Class Comparison Table

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Class comparison table

Subject documentation be second domain of be first domain of have axiom

MutuallyDisjointClass A Class of Classes is a MutuallyDisjointClass just in case there exists no instance of an instance of the original Class which is an instance of all of the instances of the original Class UnionFn UnionFn
(=>
(instance ?CLASS MutuallyDisjointClass)
(equal (GeneralizedIntersectionFn ?CLASS) NullSet))

PairwiseDisjointClass A Class of Classes is a PairwiseDisjointClass just in case every instance of the Class is either equal to or disjoint from every other instance of the Class UnionFn UnionFn
(=>
(instance ?SUPERCLASS PairwiseDisjointClass)
(forall (?CLASS1 ?CLASS2)
(=>
(and
(instance ?CLASS1 ?SUPERCLASS)
(instance ?CLASS2 ?SUPERCLASS))
(or
(equal ?CLASS1 ?CLASS2)
(disjoint ?CLASS1 ?CLASS2)))))

Relation A Class of ordered tuples subrelation valence
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

Set A Class that satisfies extensionality as well as other conditions specified by some choice of set theory. Unlike Classes generally, Sets need not have an associated condition that determines their membership. Rather, they are thought of metaphorically as `built up' from some initial stock of objects by means of certain constructive operations (such as the pairing or power set operations). Note that extensionality alone is not sufficient for identifying Classes with Sets, since some Classes (e.g. Entity) cannot be assumed to be Sets without contradiction subset subset
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

Subject	documentation	be second domain of	be first domain of	have axiom
MutuallyDisjointClass	A Class of Classes is a MutuallyDisjointClass just in case there exists no instance of an instance of the original Class which is an instance of all of the instances of the original Class	UnionFn	UnionFn	(=> (instance ?CLASS MutuallyDisjointClass) (equal (GeneralizedIntersectionFn ?CLASS) NullSet))
PairwiseDisjointClass	A Class of Classes is a PairwiseDisjointClass just in case every instance of the Class is either equal to or disjoint from every other instance of the Class	UnionFn	UnionFn	(=> (instance ?SUPERCLASS PairwiseDisjointClass) (forall (?CLASS1 ?CLASS2) (=> (and (instance ?CLASS1 ?SUPERCLASS) (instance ?CLASS2 ?SUPERCLASS)) (or (equal ?CLASS1 ?CLASS2) (disjoint ?CLASS1 ?CLASS2)))))
Relation	A Class of ordered tuples	subrelation	valence	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
Set	A Class that satisfies extensionality as well as other conditions specified by some choice of set theory. Unlike Classes generally, Sets need not have an associated condition that determines their membership. Rather, they are thought of metaphorically as `built up' from some initial stock of objects by means of certain constructive operations (such as the pairing or power set operations). Note that extensionality alone is not sufficient for identifying Classes with Sets, since some Classes (e.g. Entity) cannot be assumed to be Sets without contradiction	subset	subset	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

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