Differentiable Inductive Logic Programming with Unbound Logic

Differentiable inductive logic programming is an emerging area where logical rules are learned by differentiable models. The fundamental principle behind existing methods is relaxing forward chaining, a symbolic deduction procedure, into a continuous space. However, these methods rely on bound truth values and/or selective fuzzy logic operators, which suffer from gradient vanishing or imbalanced gradient flow. To this end, we propose using unbound logic, where truth values are further relaxed into unbound real numbers and fuzzy logic operators are non-selective, which theoretically alleviates the local gradient issues. Experiments show that our method achieves superior performance on inductive logic programming tasks. In addition, we explore combining neural perception networks with our fully differentiable logical models, resulting in an end-to-end differentiable model that achieves comparable performance with non-end-to-end visual ILP methods.