Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Engine

Chao Li; Yuru Wang

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arXiv · 2604.10908

Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Engine

Chao Li·Yuru Wang

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Abstract

Every existing knowledge system separates storage from computation. We show this separation is unnecessary and eliminate it. In a standard triple is_a(Apple, Company), domain context lives in the query or the programmer's mind. In a CDC four-tuple is_a(Apple, Company, @Business), domain becomes a structural field embedded in predicate arity. Any system respecting arity automatically performs domain-scoped inference without external rules. We call this representation-computation unity (RCU). From the four-tuple structure, three inference mechanisms emerge: domain-scoped closure, typed inheritance, and write-time falsification via cycle detection per domain fiber. We establish RCU formally via four theorems. RCU is implementable. We present a working symbolic engine (2400 lines Python+Prolog) resolving four engineering issues: rule-data separation, shared-fiber handling, read-only meta-layer design, and intersective convergence. A central result: CDC domain-constrained inference is distinct from Prolog with a domain argument. Two case studies validate the engine. ICD-11 classification (1247 entities, 3 axes) shows fibers resolve multiple inheritance. CBT clinical reasoning shows generalization to temporal reasoning with session turn as ordered domain index. Multi-constraint queries realize CSP arc-consistency with complexity O(m (N/K)^2), confirming the domain lattice's sparsity governs performance. When domain is structural, data computes itself.

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Chao Li, Yuru Wang. 2026-04-13. Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Engine. https://arxiv.org/abs/2604.10908

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