Ternary Memristive Logic: Hardware for Reasoning Realized via Domain Algebra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910171994783744 |
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| author | Li, Chao |
| author_facet | Li, Chao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20891 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ternary Memristive Logic: Hardware for Reasoning Realized via Domain Algebra Li, Chao Hardware Architecture Artificial Intelligence Emerging Technologies Logic in Computer Science 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. |
| title | Ternary Memristive Logic: Hardware for Reasoning Realized via Domain Algebra |
| topic | Hardware Architecture Artificial Intelligence Emerging Technologies Logic in Computer Science |
| url | https://arxiv.org/abs/2604.20891 |