Towards Logic: The Language of AI (arxiv.org)

Pedro Domingos proposes "Tensor Logic," a single-construct programming language for AI in which every program is a tensor equation. The core observation is that logical rules and Einstein summation (tensor contraction) are the same algebraic operation, so neural, symbolic and statistical methods can all be expressed as tensor equations. The paper shows how common AI components—transformers, formal deductive reasoning, kernel machines and graphical models—map naturally into this language, and argues it supports automatic differentiation and efficient GPU execution while natively enabling symbolic operations like rule application and knowledge acquisition. The significance is practical and conceptual: Tensor Logic promises a unified, scalable neuro-symbolic substrate that combines neural models’ learnability and hardware efficiency with the transparency and soundness of symbolic reasoning. That could reduce the "glue" hacks currently needed to bolt reasoning onto deep-learning stacks (PyTorch/TensorFlow + Python) or to add learning to classic AI languages (LISP/Prolog). A standout implication is "sound reasoning in embedding space"—performing provably correct inference directly on learned representations—opening new directions for interpretable, provably consistent AI systems and a cleaner foundation for future models and toolchains.