We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of regularization constraints to the learning problem, we exploit a pooling mechanism that incorporates such notion of fragments within the node soft assignment function that produces the embeddings. We present an extensive experimental evaluation on a collection of sentence classification tasks conducted on several argument mining corpora, showing that the proposed approach performs well with respect to state-of-the-art techniques.