This paper presents a new task, learning logical structures of paragraphs in legal articles, which is studied in research on Legal Engineering (Katayama, 2007). The goals of this task are recognizing logical parts of law sentences in a paragraph, and then grouping related logical parts into some logical structures of formulas, which describe logical relations between logical parts. We present a two-phase framework to learn logical structures of paragraphs in legal articles. In the first phase,

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... e model the problem of recognizing logical parts in law sentences as a multi-layer sequence learning problem, and present a CRF-based model to recognize them. In the second phase, we propose a graph-based method to group logical parts into logical structures. We consider the problem of finding a subset of complete sub-graphs in a weighted-edge complete graph, where each node corresponds to a logical part, and a complete sub-graph corresponds to a logical structure. We also present an integer linear programming formulation for this optimization problem. Our models achieve 74.37% in recognizing logical parts, 79.59% in recognizing logical structures, and 55.73% in the whole task on the Japanese National Pension Law corpus.