minCardinality

MinCardinality is a cardinality restriction used in description logics and the Web Ontology Language (OWL) to express that an individual must be related by a given property to at least a specified number of distinct fillers. It is part of the family of cardinality constraints, alongside maxCardinality and exact cardinality restrictions. In OWL 2 DL, the construct is typically written as ObjectMinCardinality(n R) for object properties or DataMinCardinality(n R) for data properties, where n is a non-negative integer. A qualified form may also specify a filler class C, written as ObjectMinCardinality(n R C) or DataMinCardinality(n R C), indicating that at least n related fillers must be instances of C.

Semantically, for an individual x, ObjectMinCardinality(n R) requires that the set of R-successors of x contains at least n distinct individuals. If a filler class C is provided, at least n of those successors must be instances of C. These constraints are interpreted under the open-world assumption, meaning that absence of knowledge about additional fillers does not violate the restriction.

Usage examples include statements such as “every person has at least two email addresses” or “an organization has at least three departments,” where the restriction is attached to a class via a property. MinCardinality can be combined with other restrictions (such as other properties or class memberships) to form more complex inferences. It is distinct from maxCardinality (an upper bound) and from exact cardinality restrictions, which require a precise total count. Reasoners use minCardinality to check consistency and to derive implicit class memberships.