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arXiv · 2603.05685

From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs

Moses Boudourides
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Abstract

This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices and line knowledge digraph constructions. The graph induces a free category whose morphisms correspond to relational paths. To model context-dependent meaning, a Grothendieck topology is defined on the free category generated by the graph leading to a topos of sheaves that supports local-to-global semantic reasoning. The framework connects graph-theoretic structure, categorical composition, and sheaf semantics in a unified mathematical model for contextual relational reasoning.

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Moses Boudourides. 2026-03-05. From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs. https://arxiv.org/abs/2603.05685

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