Description Logic and Graph Theory
Descriptions Logics are more developed methods of knowledge representation. They are made up of classes (concepts) and properties (roles). They use a set of domain-independent primitives to construct object descriptions. Defining higher-level terms from primitive language (hasName).
Description logics contain rules to construct knowledge representations that are decidable. They can produce an answer, also providing formal descriptions of semantic networks. One feature of description logic is the emphasis on reasoning as a central service. It also allows the specifying of a terminological hierarchy using a restricted set of first-order formulas.
Graph theory is a part of mathematics that has played an important role in the development of the Semantic Web.
A graph will contain nodes and relationships. The current web can be viewed as a graph. Where each page represents a node, and the hyperlinks translate to directed edges between nodes. The Semantic Web is one large graph. Objects are connected by properties, by modelling Semantic Web solutions this way, will lead to data processing efficiencies.
Both Description Logics and Graph theory play a vital role in modelling the Semantic Web, they have contributed in developing ontology languages that are used on the Semantic Web.