From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910042904592384 |
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| author | Boudourides, Moses |
| author_facet | Boudourides, Moses |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05685 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs Boudourides, Moses Social and Information Networks 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. |
| title | From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2603.05685 |