First-order logical neural networks

Inductive logic programming (ILP) is a well known machine learning technique in learning concepts from relational data. Nevertheless, ILP systems are not robust enough to noisy or unseen data in real world domains. Furthermore, in multiclass problems, if the example is not matched with any learned rules, it cannot be classified. This paper presents a novel hybrid learning method to alleviate this restriction by enabling neural networks to handle first-order logic programs directly. The proposed method, called first-order logical neural network (FOLNN), is based on feedforward neural networks and integrates inductive learning from examples and background knowledge. We also propose a method for determining the appropriate variable substitution in FOLNN learning by using multiple-instance learning (MIL). In the experiments, the proposed method has been evaluated on two first-order learning problems, i.e., the finite element mesh design and mutagenesis and compared with the state-of-the-art, the PROGOL system. The experimental results show that the proposed method performs better than PROGOL.