Learning first-order logic programs (LPs) from relational facts which yields
intuitive insights into the data is a challenging topic in neuro-symbolic
research. We introduce a novel differentiable inductive logic programming (ILP)
model, called differentiable first-order rule learner (DFOL), which finds the
correct LPs from relational facts by searching for the interpretable matrix
representations of LPs. These interpretable matrices are deemed as trainable
tensors in neural networks (NNs). The NNs are devised according to the
differentiable semantics of LPs. Specifically, we first adopt a novel
propositionalization method that transfers facts to NN-readable vector pairs
representing interpretation pairs. We replace the immediate consequence
operator with NN constraint functions consisting of algebraic operations and a
sigmoid-like activation function. We map the symbolic forward-chained format of
LPs into NN constraint functions consisting of operations between subsymbolic
vector representations of atoms. By applying gradient descent, the trained well
parameters of NNs can be decoded into precise symbolic LPs in forward-chained
logic format. We demonstrate that DFOL can perform on several standard ILP
datasets, knowledge bases, and probabilistic relation facts and outperform
several well-known differentiable ILP models. Experimental results indicate
that DFOL is a precise, robust, scalable, and computationally cheap
differentiable ILP model.

本研究提出一种名为 DFOL 的新型可微分归纳逻辑编程模型，通过搜索可解释的矩阵来从关系事实中找到正确的一阶逻辑程序，并将符号前向链接格式转换为 NN 约束函数，并采用梯度下降将 NN 的训练参数解码成精确的符号逻辑程序。