neural theorem provers

**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).