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Learning first-order logic programs (LPs) from relational facts which yieldsintuitive insights into the data is a challenging topic in neuro-symbolicresearch. We introduce a novel differentiable inductive logic programming (ILP)model, called differentiable first-order rule learner (DFOL), which finds thecorrect LPs from relational facts by searching for the interpretable matrixrepresentations of LPs. These interpretable matrices are deemed as trainabletensors in neural networks (NNs). The NNs are devised according to thedifferentiable semantics of LPs. Specifically, we first adopt a novelpropositionalization method that transfers facts to NN-readable vector pairsrepresenting interpretation pairs. We replace the immediate consequenceoperator with NN constraint functions consisting of algebraic operations and asigmoid-like activation function. We map the symbolic forward-chained format ofLPs into NN constraint functions consisting of operations between subsymbolicvector representations of atoms. By applying gradient descent, the trained wellparameters of NNs can be decoded into precise symbolic LPs in forward-chainedlogic format. We demonstrate that DFOL can perform on several standard ILPdatasets, knowledge bases, and probabilistic relation facts and outperformseveral well-known differentiable ILP models. Experimental results indicatethat DFOL is a precise, robust, scalable, and computationally cheapdifferentiable ILP model.

Learning First-Order Rules with Differentiable Logic Program Semantics