Tensor Logic: The Language of AI
Authors: name: Pedro Domingos
Published: 2025-10-14 08:24:08

Abstract: Progress in AI is hindered by the lack of a programming language with all the
requisite features. Libraries like PyTorch and TensorFlow provide automatic
differentiation and efficient GPU implementation, but are additions to Python,
which was never intended for AI. Their lack of support for automated reasoning
and knowledge acquisition has led to a long and costly series of hacky attempts
to tack them on. On the other hand, AI languages like LISP an Prolog lack
scalability and support for learning. This paper proposes tensor logic, a
language that solves these problems by unifying neural and symbolic AI at a
fundamental level. The sole construct in tensor logic is the tensor equation,
based on the observation that logical rules and Einstein summation are
essentially the same operation, and all else can be reduced to them. I show how
to elegantly implement key forms of neural, symbolic and statistical AI in
tensor logic, including transformers, formal reasoning, kernel machines and
graphical models. Most importantly, tensor logic makes new directions possible,
such as sound reasoning in embedding space. This combines the scalability and
learnability of neural networks with the reliability and transparency of
symbolic reasoning, and is potentially a basis for the wider adoption of AI.