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
Figure 1: Operational structure of the CDC inference engine.
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.
Compositional generalization remains challenging when language models must combine familiar reasoning operations in unfamiliar ways. The Scenario-Based Commonsense Reasoning Evaluation (SCoRE) 2026 tests this ability on three mixed domains absent from training and requires models to identify the complete set of correct options for each question. We introduce Route-Verify-Vote (RVV), a framework for procedure-conditioned self-consistency that uses language models without parameter updates. Route uses the provided domain label to select a reasoning procedure that guides the model in representing and applying the relevant constraints. Verify prompts the model to assess each option against those constraints. Vote aggregates complete answer sets and allocates additional samples to questions with a small vote-count margin between the two most frequent sets. Samples for each question follow the same domain-specific procedure. On the official test set, voting over 16 sampled answer sets per question achieves an exact-set accuracy of 74.6%. Adaptive RVV reaches 77.3%, and combining models on selected domain routes raises accuracy to 79.4%. The final system ranked second among participating systems. These results support domain-specific reasoning procedures and answer-set disagreement as useful tools for allocating inference-time computation in mixed-domain reasoning.
Large language models compress heterogeneous knowledge into a single parameter space, allowing facts from different domains to interfere during generation. We propose DALM, a Domain-Algebraic Language Model that replaces unconstrained token generation with structured denoising over a domain lattice. DALM follows a three-phase generation path: it first resolves domain uncertainty, then relation uncertainty, and finally concept uncertainty, so each stage operates under explicit algebraic constraints. The framework requires only three ingredients: a lattice of domains with computable meet, join, and implication; a typing function over relations that controls inheritance across domains; and a fiber partition that localizes knowledge to domain-specific subsets. Given these ingredients, DALM yields a three-phase encoder-decoder architecture in which generation is confined to a domain fiber, cross-domain contamination is structurally prevented in closed-vocabulary mode and auditably bounded in open-vocabulary mode, and a single query can produce a domain-indexed multi-perspective answer space. We instantiate the framework with the CDC knowledge representation system and outline training and evaluation on validated domain-annotated crystal libraries. DALM reframes language generation as algebraically constrained structured denoising rather than unconstrained decoding over a flat token space.