A Logically Complete Model Family for Gradient-Based Rule Learning

Inductive Logic Programming (ILP) learns logical rules from data, forming an interpretable machine learning model. Neuro-symbolic ILP is an emerging area where logical rules are discovered via gradient-based learning. However, existing models are limited to constrained language biases, hampering further applicability for complex rules. In this work, we propose a neuro-symbolic ILP model family that is logically complete for Horn rules. Our model relaxes all syntactically correct rules into continuous spaces and estimates the gradient to search for the semantically correct solutions. In particular, the gradient involves direct learning of logical variables, which is intractable in existing models. Experiments on standard benchmarks and recently proposed benchmarks with complex rules show that our model outperforms existing methods and LLMs.