Tensor Logic: A Proposed Unified Language for Neural-Symbolic AI

This paper proposes "tensor logic" as a new programming language for AI that unifies neural and symbolic AI at a fundamental level. It argues that current approaches are inadequate: Python libraries like PyTorch and TensorFlow lack support for automated reasoning and knowledge acquisition, while traditional AI languages like LISP and Prolog lack scalability and learning support. The core idea is that logical rules and Einstein summation are essentially the same operation, reducible to tensor equations. The author demonstrates how tensor logic can elegantly implement transformers, formal reasoning, kernel machines, and graphical models, and enable new capabilities like sound reasoning in embedding space — combining neural network scalability with symbolic reasoning reliability.