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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.09921 |
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| _version_ | 1866916160166952960 |
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| author | Easthope, Eric |
| author_facet | Easthope, Eric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fregean Flows Easthope, Eric Logic Graphics Logic in Computer Science 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. |
| title | Fregean Flows |
| topic | Logic Graphics Logic in Computer Science |
| url | https://arxiv.org/abs/2403.09921 |