exactCardinality

exactCardinality is a type of cardinality restriction used in knowledge representation and ontology languages, notably the Web Ontology Language (OWL). It specifies that for a given property, an individual is related to exactly n fillers. Fillers are distinct individuals when the property is an object property, or literal values when it is a data property.

In OWL 2, exact cardinality restrictions come in two forms: ObjectExactCardinality for object properties and DataExactCardinality for data properties. In description logic-style syntax these are expressed as ObjectExactCardinality(n, P) and DataExactCardinality(n, P, D), with Manchester syntax presenting them as ObjectExactCardinality(n P) or DataExactCardinality(n P D). Formally, an interpretation I satisfies such a restriction for an individual a if the set P^I(a) has cardinality n (for object properties), or the set of values {y | (a,y) in P^I} has cardinality n with respect to the datatype D (for data properties).

Applications include modeling constraints in ontologies, such as a Person having exactly two email addresses, a Professor with exactly three supervised students, or a Product that has exactly one primary category. Reasoners can use exact cardinality to infer class membership, detect inconsistencies, and perform validation, though exact cardinality can increase reasoning complexity and interact with other restrictions. Limitations include language and tool support variations, and potential computational costs in large or complex ontologies. See also: minCardinality, maxCardinality, cardinality restrictions, OWL.