| 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 | 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. |
Keywords: | Ceva-Menelaus proof | Connected sum | Cyclic operad | Incidence theorem | Sequent system | Simplicial homology | Publisher: | Elsevier |
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