The Equivalence Theorem: First-Class Relationships for Structurally Complete Database Systems

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.

Temporal reasoning over evolving semi-structured tables poses a challenge to current QA systems. We propose an approach that recasts the task as automated knowledge base construction: (1) prompting an LLM to synthesize a 3NF-compliant relational schema from Wikipedia infobox timelines, (2) populating the schema to obtain a queryable database, and (3) generating and executing SQL queries against it, with QA accuracy serving as an extrinsic evaluation of the constructed knowledge base. In a controlled grid of three schema generators crossed with six query models, the schema source accounts for 79.5% of the exact match (EM) variance against 1.6% for the query model: replacing the schema, and the prompt scaffolding derived from it, shifts EM by 14.7 to 20.0 points, whereas replacing the query model under a fixed schema shifts it by 4.4 to 12.1. From this evidence, we distill three candidate schema-design principles: balanced normalization, semantic naming, and consistent temporal anchoring, framed as correlational hypotheses. Our best configuration (Gemini 2.5 Flash schemas + Gemini-2.0-Flash queries) reaches 80.39 EM, 11.5 points above the strongest reported baseline (68.89 EM); an open-weights configuration reaches 79.52.

Relational databases (RDBs) remain the primary infrastructure for storing and managing structured data across enterprise and scientific domains. Natural-language (NL) interfaces to RDBs aim to let users ask questions without writing SQL, but real user needs go beyond SQL-style lookup: some questions require reasoning over the observable database state, while others require predictive inference from historical relational records under temporal constraints. Existing benchmarks address these goals in isolation. To address this gap, we introduce RDL-Bench, a benchmark for task-aware question answering (QA) over real RDBs. RDL-Bench organizes diverse user questions into reasoning-oriented questions, whose answers are determined by the current database state, and prediction-oriented questions, whose answers depend on future outcomes under temporal constraints. Each instance contains an NL question, task metadata, schema information, temporal context, either executable evidence or target-construction logic, and denotation-level ground truth. RDL-Bench supports two evaluation settings: native solvers under their intended capabilities, and task-aware modular systems where a router dispatches each question to an appropriate execution module.