**Defined in ontology: Frame-ontology****Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/ontolingua/../../all-ontologies/ontolingua/frame-ontology.lisp**

**Arity: **3
**Documentation: **
If a SLOT-CARDINALITY of relation R with respect to a domain
class C is N, then for all instances c of class C, R maps c to exactly
N individuals in the range. For single valued relations, the
slot-cardinality is 1. Specifying a SLOT-CARDINALITY is a constraint
between classes and binary-relations which does not always hold; there
need not be any fixed value-cardinality for R on all instances of C.
### Notes:

**See-Also:
**Specifying that the slot cardinality is = to some integer
is equivalent to using the Loom and CLASSIC `EXACTLY'
operator.
- Note that slot-cardinality is a function. That means
that for any domain and relation, there is at most one
integer N that can be the slot-cardinality. If there is
no such fixed number, then the value of the function is
undefined for the given domain and relation.

**Instance-Of: **Function, *Relation*, *Set*

## Equivalence Axioms for Slot-Cardinality:

(<=> (Slot-Cardinality ?Domain-Class ?Binary-Relation)
(=> (Instance-Of ?Instance ?Domain-Class)
(= (Value-Cardinality ?Instance ?Binary-Relation) ?N)))

## Axioms for Slot-Cardinality:

(Nth-Domain Slot-Cardinality 3 Nonnegative-Integer)
(Nth-Domain Slot-Cardinality 2 Binary-Relation)
(Nth-Domain Slot-Cardinality 1 Class)

## Frame References to Slot-Cardinality:

### Slots:

**Year-Of@Simple-Time: **
- Slot-Cardinality: 1

### In class Agent@Agents:

### Slots:

**Name: **
- Slot-Cardinality: 1

### In class Publisher@Agents:

### Slots:

**Name: **
- Slot-Cardinality: 1

### Slots:

**Inverse: **
- Slot-Cardinality: 1

### Slots:

**First: **
- Slot-Cardinality: 1

...

## Implication Axioms mentioning Slot-Cardinality:

(=> (= (Slot-Cardinality ?Domain-Class ?Binary-Relation) ?N)
(=> (Instance-Of ?Instance ?Domain-Class)
(= (Value-Cardinality ?Instance ?Binary-Relation) ?N)))

## Equivalence Axioms mentioning Slot-Cardinality:

(<=> (Single-Valued-Slot ?Class ?Binary-Relation)
(= (Slot-Cardinality ?Class ?Binary-Relation) 1))

## Axioms mentioning Slot-Cardinality:

(= (Slot-Cardinality ?Class ?Binary-Relation) 1)