The Japanese Society for Artificial Intelligence

We propose a method that integrates data-driven approaches and symbolic reasoning in Neural-Symbolic AI (NeSy). This method evaluates implication rules and constraints in a differentiable way by using the output of neural networks and logic programs embedded in matrices, enabling efficient learning under distant supervision where direct labels are not provided. When the number of training data was fixed, our method achieved accuracy comparable to or higher than the existing methods in most tasks and completed the learning process faster than the existing methods. These results demonstrate the effectiveness of our proposed method as an approach for achieving high accuracy and rapid learning in NeSy.