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

TL;DR

This paper introduces a unified representation-computation approach called RCU that embeds domain context within predicates, enabling inference without external rules, demonstrated through a symbolic engine and case studies.

Contribution

It formalizes RCU, a novel framework that unifies data storage and computation, and implements it in a symbolic engine validated by real-world case studies.

Findings

RCU formalized via four theorems.

Engine resolves multiple inheritance and temporal reasoning.

Performance depends on domain lattice sparsity.

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.