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.

翻译：忆阻交叉阵列存储数值权重需要聚合和解码，单个交叉点本身不包含任何意义。本文提出了一种根本不同的应用方式：每个交叉点存储一个完整的、限定领域的逻辑断言（成立/否定/未定义），并通过三元电阻状态直接编码这些值。我们建立了从领域代数到交叉阵列拓扑的结构保持映射：领域映射为独立阵列，特化映射为有向布线，关系类型控制继承门控，跨域链接映射为显式寄存器。物理布局因此直接体现代数结构，改变布线即改变推理语义。我们详细设计了一款ICD-11呼吸系统疾病分类芯片（1,247个实体，约136k个1T1R交叉点），支持领域限定、三值逻辑、传递级联、类型化继承和跨轴查询。行为仿真（sigma_log=0.15，SNR=20dB）显示，每项任务在10万次试验中均能无误差运行，且具有宽裕的容限范围。此前的工作在软件中统一了表示与计算，而本工作则在硬件中实现了这种统一：读取一个交叉点即可回答一个问题，无需符号解释。