Proofs and surfaces

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Annals of Pure and Applied Logic 171 (9):102845 (2020)
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Abstract

A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.

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10.1016/j.apal.2020.102845

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The structure of multiplicatives.Vincent Danos & Laurent Regnier - 1989 - Archive for Mathematical Logic 28 (3):181-203.
A minimal classical sequent calculus free of structural rules.Dominic Hughes - 2010 - Annals of Pure and Applied Logic 161 (10):1244-1253.

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