A neuro-symbolic knowledge graph is a hybrid AI model that combines neural embeddings of entities and relations with symbolic logic and knowledge representation to enable robust reasoning and flexible generalization.
Formally, the knowledge graph consists of a set of entities \( \mathcal{E} \), relations \( \mathcal{R} \), and facts \( \mathcal{F} \subseteq \mathcal{E} \times \mathcal{R} \times \mathcal{E} \).
Neural networks learn continuous embeddings \( \mathbf{e}, \mathbf{r} \in \mathbb{R}^d \) for entities and relations, while symbolic logic formulas \( \phi \) are defined as constraints or rules that support the model in knowledge completion and inference.
The combination allows integrating both fuzzy, learning-based patterns and precise, rule-based conclusions.
Definition:
“A neuro-symbolic knowledge graph is an AI architecture that links neural representations of knowledge with symbolic logic to create both learnable and explainable knowledge models.”
Source:
Garcez, A. d'A., Lamb, L. C., & Gabbay, D. M. (2019). Neural-Symbolic Cognitive Reasoning. Springer.