While existing neural networks demonstrate excellent classification performance, they suffer from limitations in that they cannot be inspected, validated, or extracted from the learning process. In this paper, we generalize neural logic networks (NNs) with an interpretable structure that can learn the logical mechanism between inputs and outputs using AND and OR operations. We add NOT operations and biases to account for unobserved data, and develop rigorous logical and probabilistic modeling in terms of concept combinations to support the network's usability. Furthermore, we propose a novel factorized IF-THEN rule structure and a modified learning algorithm. This study advances the state-of-the-art in Boolean network discovery, enabling the learning of relevant and interpretable rules, particularly for examples in healthcare and industrial settings where interpretability has practical value.
