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A Classificatory Topos: Refining Evolving Knowledge in Multi-agent Learning Systems

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Manuel Hernández
Eduardo Sánchez-Soto
C.H. Castañeda-Roldán
Published in
Multi-disciplinary Trends in Artificial Intelligence
Publisher
Springer Nature Singapore

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Abstract

The chapter introduces a mathematical framework called a Classificatory Topos, designed to model the dynamic evolution of knowledge within multi-agent learning systems. The framework is grounded in category theory and provides a rich, non-linear model of system evolution. It ensures causal consistency in the historical record of knowledge refinement through the use of sheaves and a Grothendieck topology. The text also presents a concrete example of how the framework can be applied to validate hypotheses, such as classifying an object as a chair. The chapter concludes by discussing the potential extensions of the framework into probabilistic and fuzzy domains, as well as its implications for the formal verification of system properties such as consistency, explainability, and fairness.
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previous chapter Multimodal Tree Crown Detection and Carbon Stock Estimation from Remote Sensing Imagery
next chapter A Survey of Algorithmic and Contextual Decomposition Methods Across Language Model Pipelines
Title
A Classificatory Topos: Refining Evolving Knowledge in Multi-agent Learning Systems
Authors
Manuel Hernández
Eduardo Sánchez-Soto
C.H. Castañeda-Roldán
Copyright Year
2026
Publisher
Springer Nature Singapore
Book
Multi-disciplinary Trends in Artificial Intelligence

Print ISBN: 978-981-9549-59-7

Electronic ISBN: 978-981-9549-60-3

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-981-95-4960-3_4
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