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

arXiv: https://arxiv.org/abs/2604.10908 · HTML: https://mlsanity.com/paper/2604.10908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Domain-constrained knowledge representation: A modal framework](https://mlsanity.com/paper/2604.01770/) (2026)
- [Domain-Contextualized Inference: A Computable Graph Architecture for Explicit-Domain Reasoning](https://mlsanity.com/paper/2604.04344/) (2026)

## Built on by (most cited first, 1 of 1)

- [DALM: A Domain-Algebraic Language Model via Three-Phase Structured Generation](https://mlsanity.com/paper/2604.15593/) (2026)

## Abstract (arXiv)

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.