🤖 AI Summary
This work addresses the challenge that traditional knowledge systems, due to their separation of storage and computation, struggle to perform automated, structured domain-constrained reasoning. To overcome this limitation, the paper proposes a Representation-Computation Unified (RCU) paradigm, which embeds domain semantics directly into data by treating domains as structured fields within predicates (e.g., is_a(Apple, Company, @Business)). This enables domain-scoped inference without external rules. The core contributions include a novel representation method embedding domains into predicates, three key inference mechanisms—closure over domain fibers, typed inheritance, and write-time cycle detection—and their formal theoretical foundation. A symbolic reasoning engine implemented in 2,400 lines of Python and Prolog, based on a quadruple model, supports multi-constraint queries and arc-consistency solving. Empirical validation on ICD-11 multiple inheritance resolution and CBT clinical temporal reasoning demonstrates effectiveness, with complexity O(m(N/K)²), highlighting the critical impact of domain lattice sparsity on performance.
📝 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.