Integrating logical reasoning and machine learning by approximating logical inference with differentiable operators is a widely used technique in Neuro-Symbolic systems. However, some differentiable operators could bring a significant bias during backpropagation and degrade the performance of Neuro-Symbolic learning. In this paper, we reveal that this bias, named \textit{Implication Bias} is common in loss functions derived from fuzzy logic operators. Furthermore, we propose a simple yet effective method to transform the biased loss functions into \textit{Reduced Implication-bias Logic Loss (RILL)} to address the above problem. Empirical study shows that RILL can achieve significant improvements compared with the biased logic loss functions, especially when the knowledge base is incomplete, and keeps more robust than the compared methods when labelled data is insufficient.

翻译：通过可微算子近似逻辑推理，将逻辑推理与机器学习相融合是神经符号系统中广泛使用的技术。然而，部分可微算子在反向传播过程中可能引入显著偏差，从而降低神经符号学习的性能。本文揭示了此类偏差（称为蕴含偏差）在基于模糊逻辑算子的损失函数中具有普遍性。进一步地，我们提出了一种简单有效的方法，将存在偏差的损失函数转化为降低蕴含偏差逻辑损失函数（RILL）以解决上述问题。实证研究表明，与存在偏差的逻辑损失函数相比，RILL能够实现显著性能提升，尤其在知识库不完备的情况下；同时，当标注数据不足时，该方法相比对比方法表现出更强的鲁棒性。