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A Classificatory Topos: Refining Evolving Knowledge in Multi-agent Learning Systems
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AI
DOI：10.1007/978-981-95-4960-3_4.png)
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Abstract
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We propose a Classificatory Topos, a mathematical framework to model the dynamic evolution of knowledge within a finite system of interacting learning machines. Following guidelines of category theory, the construction establishes a Grothendieck topos, (C-learn, J) , as a mathematical universe for this problem domain. By defining a base site on a category of epistemic states with causal morphisms, and equipping it with a Grothendieck topology that formalizes a logic of justification, the framework provides a rich, non-linear model of system evolution. The use of sheaves ensures causal consistency, while the internal logic of the topos, governed by a subobject classifier, provides the machinery to trace, verify, and explain the refinement of classifications
Keywords:
Classificatory Topos
Grothendieck topos
multi-agent learning systems
sheaves
internal logic
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Papers:
36
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