Neuro-Symbolic Reasoning refers to the integration of neural learning models f_θ with symbolic knowledge representations S and logical reasoning operators R to improve explainability and inferencing capability.
Formally, differentiable neural functions f_θ are combined with symbolic structures S (e.g., logic formulas, knowledge graphs), where reasoning operators R are applied to S to draw logical consequences.
An example are Logic Tensor Networks (LTNs), which embed logic rules as differentiable constraints into neural networks, thus enabling training with symbolic knowledge:
\[ L = L_{data} + \lambda L_{logic} \]
where \(L_{logic}\) measures the violation of symbolic rules and \(\lambda\) controls their weighting.
Neuro-Symbolic Reasoning addresses central challenges in AI, such as interpretability, knowledge integration, and robust generalization across symbolic and subsymbolic representations.
Definition:
“Neuro-Symbolic Reasoning is a hybrid AI approach that combines neural learning models with symbolic knowledge representation and logical reasoning to enable explainable and generalizable inferences.”
Source:
Garcez, A. d’Avila, Lamb, L. C., & Gabbay, D. M. (2019). Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning. Frontiers in Artificial Intelligence and Applications, 320.