Topos de grafos existenciais sobre superfícies de Riemann

Angie Hugueth

doi:10.23925/2316-5278.2025v26i1:e70114

Authors

Angie Hugueth Universidade Estadual de Campinas

DOI:

https://doi.org/10.23925/2316-5278.2025v26i1:e70114

Keywords:

Existential Graphs, Logic, Peirce, Sheaves, Topos

Abstract

Peirce’s Existential Graphs provide a geometrical understanding of a variety of logics (classical, intuitionistic, modal, first-order). The geometrical interpretation is given by topological transformations of closed (Jordan) curves on the plane, but it can be extended to other surfaces (sphere, cylinder, torus, etc.) The result provides the appearance of new logics related to the shapes of the surfaces. Going beyond, one can draw existential graphs over general Riemann Surfaces, and, introducing tools from algebraic geometry (Sheaves, Grothendieck Toposes, Elementary Toposes), one can try to capture both the logics and the geometrical shapes through a new Topos of Existential Graphs over Riemann Surfaces, and through the classifier subobject of the topos. We offer new perspectives (concepts, definitions, examples, conjectures) along this road.

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