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The three dimensions of proofs

Yves Guiraud
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Abstract

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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Yves Guiraud. 2006-12-04. The three dimensions of proofs. https://doi.org/10.1016/j.apal.2005.12.012

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