data, and find that it achieves more accurate retrieval of relevant legal provisions from facts than large language model baselines and retrieval-augmented methods.