Abstract

OOSTRA, ARNOLD. Existential Graphs on nonplanar surfaces. Rev.colomb.mat. [online]. 2019, vol.53, n.2, pp.205-219.  Epub Mar 20, 2020. ISSN 0034-7426.

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.

Keywords : Existential graphs; 2-dimensional topological manifolds; Jordan's Curve Theorem.

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