Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks
This addresses the challenge of interpretability and data fitting in rule learning for AI, though it is incremental as it builds on existing LNNs by extending them to first-order logic.
The paper tackles the problem of learning interpretable rules from noisy data in neuro-symbolic inductive logic programming by proposing logical neural networks (LNNs) that combine classical Boolean logic with trainable parameters, achieving comparable or higher accuracy on standard benchmarks.
Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned "rules". In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer strong connection to classical Boolean logic thus allowing for precise interpretation of learned rules while harboring parameters that can be trained with gradient-based optimization to effectively fit the data. We extend LNNs to induce rules in first-order logic. Our experiments on standard benchmarking tasks confirm that LNN rules are highly interpretable and can achieve comparable or higher accuracy due to their flexible parameterization.