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Tensor Logic Reasoning

A small experiment inspired by Pedro Domingos' paper
"Tensor Logic: The Language of AI" and his appearance on
Machine Learning Street Talk.

Goal: Show on minimal surface area how

  • Facts (Parent(Alice, Bob))
  • Rules (Ancestor(x, z) as the transitive closure of Parent)
  • Logical inference
  • Embeddings
  • Reasoning in embedding space

can be thought of within a unified tensor formalism.

Concept

The script tensor_logic_demo.py:

  1. Defines a small world with four entities:

  2. Alice, Bob, Charlie, David

  3. Creates a Parent relation as a boolean matrix.

  4. Computes the Ancestor relation as the transitive closure of Parent.

  5. Generates random, normalized embeddings for each entity.

  6. Builds a relation tensor EmbParent[i, j] containing the superposition of tensor products of all Parent pairs.

  7. Answers queries Parent(a, b) in two ways:

  8. Logical: directly from the Parent matrix

  9. Embedding-based: via

    [ \text{score}(a,b) = Emb[a]^T \cdot EmbParent \cdot Emb[b] ]

    and a logistic function with temperature \(T\).

Usage

```bash cd simulation-models/tensor-logic-reasoning python3 tensor_logic_demo.py