Keys for graphs incorporate the topology and value constraints needed to uniquely identify entities in a graph. They have been studied to support object identification, knowledge fusion, and social network reconciliation. Existing key constraints identify entities as the matches of a graph pattern by subgraph isomorphism, which enforce label equality on node types. These constraints can be too restrictive to characterize structures and node labels that are syntactically different but semantically equivalent. We propose a new class of key constraints, Ontological Graph Keys (OGKs) that extend conventional graph keys by ontological subgraph matching between entity labels and an external ontology. We show that the implication and validation problems for OGKs are each NP-complete. To reduce the entity matching cost, we also provide an algorithm to compute a minimal cover for OGKs. We then study the entity matching problem with OGKs, and a practical variant with a budget on the matching cost. We develop efficient algorithms to perform entity matching based on a (budgeted) Chase procedure. Using real-world graphs, we experimentally verify the efficiency and accuracy of OGK-based entity matching.

Functional Dependencies (FDs) define attribute relationships based on syntactic equality, and, when used in data cleaning, they erroneously label syntactically different but semantically equivalent values as errors. We explore dependency-based data cleaning with Ontology Functional Dependencies (OFDs), which express semantic attribute relationships such as synonyms defined by an ontology. We study the theoretical foundations of OFDs, including sound and complete axioms and a linear-time inference procedure. We then propose an algorithm for discovering OFDs (exact ones and ones that hold with some exceptions) from data that uses the axioms to prune the search space. Towards enabling OFDs as data quality rules in practice, we study the problem of finding minimal repairs to a relation and ontology with respect to a set of OFDs. We demonstrate the effectiveness of our techniques on real datasets, and show that OFDs can significantly reduce the number of false positive errors in data cleaning techniques that rely on traditional FDs.

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We propose a class of functional dependencies for temporal graphs, called TGFDs. TGFDs capture both attribute-value dependencies and topological structures of entities over a valid period of time in a temporal graph. It subsumes graph functional dependencies (GFDs) and conditional functional dependencies (CFDs) as a special case. We study the foundations of TGFDs including satisfiability, implication and validation. We show that the satisfiability and validation problems are coNP-complete and the implication problem is NP-complete. We also present an axiomatization of TGFDs and provide the proof of the soundness and completeness of the axiomatization.

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