The branch of mathematical logic that studies collections of objects called sets, providing a foundational language for most of modern mathematics including logic, topology, algebra, and knowledge representation.
Semantic Classification
Content
- Set theory formalises the notion of a collection of elements and the operations of union, intersection, and complement. Axiomatic systems such as Zermelo-Fraenkel set theory provide a rigorous basis from which the rest of mathematics can be constructed.
- In the context of knowledge representation, set-theoretic semantics underpin description logics and ontology languages, where classes are interpreted as sets of individuals and subclass relations correspond to subset relations.