THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture
We present THEIA, a 2.75M-parameter modular neural architecture that learns the complete Kleene three-valued logic (K3) truth table from task data without external symbolic inference or hand-encoded K3 gate primitives. Across 5 seeds it passes all 39 K3 rules at >99% per-rule accuracy. K3 learnability is not the central finding: Transformer baselines also pass all 39 rules, and flat MLPs match THEIA on Phase-1 accuracy within 0.04pp. The contributions are two properties of the learned system. (1) Uncertainty-verdict asymmetric propagation. THEIA preserves Has-Unknown at every upstream boundary (80.0/91.1/90.8/99.7% across Arith/Order/Set/Logic vs. ~52% majority) while final-verdict decoda...
| Authors | Augustus Haoyang Li |
|---|---|
| Primary category | cs.LG |
| Published | 13 April 2026 |
| Last updated at source | 23 June 2026 |
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