member Comparison Table

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

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member comparison table

Subject have domain2 have domain1 be first domain of be second domain of documentation have axiom is a kind of is an instance of have relatedInternalConcept

AsymmetricRelation trichotomizingOn inverse A BinaryRelation is asymmetric only if it is both an AntisymmetricRelation and an IrreflexiveRelation
(=>
(instance ?REL IrreflexiveRelation)
(forall (?INST)
(not
(holds ?REL ?INST ?INST))))
IrreflexiveRelation

BinaryPredicate singleValued inverse A Predicate relating two items - its valence is two
(=>
(instance ?REL BinaryPredicate)
(valence ?REL 2))
Predicate

IntransitiveRelation trichotomizingOn inverse 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
(=>
(instance ?REL IntransitiveRelation)
(forall (?INST1 ?INST2 ?INST3)
(=>
(and
(holds ?REL ?INST1 ?INST2)
(holds ?REL ?INST2 ?INST3))
(not
(holds ?REL ?INST1 ?INST3)))))
BinaryRelation

SpatialRelation valence subrelation The Class of Relations that are spatial in a wide sense. This Class includes mereological relations, topological relations, and positional relations
(=>
(and
(instance ?REL SpatialRelation)
(holds ?REL ?OBJ1 ?OBJ2))
(overlapsTemporally (WhenFn ?OBJ1) (WhenFn ?OBJ2)))
Relation

member Collection SelfConnectedObject valence subrelation A specialized common sense notion of part for uniform parts of Collections. For example, each sheep in a flock of sheep would have the relationship of member to the flock
(=>
(instance ?COLL Collection)
(exists (?OBJ)
(member ?OBJ ?COLL)))
SpatialRelation instance

Subject	have domain2	have domain1	be first domain of	be second domain of	documentation	have axiom	is a kind of	is an instance of	have relatedInternalConcept
AsymmetricRelation			trichotomizingOn	inverse	A BinaryRelation is asymmetric only if it is both an AntisymmetricRelation and an IrreflexiveRelation	(=> (instance ?REL IrreflexiveRelation) (forall (?INST) (not (holds ?REL ?INST ?INST))))	IrreflexiveRelation
BinaryPredicate			singleValued	inverse	A Predicate relating two items - its valence is two	(=> (instance ?REL BinaryPredicate) (valence ?REL 2))	Predicate
IntransitiveRelation			trichotomizingOn	inverse	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	(=> (instance ?REL IntransitiveRelation) (forall (?INST1 ?INST2 ?INST3) (=> (and (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST3)) (not (holds ?REL ?INST1 ?INST3)))))	BinaryRelation
SpatialRelation			valence	subrelation	The Class of Relations that are spatial in a wide sense. This Class includes mereological relations, topological relations, and positional relations	(=> (and (instance ?REL SpatialRelation) (holds ?REL ?OBJ1 ?OBJ2)) (overlapsTemporally (WhenFn ?OBJ1) (WhenFn ?OBJ2)))	Relation
member	Collection	SelfConnectedObject	valence	subrelation	A specialized common sense notion of part for uniform parts of Collections. For example, each sheep in a flock of sheep would have the relationship of member to the flock	(=> (instance ?COLL Collection) (exists (?OBJ) (member ?OBJ ?COLL)))		SpatialRelation	instance

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