Learning First-Order Rules with Differentiable Logic Program Semantics

TL;DR

This paper introduces DFOL, a differentiable ILP model that learns first-order logic rules from relational data using neural networks and interpretable matrix representations, enabling scalable and accurate rule induction.

Contribution

The paper presents a novel differentiable ILP approach, DFOL, which learns interpretable first-order logic rules from relational facts using neural network-based matrix representations.

Findings

DFOL outperforms existing differentiable ILP models on standard datasets.

DFOL is scalable and robust in learning first-order rules.

DFOL is computationally efficient and precise.

Abstract

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.