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Entity > Abstract > Class > Relation > BinaryRelation

BinaryRelation
subject			fact

BinaryRelation	documentation BinaryRelations map instances of a Class to instances of another Class. BinaryRelations are represented as slots in frame systems
	has axiom (=> (and (instance ?REL RelationExtendedToQuantities) (instance ?REL BinaryRelation) (instance ?NUMBER1 RealNumber) (instance ?NUMBER2 RealNumber) (holds ?REL ?NUMBER1 ?NUMBER2)) (forall (?UNIT) (=> (instance ?UNIT UnitOfMeasure) (holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))
	has axiom (=> (and (inverse ?REL1 ?REL2) (instance ?REL1 BinaryRelation) (instance ?REL2 BinaryRelation)) (forall (?INST1 ?INST2) (<=> (holds ?REL1 ?INST1 ?INST2) (holds ?REL2 ?INST2 ?INST1))))
	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
	is a kind of Relation
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of BinaryRelation :

• AntisymmetricRelation (97 kinds, 821 facts) - BinaryRelation ?REL is an AntisymmetricRelation if for distinct ?INST1 and ?INST2, (?REL ?INST1 ?INST2) implies not (?REL ?INST2 ?INST1). In other words, for all ?INST1 and ?INST2, (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST1) imply that ?INST1 and ?INST2 are identical. Note that it is possible for an AntisymmetricRelation to be a ReflexiveRelation
• BinaryPredicate (96 kinds, 886 facts) - A Predicate relating two items - its valence is two
• distributes (6 facts) - A BinaryFunction ?FUNCTION1 is distributive over another BinaryFunction ?FUNCTION2 just in case (?FUNCTION1 ?INST1 (?FUNCTION2 ?INST2 ?INST3)) is equal to (?FUNCTION2 (?FUNCTION1 ?INST1 ?INST2) (?FUNCTION1 ?INST1 ?INST3)), for all ?INST1, ?INST2, and ?INST3
• IntransitiveRelation (6 kinds, 55 facts) - A BinaryRelation ?REL is intransitive only if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply not (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
• IrreflexiveRelation (98 kinds, 765 facts) - Relation ?REL is irreflexive if (?REL ?INST ?INST) holds for no value of ?INST
• ReflexiveRelation (27 kinds, 276 facts) - Relation ?REL is reflexive if (?REL ?INST ?INST) for all ?INST
• SymmetricRelation (16 kinds, 115 facts) - A BinaryRelation ?REL is symmetric just in case (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2
• TransitiveRelation (51 kinds, 436 facts) - A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
• TrichotomizingRelation (1 kind, 7 facts) - A BinaryRelation ?REL is a TrichotomizingRelation just in case all ordered pairs consisting of distinct individuals are elements of ?REL
• UnaryFunction (60 kinds, 413 facts) - The Class of Functions that require a single argument

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