In the recent past, there has been a growing interest in Neural-Symbolic
Integration frameworks, i.e., hybrid systems that integrate connectionist and
symbolic approaches to obtain the best of both worlds. In this work we focus on
a specific method, KENN (Knowledge Enhanced Neural Networks), a Neural-Symbolic
architecture that injects prior logical knowledge into a neural network by
adding on its top a residual layer that modifies the initial predictions
accordingly to the knowledge. Among the advantages of this strategy, there is
the inclusion of clause weights, learnable parameters that represent the
strength of the clauses, meaning that the model can learn the impact of each
rule on the final predictions. As a special case, if the training data
contradicts a constraint, KENN learns to ignore it, making the system robust to
the presence of wrong knowledge. In this paper, we propose an extension of KENN
for relational data. One of the main advantages of KENN resides in its
scalability, thanks to a flexible treatment of dependencies between the rules
obtained by stacking multiple logical layers. We show experimentally the
efficacy of this strategy. The results show that KENN is capable of increasing
the performances of the underlying neural network, obtaining better or
comparable accuracies in respect to other two related methods that combine
learning with logic, requiring significantly less time for learning.

本研究介绍了一种名为 KENN 的神经符号一体化框架，其将先前的逻辑知识注入神经网络。通过增加一个残差层来修改初始预测，这种方法的优点之一是包含条款权重，这些可学习参数表示条款的强度和影响。本研究的扩展版本更适用于关系数据，并在实验中验证了其有效性和可扩展性。