Neuro-Symbolic AI refers to hybrid AI models that combine neural networks with symbolic knowledge representation and logical reasoning to enable both learning-based pattern recognition and explainable inference.
Formally, neuro-symbolic systems can be defined as a pair \( (N, S) \), where \( N \) is a neural network with parameters \( \theta \) for processing fuzzy data, and \( S \) is a symbolic system with a knowledge base \( \mathcal{K} \) and logical rules \( \mathcal{R} \) that enable deductive inference.
The integration is achieved through techniques such as symbolic constraints during training, neural embeddings of symbolic expressions, or differentiable logical modules embedded in neural architectures.
This allows efficient learning from data while maintaining interpretability and verifiability through symbolic logic.
Definition:
“Neuro-Symbolic AI is an approach that combines neural and symbolic methods to unite the strengths of both paradigms – learning-based pattern recognition and logical reasoning – in one system.”
Source:
Garcez, A. d’Avila, Lamb, L. C., & Gabbay, D. M. (2020). Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning. Frontiers in Artificial Intelligence and Applications.