THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture

2026-04-16 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Neuro-Symbolic AI & Reasoning · Depth: Expert, extended

Summary

THEIA is a novel, modular neural architecture designed to learn complete Kleene three-valued logic (K3) end-to-end without relying on external symbolic solvers. It processes four mathematical domains—arithmetic, order, set membership, and propositional logic—through dedicated neural engines that converge in a final logic module. Trained on a 2-million-sample dataset, THEIA achieves 12/12 Kleene K3 rule coverage across 5 seeds in an average of 9.2 minutes, demonstrating a 5.6x speedup compared to a parameter-comparable Transformer baseline under matched settings. The architecture exhibits strong compositional generalization, extending from 5-step training to 500-step evaluation with 99.97% accuracy in a mod-3 sequential composition task. Mechanistic probing reveals a "delayed verdict" phenomenon, where upstream engines encode domain-specific variables without committing to the final truth value, which emerges only at the Logic Engine boundary, a finding causally confirmed by activation patching.

Key takeaway

For Research Scientists developing neural reasoning systems, THEIA demonstrates that modular architectures offer significant advantages in learning complex logical systems like Kleene three-valued logic. You should consider implementing structured inductive biases, such as domain-separated engines, to achieve superior compositional generalization and faster convergence compared to monolithic Transformers, especially when dealing with uncertainty propagation and requiring mechanistic interpretability. This approach can lead to more robust and understandable AI systems for tasks like database query optimization or medical diagnosis.

Key insights

Structured inductive bias is crucial for compositional generalization in neural networks learning three-valued logic.

Principles

• Modularity enables faster convergence and interpretability.
• Delayed verdict is a signature of compositional reasoning.
• Flat MLPs fail compositional generalization regardless of capacity.

Method

THEIA employs domain-separated encoding with dedicated neural engines for arithmetic, order, set, and logic, converging outputs in a final logic module, and uses Gumbel-softmax for discretization in sequential composition.

In practice

• Use modular architectures for complex logical tasks.
• Prioritize Kleene-aware metrics for logic system evaluation.
• Implement activation patching for causal verification of information flow.

Topics

• Kleene Three-Valued Logic
• Modular Neural Architecture
• Compositional Generalization
• Structured Inductive Bias
• Delayed Verdict

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.