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Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > disjoint

disjoint
subject			fact

disjoint	documentation Classes are disjoint only if they share no instances, i.e. just in case the result of applying IntersectionFn to them is empty
	has axiom (=> (disjoint ?CLASS1 ?CLASS2) (forall (?INST) (not (and (instance ?INST ?CLASS1) (instance ?INST ?CLASS2)))))
	has axiom (=> (disjointDecomposition ?CLASS1 ?CLASS2 ?CLASS3) (and (subclass ?CLASS2 ?CLASS1) (subclass ?CLASS3 ?CLASS1) (disjoint ?CLASS2 ?CLASS3)))
	has axiom (=> (disjointDecomposition ?CLASS1 ?CLASS2 ?CLASS3 ?CLASS4) (and (subclass ?CLASS2 ?CLASS1) (subclass ?CLASS3 ?CLASS1) (subclass ?CLASS4 ?CLASS1) (disjoint ?CLASS2 ?CLASS3) (disjoint ?CLASS3 ?CLASS4) (disjoint ?CLASS2 ?CLASS4)))
	has axiom (=> (disjointDecomposition ?CLASS1 ?CLASS2 ?CLASS3 ?CLASS4 ?CLASS5) (and (subclass ?CLASS2 ?CLASS1) (subclass ?CLASS3 ?CLASS1) (subclass ?CLASS4 ?CLASS1) (subclass ?CLASS5 ?CLASS1) (disjoint ?CLASS2 ?CLASS3) (disjoint ?CLASS3 ?CLASS4) (disjoint ?CLASS2 ?CLASS4) (disjoint ?CLASS5 ?CLASS4) (disjoint ?CLASS5 ?CLASS3) (disjoint ?CLASS5 ?CLASS2)))
	has axiom (=> (instance ?SUPERCLASS PairwiseDisjointClass) (forall (?CLASS1 ?CLASS2) (=> (and (instance ?CLASS1 ?SUPERCLASS) (instance ?CLASS2 ?SUPERCLASS)) (or (equal ?CLASS1 ?CLASS2) (disjoint ?CLASS1 ?CLASS2)))))
	has domain1 Class
	has domain2 Class
	is an instance of BinaryPredicate
	is an instance of SymmetricRelation
BinaryRelation	is first domain of DomainFn
	is first domain of equivalenceRelationOn
	is first domain of inverse
	is first domain of irreflexiveOn
	is first domain of partialOrderingOn
	is first domain of RangeFn
	is first domain of reflexiveOn
	is first domain of totalOrderingOn
	is first domain of trichotomizingOn
	is second domain of inverse
Predicate	is first domain of singleValued
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

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