Differentiable Logic Programming to Mitigate Reasoning Shortcuts in Neurosymbolic Systems

2026-07-23

AI Summary

This work addresses the susceptibility of neurosymbolic systems to reasoning shortcuts—such as constraint-satisfaction and cognitive shortcuts—that often result in incomplete task execution or inaccurate concept grounding. To mitigate this issue, the authors propose a matrix-based differentiable logic programming approach that unifies logical rules and constraints within a single matrix, enabling one-to-one grounding between neural network outputs and logical atoms. The method establishes a theoretical connection to fuzzy logic t-norms and leverages t-norm gradient flow analysis to elucidate the critical role of neurosymbolic coupling architectures in suppressing reasoning shortcuts. Experimental results on MNIST variants demonstrate that the proposed approach significantly reduces both types of shortcuts and outperforms existing methods relying on soft probabilistic distributions.

Abstract

Neurosymbolic (NeSy) systems integrate neural networks with logical reasoning to achieve both generalization and interpretability, but recent work has shown they are susceptible to shortcut reasoning behaviors. We propose a novel method using matrix-based differentiable logic programming to mitigate reasoning shortcuts in two phenomena: constraint satisfaction shortcuts, where constraints are satisfied without achieving the intended task, and cognition shortcuts, where biased data leads to semantically incorrect concept mappings despite logically sound inference. Building on recent matrix-based logic programming semantics, we introduce design elements to mitigate shortcuts, including a unified encoding of rules and constraints in a single matrix. We also identify connections to fuzzy logic t-norms and empirically compare their gradient flow properties. Through carefully designed experiments on MNIST variants, we show that one-to-one grounding of neural outputs to logical atoms significantly reduces both shortcut types compared to previous methods that rely on soft probability distributions. We then confirm that architectural choices in coupling symbolic knowledge with neural learning play a critical role in shortcut mitigation.

Problem

• neurosymbolic systems
• reasoning shortcuts
• constraint satisfaction shortcuts
• cognition shortcuts

Innovation

• differentiable logic programming
• neurosymbolic systems
• reasoning shortcuts
• matrix-based semantics
• t-norms