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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 no.2 Bogotá July/Dec. 2019 Epub Mar 20, 2020
Artículos originales
Existential Graphs on nonplanar surfaces
Gráficos existenciales sobre superficies no planas
1Departamento de Matemáticas y Estadística Universidad del Tolima Facultad de Ciencias Barrio Santa Helena Ibagué, Colombia e-mail: noostra@ut.edu.co
Existential graphs on the plane constitute a two-dimensional representation of classical logic, in which a Jordan curve stands for the negation of its inside. In this paper we propose a program to develop existential Alpha graphs, which correspond to propositional logic, on various surfaces. The geometry of each manifold determines the possible Jordan curves on it, leading to diverse interpretations of negation. This may open a way for appointing a "natural" logic to any surface.
Key words and phrases. Existential graphs; 2-dimensional topological manifolds; Jordan's Curve Theorem
Los gráficos existenciales sobre el plano constituyen una representación bidimensional de la lógica clásica, en la cual una curva de Jordan indica la négation de su interior. En este artículo se propone un programa para desarrollar los gráficos existenciales Alfa, que corresponden a la lógica preposicional, sobre diferentes superficies. La geometría de cada variedad determina las posibles curvas de Jordan sobre ella, lo cual conduce a interpretaciones diversas de la negación. Esto puede abrir el camino para asignar una lógica "natural" a cualquier superficie.
Palabras y frases clave. Gráficos existenciales; 2-variedades topolágicas; teorema de la curva de Jordan
Aknowledgements
Parts of this paper were presented in talks at the Universidad del Tolima (Ibague) and at the Universidad Nacional de Colombia (Bogota). Special thanks to Fernando Zalamea, Leonardo Solanilla, Andres Villaveces, and Franciso Vargas for very enlightening discussions on this topic, and also for their substantial comments on earlier versions of this paper. The author wishes to thank the anonymous referee for his valuable suggestions, which improved the submitted draft. The drawings in this paper were created with pst-solides3d.
References
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Revised: April 2019; Accepted: August 2019
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
