A new neural architecture can handle 'I don't know' as a logical state with 99.97% accuracy across 500-step problems.
April 14, 2026
Original Paper
THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture
arXiv · 2604.11284
The Takeaway
By implementing Kleene Three-Valued Logic, this modular architecture bridges the gap between neural networks and strict symbolic logic. It maintains near-perfect consistency even when tasks are 100x longer than those seen in training.
From the abstract
We present THEIA, a modular neural architecture that learns complete Kleene three-valued logic (K3) end-to-end without any external symbolic solver, and investigate what architectural prior enables compositional generalization under uncertainty. THEIA processes four mathematical domains (arithmetic, order, set membership, propositional logic) through dedicated engines that converge in a final logic module. Trained on a 2M-sample dataset with input space ~3.4x10^13, it achieves 12/12 Kleene K3 ru