classdenotation

Class denotation is the extension or referent of a class term in logic, semantics, and ontology: it is the collection of all objects that fall under the defining property of the class. For example, the class denotation of the term dog is the set of all dogs.

In formal theories, a class denotation may be a set or a more general collection known as a class. Some logical frameworks distinguish between sets and proper classes; a proper class is a collection too large to be a set, such as the class of all sets, and its denotation is a class rather than a set. This distinction helps avoid certain paradoxes that arise when attempting to form the totality of all sets.

In formal semantics and description logics, the denotation function assigns to each predicate or concept its extension—the entities that satisfy the predicate. This extension often serves as the interpretation of the term within a model, enabling truth conditions for quantified statements like All X are Y. The denotation can be empty if no objects satisfy the property, as in unicorn.

Applications of class denotation appear in ontology development, database schema design, and natural language semantics, where reasoning about categories and their relationships is important. The term is sometimes used interchangeably with extension; the related notions intension (the concept or property) and denotation (extension) are common in philosophy of language.

See also Denotation, Extension (logic), Intension, Description logic.