We propose using confusion hypergraphs (hyperconfusions) as a model of information. In contrast to the conventional approach using random variables, we can now perform conjunction, disjunction and implication of information, forming a Heyting algebra. Using the connection between Heyting algebra and intuitionistic logic, we can express the requirements of a communication network (e.g., network coding, index coding, Slepian-Wolf coding) as a logical formula, allowing us to use the hypergraph Heyting algebra to directly compute the optimal coding scheme. The optimal communication cost is simply given by the entropy of the hypergraph (within a logarithmic gap). This gives a surprising correspondence between coding settings and logical formulae, similar to the Curry-Howard correspondence between proofs and computer programs.

翻译：我们提出使用混淆超图（超混淆）作为信息模型。与使用随机变量的传统方法不同，我们现在可以对信息进行合取、析取和蕴涵运算，从而形成Heyting代数。利用Heyting代数与直觉主义逻辑之间的联系，我们可以将通信网络的要求（例如网络编码、索引编码、Slepian-Wolf编码）表达为逻辑公式，从而允许我们使用超图Heyting代数直接计算最优编码方案。最优通信成本仅由超图的熵给出（在对数间隙内）。这揭示了编码设置与逻辑公式之间惊人的对应关系，类似于证明与计算机程序之间的Curry-Howard对应。