# Ternary Memristive Logic: Hardware for Reasoning Realized via Domain Algebra

arXiv: https://arxiv.org/abs/2604.20891 · HTML: https://mlsanity.com/paper/2604.20891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 11 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Abstract (arXiv)

Memristive crossbars store numerical weights needing aggregation and decoding; a single junction means nothing alone. This paper presents a fundamentally different use: each junction stores a complete, domain-scoped logical assertion (holds/negated/undefined). Ternary resistance states encode these values directly. We establish a structure-preserving mapping from a domain algebra to crossbar topology: domains become isolated arrays, specialization becomes directed wiring, relation typing controls inheritance gates, and cross-domain links become explicit registers. The physical layout thus embodies the algebra; changing wiring changes reasoning semantics. We detail an ICD-11 respiratory disease classification chip (1,247 entities, ~136k 1T1R junctions) enabling domain scoping, three-valued logic, transitive cascade, typed inheritance, and cross-axis queries. Behavioral simulation (sigma_log=0.15, SNR=20dB) shows error-free operation across 100,000 trials per task with wide tolerance margins. Where prior work unified representation and computation in software, this work unifies them in hardware: reading one junction answers one question, without symbolic interpretation.