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.
Highlights
Existential graphs, which were considered by his creator Charles S
Just as geometry changes when the plane is replaced by a different surface, if existential graphs are drawn on a non planar surface the outcoming system most surely corresponds to some non classical logic
It is the first time that Geometry returns through existential graphs to Logic, if not results at least some genuine mathematical problems
Summary
Existential graphs, which were considered by his creator Charles S Peirce his chef d’œvre [11], may be seen as a geometric representation of mathematical logic. It is the first time that Geometry returns through existential graphs to Logic, if not results at least some genuine mathematical problems. In this first approach we will consider only propositional logic, which is expressed graphically by the subsystem of existential graphs called Alpha. In this paper we will consider only the representation of propositional formulas, leaving the general study of the transformation rules on surfaces as an open problem.
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