Modelling across engineering, systems science, and formal methods remains limited by binary relations, implicit semantics, and diagram-centred notations that obscure multilevel structure and hinder mechanisation. Hypernetwork Theory (HT) addresses these gaps by treating the n-ary relation as the primary modelling construct. Each relation is realised as a typed hypersimplex - alpha (conjunctive, part-whole) or beta (disjunctive, taxonomic) - bound to a relation symbol R that fixes arity and ordered roles. Semantics are embedded directly in the construct, enabling hypernetworks to represent hierarchical and heterarchical systems without reconstruction or tool-specific interpretation. This paper presents the structural kernel of HT. It motivates typed n-ary relational modelling, formalises the notation and axioms (A1-A5) for vertices, simplices, hypersimplices, boundaries, and ordering, and develops a complete algebra of structural composition. Five operators - merge, meet, difference, prune, and split - are defined by deterministic conditions and decision tables that ensure semantics-preserving behaviour and reconcile the Open World Assumption with closure under rules. Their deterministic algorithms show that HT supports reproducible and mechanisable model construction, comparison, decomposition, and restructuring. The resulting framework elevates hypernetworks from symbolic collections to structured, executable system models, providing a rigorous and extensible foundation for mechanisable multilevel modelling.

翻译：工程学、系统科学与形式化方法中的建模仍受限于二元关系、隐式语义及以图表为中心的符号表示，这些因素掩盖了多层次结构并阻碍了机械化。超网络理论通过将n元关系作为核心建模构造来解决这些局限。每个关系被实现为一个类型化的超单纯形——α型（合取性，部分-整体）或β型（析取性，分类性）——绑定于一个关系符号R，该符号固定了元数和有序角色。语义直接嵌入构造中，使得超网络能够表示层次与非层次系统，而无需重构或依赖工具特定解释。本文提出HT的结构核。它阐述了类型化n元关系建模的动机，形式化了顶点、单纯形、超单纯形、边界与排序的符号表示及公理（A1-A5），并发展了一套完整的结构组合代数。通过确定性条件与决策表定义了五种算子——合并、交、差、剪枝与分割——以确保语义保持行为，并在规则下协调开放世界假设与闭包性。其确定性算法表明，HT支持可复现、可机械化的模型构建、比较、分解与重构。该框架将超网络从符号集合提升为结构化、可执行的系统模型，为可机械化的多层次建模提供了严谨且可扩展的基础。