Implementing Tensor Logic: Unifying Datalog and Neural Reasoning via Tensor Contraction

TL;DR

This paper empirically validates Tensor Logic, unifying symbolic Datalog reasoning with neural networks through tensor contraction, enabling scalable, interpretable reasoning in large knowledge graphs.

Contribution

It demonstrates the equivalence between Datalog rules and tensor contractions, and shows how neural embeddings can perform zero-shot and multi-hop reasoning using tensor-based methods.

Findings

Transitive closure computed in 74 iterations on a biblical genealogy graph.

Neural network trained for zero-shot compositional inference successfully.

Achieved MRR of 0.3068 on link prediction and 0.3346 on compositional reasoning on FB15k-237.

Abstract

The unification of symbolic reasoning and neural networks remains a central challenge in artificial intelligence. Symbolic systems offer reliability and interpretability but lack scalability, while neural networks provide learning capabilities but sacrifice transparency. Tensor Logic, proposed by Domingos, suggests that logical rules and Einstein summation are mathematically equivalent, offering a principled path toward unification. This paper provides empirical validation of this framework through three experiments. First, we demonstrate the equivalence between recursive Datalog rules and iterative tensor contractions by computing the transitive closure of a biblical genealogy graph containing 1,972 individuals and 1,727 parent-child relationships, converging in 74 iterations to discover 33,945 ancestor relationships. Second, we implement reasoning in embedding space by training a neural network with learnable transformation matrices, demonstrating successful zero-shot compositional inference on held-out queries. Third, we validate the Tensor Logic superposition construction on FB15k-237, a large-scale knowledge graph with 14,541 entities and 237 relations. Using Domingos's relation matrix formulation $R_r = E^\top A_r E$, we achieve MRR of 0.3068 on standard link prediction and MRR of 0.3346 on a compositional reasoning benchmark where direct edges are removed during training, demonstrating that matrix composition enables multi-hop inference without direct training examples.