Function Slot-Cardinality

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:

In class Calendar-Year@Simple-Time:

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

In class One-To-Many-Relation:

Slots:

Inverse:
Slot-Cardinality: 1

In class Funterm:

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)