We prove The Equivalence Theorem: structurally complete knowledge representation requires exactly four mutually entailing capabilities -- n-ary relationships with attributes, temporal validity, uncertainty quantification, and causal relationships between relationships -- collectively equivalent to treating relationships as first-class objects. Any system implementing one capability necessarily requires all four; any system missing one cannot achieve structural completeness. This result is constructive: we exhibit an Attributed Temporal Causal Hypergraph (ATCH) framework satisfying all four conditions simultaneously. The theorem yields a strict expressiveness hierarchy -- SQL < LPG < TypeDB < ATCH -- with witness queries that are structurally inexpressible at each lower level. We establish computational complexity bounds showing NP-completeness for general queries but polynomial-time tractability for practical query classes (acyclic patterns, bounded-depth causal chains, windowed temporal queries). As direct corollaries, we derive solutions to classical AI problems: the Frame Problem (persistence by default from temporal validity), conflict resolution (contradictions as unresolved metadata with hidden variable discovery), and common sense reasoning (defaults with causal inhibitors). A prototype PostgreSQL extension in C validates practical feasibility within the established complexity bounds.

翻译：我们证明了等价性定理：结构完备的知识表示需要恰好四种相互蕴含的能力——带属性的n元关系、时间有效性、不确定性量化以及关系间的因果联系——这些能力共同等价于将关系视为一等对象。任何实现其中一种能力的系统必然需要所有四种能力；任何缺失一种能力的系统都无法实现结构完备性。该结果是构造性的：我们展示了一个同时满足所有四个条件的属性化时序因果超图（ATCH）框架。该定理导出了一个严格的表达能力层级——SQL < LPG < TypeDB < ATCH——并通过见证查询证明每个较低层级在结构上无法表达相应查询。我们建立了计算复杂度界限，表明一般查询具有NP完全性，但实际查询类别（无环模式、有界深度因果链、窗口时序查询）具有多项式时间可处理性。作为直接推论，我们推导出经典人工智能问题的解决方案：框架问题（通过时间有效性实现默认持续性）、冲突消解（将矛盾视为具有隐变量发现的未解析元数据）以及常识推理（带因果抑制器的默认规则）。一个用C语言实现的原型PostgreSQL扩展验证了在既定复杂度界限内的实际可行性。