Authors: Baralić, Đorđe 
Curien, Pierre Louis
Milićević, Marina
Obradović, Jovana 
Petrić, Zoran 
Zekić, Mladen 
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Proofs and surfaces
Journal: Annals of Pure and Applied Logic
Volume: 171
Issue: 9
First page: 102845
Issue Date: 1-Oct-2020
Rank: M21
ISSN: 0168-0072
DOI: 10.1016/j.apal.2020.102845
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.
Keywords: Ceva-Menelaus proof | Connected sum | Cyclic operad | Incidence theorem | Sequent system | Simplicial homology
Publisher: Elsevier

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