A Topological Application of Labelled Natural Deduction
Logic in Computer Science
2021-05-11 v4 Algebraic Topology
Abstract
We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these computational paths, establishing equalities between equalities. We then proceed to show the main result here: using this system to obtain the calculation of the fundamental group of the circle, of the torus and the real projective plane.
Keywords
Cite
@article{arxiv.1906.09105,
title = {A Topological Application of Labelled Natural Deduction},
author = {Tiago M. L. Veras and Arthur F. Ramos and Ruy J. G. B. de Queiroz and Anjolina G. de Oliveira},
journal= {arXiv preprint arXiv:1906.09105},
year = {2021}
}
Comments
42 pages, 5 figures. arXiv admin note: text overlap with arXiv:1804.01413, arXiv:1803.01709, arXiv:1906.09107