=== Base Templates !CardinalityMin, !CardinalityMax, !CardinalityMinMax ===

[[br]]!CardinalityMin, !CardinalityMax, and !CardinalityMinMax are templates for expressing the 
[[br]]values of cardinalities. 
[[br]]
[[br]]!CardinalityMinMax(a, b, c) means that a is a cardinality and b and c are integers, and that 
[[br]]b is the minimal, c the maximal, constraint of a. !CardinalityMin and !CardinalityMax are 
[[br]]similar, and apply to just the minimal, resp. the maximal constraint. 
[[br]]!CardinalityMin 
[[br]]
[[br]]Roles: 
[[br]]1 hasCardinality Cardinality 
[[br]]2 valMinimumCardinality INTEGER 
[[br]]
[[br]]!CardinalityMax 
[[br]]
[[br]]Roles: 
[[br]]1 hasCardinality Cardinality 
[[br]]2 valMaximumCardinality INTEGER 
[[br]]
[[br]]!CardinalityMinMax 
[[br]]
[[br]]Roles: 
[[br]]1 hasCardinality Cardinality 
[[br]]2 valMinimumCardinality INTEGER 
[[br]]3 valMaximumCardinality INTEGER 

Axiom: 
{{{
CardinalityMin(x1, x2) <-> 
Cardinality(x1) & 
INTEGER(x2) & 
hasMinimumCardinality(x1, x2) . 
}}}

Axiom: 
{{{
CardinalityMax(x1, x2) <-> 
Cardinality(x1) & 
INTEGER(x2) & 
hasMaximumCardinality(x1, x2) . 
}}}

Axiom: 
{{{
CardinalityMinMax(x1, x2, x3) <-> 
Cardinality(x1) & 
INTEGER(x2) & 
INTEGER(x3) & 
CardinalityMin(x1, x2) & 
CardinalityMax(x1, x3) . 
}}}

NOTE In ISO 15926, cardinalities are first-class objects. In ISO 15926-2, it is stated that an absence 
of specified minimum or maximum values for a cardinality should be interpreted as a absence 
of constraints (clause 5.2.13.1). The nature of the representation of ISO 15926-2 in first-order logic, with an open world assumption, mandates that both lower and upper bounds be given explicitly. 
Where no minimal constraint applies, the value 0 should be assigned. Where no maximum constraint applies, the reference item * Cardinality should be assigned (see 8.2.1).