ObjectExactCardinality

ObjectExactCardinality is a class expression used in the Web Ontology Language (OWL) to constrain the number of related individuals via an object property. It specifies that an instance must have exactly n distinct R-successors that are instances of C, where n is a non-negative integer, R is an object property, and C is a class.

In formal terms, for an interpretation I, the extension of ObjectExactCardinality(n, R, C) consists of all individuals x such that the set { y | (x,y) ∈ R^I and y ∈ C^I } has cardinality exactly n. This expression allows precise restrictions on the number of related fillers satisfying a given class, enabling detailed modeling of relational structures.

ObjectExactCardinality is closely related to ObjectMinCardinality and ObjectMaxCardinality. In OWL 2, ObjectExactCardinality(n, R, C) is equivalent to the conjunction of ObjectMinCardinality(n, R, C) and ObjectMaxCardinality(n, R, C). This equivalence is useful for understanding and translating constraints or for reasoning tasks that treat lower and upper bounds separately.

Examples include statements like “a Person has exactly two hasPet that are Dogs” or “a Teacher has exactly one hasClassroom that is a Room.” These constraints are common in domains where precise relational counts matter, such as organizational roles, equipment inventories, or biological interactions.

Reasoning with ObjectExactCardinality can affect performance, especially with large ontologies or complex fillers. Correct use often involves balancing expressivity with decidability and selecting appropriate reasoners. See also ObjectMinCardinality, ObjectMaxCardinality, and DataExactCardinality for related constructs.