Semantic Web Foundations for Representing, Reasoning, and Traversing Contextualized Knowledge Graphs

Semantic Web technologies such as RDF and OWL have become World Wide Web Consortium (W3C) standards for knowledge representation and reasoning. RDF triples about triples, or meta triples, form the basis for a contextualized knowledge graph. They represent the contextual information about individual triples such as the source, the occurring time or place, or the certainty. However, an efficient RDF representation for such meta-knowledge of triples remains a major limitation of the RDF data model. The existing reification approach allows such meta-knowledge of RDF triples to be expressed in RDF by using four triples per reified triple. While reification is simple and intuitive, this approach does not have a formal foundation and is not commonly used in practice as described in the RDF Primer. This dissertation presents the foundations for representing, querying, reasoning and traversing the contextualized knowledge graphs (CKG) using Semantic Web technologies. A triple-based compact representation for CKGs. We propose a principled approach and construct RDF triples about triples by extending the current RDF data model with a new concept, called singleton property (SP), as a triple identifier. The SP representation needs two triples to the RDF datasets and can be queried with SPARQL. A formal model-theoretic semantics for CKGs. We formalize the semantics of the singleton property and its relationships with the triple it represents. We extend the current RDF model-theoretic semantics to capture the semantics of the singleton properties and provide the interpretation at three levels: simple, RDF, and RDFS. It provides a single interpretation of the singleton property semantics across applications and systems. A sound and complete inference mechanism for CKGs. Based on the semantics we propose, we develop a set of inference rules for validating and inferring new triples based on the SP syntax. We also derive different sets of context-based inference rules using lattices of values for provenance, time, and uncertainty. A graph-based formalism for CKGs. We propose a formal contextualized graph model for the SP representation. We formalize the RDF triples as a mathematical graph by combining the model theory and the graph theory into the same RDF formal semantics. The unified semantics allows the RDF formal semantics to be leveraged in the graph-based algorithms