Abductive Knowledge Induction from Raw Data

For many reasoning-heavy tasks, it is challenging to find an appropriate end-to-end differentiable approximation to domain-specific inference mechanisms. Neural-Symbolic (NeSy) AI divides the end-to-end pipeline into neural perception and symbolic reasoning, which can directly exploit general domain knowledge such as algorithms and logic rules. However, it suffers from the exponential computational complexity caused by the interface between the two components, where the neural model lacks direct supervision, and the symbolic model lacks accurate input facts. As a result, they usually focus on learning the neural model with a sound and complete symbolic knowledge base while avoiding a crucial problem: where does the knowledge come from? In this paper, we present Abductive Meta-Interpretive Learning (MetaAbd), which unites abduction and induction to learn perceptual neural network and first-order logic theories simultaneously from raw data. Given the same amount of domain knowledge, we demonstrate that MetaAbd not only outperforms the compared end-to-end models in predictive accuracy and data efficiency but also induces logic programs that can be re-used as background knowledge in subsequent learning tasks. To the best of our knowledge, MetaAbd is the first system that can jointly learn neural networks and recursive first-order logic theories with predicate invention.