This paper points out the limitations of existing programming languages that hinder the development of AI and proposes a new language called tensor logic, which fundamentally unifies neural networks and symbolic AI. Tensor logic is based on a single construct called tensor equations and the observation that logical rules and Einstein summation are essentially the same operation. It presents an elegant way to implement key forms of neural networks, symbolic AI, and statistical AI—such as transformers, formal inference, kernel machines, and graphical models—in tensor logic. This opens up new possibilities, such as precise inference in embedding spaces, potentially laying the foundation for widespread adoption of AI.
