Class C is a subclass of parent class P if and only if every instance of C is also an instance of P. A class may have multiple superclasses and subclasses. Subclass-of is transitive: if (subclass-of C1 C2) and (subclass-of C2 C3) then (subclass-of C1 C3).Object-centered systems sometimes distinguish between a subclass-of relationship that is asserted and one that is inferred. For example, (subclass-of C1 C3) might be inferred from asserting (subclass-of C1 C2) and (subclass-of C2 C3). The functional interfaces to such systems might call the asserted form something like `parents' and the inferred form `ancestors'. However, both are logically identical to subclass-of; distinctions based on inference procedures and the current state of the knowledge base are not captured in this ontology.
Notes:
- See-Also: direct-subclass-of
- See-Also: In CycL, subclass-of is called #%allGenls because it is a slot from a collection to all of its generalizations (superclasses).
In the KL-ONE literature, subclass relationships are also called subsumption relationships and ISA is sometimes used for subclass-of.
- Why is it called Subclass-of instead of subclass or superclass?
Because the latter are ambiguous about the order of their arguments. We are following the naming convention that a binary relationship is read as an english sentence `Domain-element Relation-name Range-value'. Thus, `person subclass-of animal' rather than `person superclass animal'.
(=> (Subclass-Of ?Child-Class ?Parent-Class) (Forall (?Instance) (=> (Instance-Of ?Instance ?Child-Class) (Instance-Of ?Instance ?Parent-Class))))
(<=> (Subclass-Of ?Child-Class ?Parent-Class) (And (Class ?Parent-Class) (Class ?Child-Class) (Forall (?Instance) (=> (Instance-Of ?Instance ?Child-Class) (Instance-Of ?Instance ?Parent-Class)))))
(=> (Inherited-Through-Class-Of-Relation ?R) (=> (And (Holds ?R ?X ?C1) (Class ?C1) (Class ?C2) (Subclass-Of ?C2 ?C1)) (Holds ?R ?X ?C2))) (=> (Domain ?Relation ?Restriction) (Subclass-Of (Exact-Domain ?Relation) ?Restriction)) (=> (Range ?Relation ?Type) (Subclass-Of (Exact-Range ?Relation) ?Type)) (=> (Subclass-Partition ?C ?Class-Partition) (Forall (?Subclass) (=> (Member ?Subclass ?Class-Partition) (Subclass-Of ?Subclass ?C))))
(<=> (Inherited-Through-Class-Of-Relation ?R) (And (Binary-Relation ?R) (=> (And (Holds ?R ?X ?C1) (Class ?C1) (Class ?C2) (Subclass-Of ?C2 ?C1)) (Holds ?R ?X ?C2)))) (<=> (Onto ?Relation ?Range-Class) (Subclass-Of (Exact-Range ?Relation) ?Range-Class)) (<=> (Domain ?Relation ?Restriction) (And (Binary-Relation ?Relation) (Class ?Restriction) (Subclass-Of (Exact-Domain ?Relation) ?Restriction))) (<=> (Range ?Relation ?Type) (And (Relation ?Relation) (Class ?Type) (Subclass-Of (Exact-Range ?Relation) ?Type))) (<=> (Subclass-Partition ?C ?Class-Partition) (And (Class ?C) (Class-Partition ?Class-Partition) (Forall (?Subclass) (=> (Member ?Subclass ?Class-Partition) (Subclass-Of ?Subclass ?C)))))
(<= (Instance-Of ?Arg1 ?Class2) (And (Instance-Of ?Arg1 ?Class1) (Subclass-Of ?Class1 ?Class2))) (<= (Subclass-Of Ontolingua-Internal::@Arg-List) (Direct-Subclass-Of Ontolingua-Internal::@Arg-List)) (<= (Subclass-Of ?X Integer) (Integer-Range@Ranges ?X)) (<= (Subclass-Of ?X Real-Number) (Real-Range@Ranges ?X))