Relation Exhaustive-Subclass-Partition

Arity: 2
Definition-Sort-Index@Interface-Ontology: 900
A subrelation-partition of a class C is a set of mutually-disjoint classes (a subclass partition) which covers C. Every instance of C is is an instance of exactly one of the subclasses in the partition.
Binary-Relation, Binary-Relation, Relation, Relation, Relation ...
Subrelation-Of: Subclass-Partition

Implication Axioms for Exhaustive-Subclass-Partition:

(=> (Exhaustive-Subclass-Partition ?C ?Class-Partition)
    (Forall (?Instance)
            (=> (Instance-Of ?Instance ?C)
                (Exists (?Subclass)
                        (And (Member ?Subclass ?Class-Partition)
                             (Member ?Instance ?Subclass))))))

(=> (Exhaustive-Subclass-Partition ?C ?Class-Partition)
    (Subclass-Partition ?C ?Class-Partition))

Equivalence Axioms for Exhaustive-Subclass-Partition:

(<=> (Exhaustive-Subclass-Partition ?C ?Class-Partition)
     (And (Subclass-Partition ?C ?Class-Partition)
          (Forall (?Instance)
                  (=> (Instance-Of ?Instance ?C)
                      (Exists (?Subclass)
                              (And (Member ?Subclass
                                   (Member ?Instance ?Subclass)))))))

Frame References to Exhaustive-Subclass-Partition:

In class Constant:

Exhaustive-Subclass-Partition: {Funconst, Objconst, Relconst}

In class Term:

Exhaustive-Subclass-Partition: {
Funterm, Listterm, Logterm, Quanterm, Quoterm, Setterm, Word}

In class Variable:

Exhaustive-Subclass-Partition: {Indvar, Seqvar}

In class Sentence:

Exhaustive-Subclass-Partition: {
Logconst, Logsent, Quantsent, Relsent}

In class Thing:

Exhaustive-Subclass-Partition: {Individual-Thing, Simple-Set}

In class Word:

Exhaustive-Subclass-Partition: {Constant, Variable}