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This paper proposes the "Hierarchical Directed Acyclic Graph (HDAG) Kernel" for structured natural language data. The HDAG Kernel directly accepts several levels of both chunks and their relations, and then efficiently computes the weighed sum of the number of common attribute sequences of the HDAGs. We applied the proposed method to question classification and sentence alignment tasks to evaluate its performance as a similarity measure and a kernel function. The results of the experiments demonstrate that the HDAG Kernel is superior to other kernel functions and baseline methods.