Existential Graphs on nonplanar surfaces

Existential Graphs on nonplanar surfaces

ABSTRACT. 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.

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Main Author: OOSTRA,ARNOLD
Format: Digital revista
Language:English
Published: Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas 2019
Online Access:http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262019000200205
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spelling oai:scielo:S0034-742620190002002052020-09-30Existential Graphs on nonplanar surfacesOOSTRA,ARNOLD Existential graphs 2-dimensional topological manifolds Jordan's Curve Theorem ABSTRACT. 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.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.53 n.2 20192019-12-01text/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262019000200205en
institution SCIELO
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country Colombia
countrycode CO
component Revista
access En linea
databasecode rev-scielo-co
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region America del Sur
libraryname SciELO
language English
format Digital
author OOSTRA,ARNOLD
spellingShingle OOSTRA,ARNOLD
Existential Graphs on nonplanar surfaces
author_facet OOSTRA,ARNOLD
author_sort OOSTRA,ARNOLD
title Existential Graphs on nonplanar surfaces
title_short Existential Graphs on nonplanar surfaces
title_full Existential Graphs on nonplanar surfaces
title_fullStr Existential Graphs on nonplanar surfaces
title_full_unstemmed Existential Graphs on nonplanar surfaces
title_sort existential graphs on nonplanar surfaces
description ABSTRACT. 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.
publisher Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
publishDate 2019
url http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262019000200205
work_keys_str_mv AT oostraarnold existentialgraphsonnonplanarsurfaces
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