Scalable Uncertainty Reasoning in Knowledge Graphs

Knowledge Graphs are pivotal for semantic data integration. The real-world data they model is often inherently uncertain. Within knowledge graphs, uncertainty manifests in three distinct levels: imprecise attribute values, probabilistic triple existence, and incomplete schema knowledge. However, current Semantic Web standards lack native support for reasoning over such uncertainty, and na"ive extensions often incur computational intractability. In this thesis, I aim to develop a modular framework that addresses each level through tailored techniques: (1) defining probabilistic literals and a corresponding query algebra for continuous attributes; (2) a compilation-based framework transforming SPARQL provenance into tractable probabilistic circuits for uncertain triples; and (3) topology-aware geometric embeddings for statistical schema reasoning. The central hypothesis is that specialized reasoning mechanisms, namely algebraic, logical, and geometric approaches, can reconcile semantic precision with computational tractability.