Neuro-symbolic Weak Supervision: Theory and Semantics

Weak supervision allows machine learning models to learn from limited or noisy labels, but it introduces challenges in interpretability and reliability - particularly in multi-instance partial label learning (MI-PLL), where models must resolve both ambiguous labels and uncertain instance-label mappings. We propose a semantics for neuro-symbolic framework that integrates Inductive Logic Programming (ILP) to improve MI-PLL by providing structured relational constraints that guide learning. Within our semantic characterization, ILP defines a logical hypothesis space for label transitions, clarifies classifier semantics, and establishes interpretable performance standards. This hybrid approach improves robustness, transparency, and accountability in weakly supervised settings, ensuring neural predictions align with domain knowledge. By embedding weak supervision into a logical framework, we enhance both interpretability and learning, making weak supervision more suitable for real-world, high-stakes applications.