Differentiable Logic Programming to Mitigate Reasoning Shortcuts in Neurosymbolic Systems

This paper proposes a matrix-based differentiable logic programming method for reducing shortcut reasoning in neurosymbolic systems. It targets two failure modes: constraint-satisfaction shortcuts, where constraints are met without solving the intended task, and cognition shortcuts, where biased data produce semantically wrong concept mappings despite valid logical inference. The method uses a unified matrix encoding for rules and constraints and studies links to fuzzy-logic t-norms and their gradient flows. Experiments on MNIST variants report that one-to-one grounding from neural outputs to logical atoms reduces both shortcut types compared with approaches using soft probability distributions. The paper also examines how neural-symbolic coupling choices affect mitigation.