A Topos-Theoretic Framework for Artistic-Oriented Knowledge Graphs

This paper introduces a novel framework for Artistic-Oriented Knowledge Graphs that synthesizes the formal power of category theory with the philosophical insights of Alain Badiou’s aesthetics. We propose a two-level arrangement where knowledge graphs serve as the foundational representation of artistic entities and their relationships, while a topos—a category of sheaves—provides the mathematical formalization of what Badiou calls the “logic of appearing.” The formal structure of topos offers a rich language for modeling interpretation, symbolism, and context-dependent meaning in art. Accordingly, the framework implies that an artistic “event” is formalized as a change of topos, representing a fundamental shift in the interpretive logic through which art is perceived. Such a synthesis enables us to model the production of artistic truth and the subtleties of aesthetic judgment while respecting the complex, multi-dimensional nature of artistic expression. We demonstrate the framework by analyzing how different topoi can be constructed over the same knowledge graph, revealing how meaning is contingent on the prevailing logic of interpretation. An approach of this kind opens new possibilities for computational art history, digital aesthetics, and the formal study of cultural repertoires.