SUMO   View all facts   Glossary   Help

Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > trichotomizingOn

trichotomizingOn
subject			fact

trichotomizingOn	documentation A BinaryRelation ?REL is trichotomizing on a Class only if, for all instances ?INST1 and ?INST2 of the Class, at least one of the following holds: (?REL ?INST1 ?INST2), (?REL ?INST2 ?INST1) or (equal ?INST1 ?INST2)
	has axiom (<=> (totalOrderingOn ?RELATION ?CLASS) (and (partialOrderingOn ?RELATION ?CLASS) (trichotomizingOn ?RELATION ?CLASS)))
	has axiom (=> (trichotomizingOn ?RELATION ?CLASS) (forall (?INST1 ?INST2) (=> (and (instance ?INST1 ?CLASS) (instance ?INST2 ?CLASS)) (or (holds ?RELATION ?INST1 ?INST2) (holds ?RELATION ?INST2 ?INST1) (equal ?INST1 ?INST2)))))
	has domain1 BinaryRelation
	has domain2 Class
	is an instance of AsymmetricRelation
	is an instance of BinaryPredicate
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

Next AsymmetricRelation: under    Up: AsymmetricRelation, BinaryPredicate    Previous AsymmetricRelation: totalOrderingOn