The three dimensions of proofs

Details The three dimensions of proofs The three dimensions of proofs

2006-12-04

arxiv.org/abs/math/0612089v1

Annals of Pure and Applied Logic, Volume 141, Issues 1-2, August 2006, Pages 266-295

Mathematics

Category Theory

38 pages, 50 figures

Scientific paper

10.1016/j.apal.2005.12.012

In this document, we study a 3-polygraphic translation for the proofs of SKS, a formal system for classical propositional logic. We prove that the free 3-category generated by this 3-polygraph describes the proofs of classical propositional logic modulo structural bureaucracy. We give a 3-dimensional generalization of Penrose diagrams and use it to provide several pictures of a proof. We sketch how local transformations of proofs yield a non contrived example of 4-dimensional rewriting.

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