From contradiction to conciliation: a way to "dualize" sheaves

TL;DR

This paper introduces a novel dualization of sheaves on topological spaces to formalize the reconciliation of contradictory statements, providing a new perspective on handling conflicting information in mathematical structures.

Contribution

It proposes a dualized sheaf structure on topological spaces that reverses global and local levels, offering a new framework for formalizing contradiction reconciliation.

Findings

Defines a dualization of sheaves on topological spaces.

Shows how to model contradictory statements using this structure.

Provides insights into formal reconciliation of conflicting ideas.

Abstract

Our aim is to give some insights about how to approach the formal description of situations where one has to conciliate several contradictory statements, rules, laws or ideas. We show that such a conciliation structure can be naturally defined on a topological space endowed with the set of its closed sets and that this specific structure is a kind of "dualization" of the sheaf concept where "global" and "local" levels are reversed.