Neural Theorem Provers (NTPs) are neuro-symbolic models that learn to reason over knowledge bases — combining the interpretability of symbolic logic (backward chaining) with the differentiability of neural networks, allowing them to learn rules from data.

What Is an NTP?

• Function: Given a Goal, recursively apply rules ("If A and B imply C, and I want C, look for A and B").
• Neural Aspect: The "matching" of symbols is soft/differentiable (using vector similarity), not hard exact match.
• Output: A proof tree + a confidence score.
• Example: learns rule "Grandfather(X, Y) :- Father(X, Z), Father(Z, Y)" automatically.

Why It Matters

• Interpretability: Output is a human-readable proof, not a black box vector.
• Generalization: Can extrapolate to unseen entities better than pure embeddings.
• Scalability: Traditional NTPs are slow (exponential search); modern versions (CTP, GNTP) use approximate methods.

Neural Theorem Provers are differentiable logic — bridging the historic divide between Connectionism (Neural Nets) and Symbolism (Logic).