使用逻辑神经网络的神经符号归纳逻辑编程

最近关于神经符号归纳逻辑编程的工作导致了有希望的方法，可以从嘈杂的真实世界数据中学习解释规则。一些建议用来自模糊逻辑或实值逻辑的可微分算子来近似逻辑算子，这些算子是无参数的，因此削弱了它们适应数据的能力，而其他方法只是松散地基于逻辑，使其难以解释学到的 "规则"。在本文中，我们提出用最近提出的逻辑神经网络（LNN）学习规则。与其他网络相比，LNN提供了与经典布尔逻辑的紧密联系，因此可以精确地解释所学到的规则，同时它的参数可以通过基于梯度的优化训练来有效适应数据。我们将LNN扩展到一阶逻辑中诱导规则。我们在标准基准任务上的实验证实，LNN规则是高度可解释的，并且由于其灵活的参数化，可以达到相当或更高的精度。

原文题目：Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks

原文：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.