Function All-Instances

Arity: 2
The instances of some classes may be specified extensionally. That is, one can list all of the instances of the class by definition. For this case we say (= (all-instances C) (setof V_1 V_2 ... V_n)), where C is a class and the V_i are its instances.

ALL-INSTANCES imposes a monotonic constraint. Any subclass of C cannot have any instances outside of the ALL-INSTANCES of C. Note that this is not indexical or modal: whether something is in all-instances is a property of the modeled world and does not depend on the facts currently stored in some knowledge base.


Domain: Class
Binary-Relation, Function, Relation, Set
Range: Set

Equivalence Axioms for All-Instances:

(<=> (All-Instances ?Class)
     (And (Class ?Class)
          (Set ?Set-Of-Instances)
          (Forall (?Instance)
                  (<=> (Member ?Instance ?Set-Of-Instances)
                       (Instance-Of ?Instance ?Class)))))

Frame References to All-Instances:

In class Month-Name@Simple-Time:

All-Instances: {
April@Simple-Time, August@Simple-Time, December@Simple-Time, February@Simple-Time, January@Simple-Time, July@Simple-Time, June@Simple-Time, March@Simple-Time, May@Simple-Time, November@Simple-Time, October@Simple-Time, September@Simple-Time}

In class Zero:

All-Instances: {0}

In class Ruleop:

All-Instances: {'<<=, '=>>}

In class Termop:

All-Instances: {
'Cond, 'Kappa, 'Lambda, 'Listof, 'Quote, 'Setof, 'Setofall, 'The}

In class Defop:

All-Instances: {
':=, ':=>, ':Axiom, ':Conservative-axiom, 'Define-function, 'Defobject, 'Defrelation}

In class Day-Name@Simple-Time:

All-Instances: {
Friday@Simple-Time, Monday@Simple-Time, Saturday@Simple-Time, Sunday@Simple-Time, Thursday@Simple-Time, Tuesday@Simple-Time, Wednesday@Simple-Time}

Implication Axioms mentioning All-Instances:

(=> (= (All-Instances ?Class) ?Set-Of-Instances)
    (Forall (?Instance)
            (<=> (Member ?Instance ?Set-Of-Instances)
                 (Instance-Of ?Instance ?Class))))

(=> (= (All-Instances ?Class) ?Set-Of-Instances)
    (Set ?Set-Of-Instances))

(=> (= (All-Instances ?Class) ?Set-Of-Instances) (Class ?Class))