I humbly introduce a concept I call "Fregean flows," a graph theoretic representation of classical logic, to show how higher-dimensional graph characteristics might be useful to prove or perhaps at best show the provability of simple deductive statements typically represented as one-dimensional strings of characters. I apply these to a very simple proof, namely proving the equivalence of two definitions for an Abelian group G, an if-and-only-if statement, using a re-representation of statements as vertices and both conjunctions and implications as differently coloured edges. This re-representation of an if-and-only-if is simple but shows unexpected geometry, and I discuss its possible utility in terms of provability through ideas of graph topology, similarities of graph contraction to deductive elimination, and recursion.

翻译：我谦逊地引入一个称为“弗雷格流”的概念，这是一种经典逻辑的图论表示，旨在展示高维图特征如何有助于证明或至少揭示通常以一维字符串表示的简单演绎语句的可证性。我将这些概念应用于一个非常简单的证明——即通过将语句重新表示为顶点，并将合取与蕴含分别用不同颜色的边表示，证明阿贝尔群G两种定义的等价性（一个当且仅当语句）。这种“当且仅当”的重新表示虽简单，却展现了意想不到的几何结构。我探讨了其在可证性方面的潜在应用，涉及图拓扑思想、图收缩与演绎消去的相似性，以及递归。