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

Chao Li; Yuru Wang

cs.AIApr 13, 2026

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

Authors: Chao Li, Yuru Wang

Organizations: Northeast Normal University

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.

Figures & tables

Database operation	Inference operation
INSERT {c, r, d, c’}	Assert a domain-scoped fact
SELECT WHERE domain=d	Query within a world
DELETE {c, r, d, c’}	Retract a belief
JOIN on domain	Compute transitive inference
FOREIGN KEY to meta-fiber	Enforce type constraint

Table 1

Dimension	SQL	RDF	LLM	RAG	Neuro-Sym	CDC
Context location	Application code	Query clause	Prompt	Retrieval filter	Bridge code	Predicate arity
Rule location	Separate code	SPARQL query	Implicit in weights	LLM forward pass	Symbolic KB	Meta-fiber data
Verification	External validator	External validator	Self-consistency	Separate checker	Symbolic layer	Write-time check
Reasoning chain	Derived	Derived	Ephemeral	Ephemeral	Partial	Native data
Domain change cost	Schema migration	Ontology realignment	Retraining	Re-embedding	Manual update	New fiber
S/C separation	Yes	Yes	Yes	Yes	Yes	No

Table 2

Panel of Figure 1 — Figure 1: Operational structure of the CDC inference engine.

Property	Prolog + domain argument	CDC engine
Write-time constraint	None	Fiber consistency check on INSERT
Inheritance rules	Hardcoded in clause files	Stored in @Meta@Logic, runtime-queryable
Typing function $\tau$	Not representable	Four-tuples in meta-fiber, modifiable as data
Domain lattice	String atom, no ordering	First-class partial order, drives reindexing
Data format	Prolog syntax, interpreter-bound	JSON, language-agnostic
Substrate	Symbolic only	Symbolic / neural / vector (same interface)

Table 4

Constraints applied	Candidates	Reduction
0 (full fiber)	1,247	—
fever	89	93%
+ productive_cough	23	74%
+ bilateral_infiltrates	7	70%
+ positive_culture	4	43%

Table 5

Operation	N=1,247
Single fiber query	< 5ms
Transitive closure (within fiber)	< 20ms
Write with validation	< 10ms
Typed reindexing (full lattice)	< 200ms
OWL $\to$ CDC migration	< 30s
Cross-domain bridge query	< 15ms

Table 6

Metric	Value
Therapy stages traced	5
Negative patterns	11
Positive changes	8
Evidence balance ratio	3.0 (positive:negative)
Correct temporal ordering	100%
False contradiction insertions rejected	100%

Table 7

Symbolic Reasoning

Symbolic reasoning uses explicit symbols, rules, and constraints to derive, verify, and explain conclusions across logic, mathematics, and planning.

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Domain-Contextualized Inference: A Computable Graph Architecture for Explicit-Domain Reasoning

Chao Li, Yuru Wang, Chunyi Zhao

Northeast Normal University · University of Otago

Efficient Inference Graph Reasoning

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We establish a computation-substrate-agnostic inference architecture in which domain is an explicit first-class computational parameter. This produces domain-scoped pruning that reduces per-query search space from O(N) to O(N/K), substrate-independent execution over symbolic, neural, vector, and hybrid substrates, and transparent inference chains where every step carries its evaluative context. The contribution is architectural, not logical. We formalize the computational theory across five dimensions: a five-layer architecture; three domain computation modes including chain indexing, path traversal as Kleisli composition, and vector-guided computation as a substrate transition; a substrate-agnostic interface with three operations Query, Extend, Bridge; reliability conditions C1 to C4 with three failure mode classes; and validation through a PHQ-9 clinical reasoning case study. The computational theory including operational semantics, complexity bounds, monad structure, substrate transitions, and boundary conditions is the contribution of this paper.

Abstract

Symbolic Reasoning

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