SymmetricRelation Comparison Table

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SymmetricRelation 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

connected Object Object valence subrelation (connected ?OBJ1 ?OBJ2) means that ?OBJ1 meetsSpatially ?OBJ2 or that ?OBJ1 overlapsSpatially ?OBJ2
(=>
(crosses ?OBJ1 ?OBJ2)
(not
(connected ?OBJ1 ?OBJ2)))
SymmetricRelation

connectedEngineeringComponents EngineeringComponent EngineeringComponent trichotomizingOn inverse This is the most general connection relation between EngineeringComponents. If (connectedEngineeringComponents ?COMP1 ?COMP2), then neither ?COMP1 nor ?COMP2 can be an engineeringSubcomponent of the other. The relation connectedEngineeringComponents is a SymmetricRelation; there is no information in the direction of connection between two components. It is also an IrreflexiveRelation; no EngineeringComponent bears this relation to itself. Note that this relation does not associate a name or type with the connection
(=>
(connectedEngineeringComponents ?COMP1 ?COMP2)
(and
(not
(engineeringSubcomponent ?COMP1 ?COMP2))
(not
(engineeringSubcomponent ?COMP2 ?COMP1))))
SymmetricRelation

contraryProperty Attribute Attribute singleValued inverse Means that the two arguments are properties that are opposed to one another, e.g. Pliable versus Rigid
(=>
(and
(attribute ?OBJ ?ATTR1)
(contraryProperty ?ATTR1 ?ATTR2))
(not
(attribute ?OBJ ?ATTR2)))
TransitiveRelation

disjoint Class Class singleValued inverse Classes are disjoint only if they share no instances, i.e. just in case the result of applying IntersectionFn to them is empty
(=>
(instance ?SUPERCLASS PairwiseDisjointClass)
(forall (?CLASS1 ?CLASS2)
(=>
(and
(instance ?CLASS1 ?SUPERCLASS)
(instance ?CLASS2 ?SUPERCLASS))
(or
(equal ?CLASS1 ?CLASS2)
(disjoint ?CLASS1 ?CLASS2)))))
SymmetricRelation

EquivalenceRelation trichotomizingOn inverse A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation
(=>
(instance ?REL TransitiveRelation)
(forall (?INST1 ?INST2 ?INST3)
(=>
(and
(holds ?REL ?INST1 ?INST2)
(holds ?REL ?INST2 ?INST3))
(holds ?REL ?INST1 ?INST3))))
TransitiveRelation

inverse BinaryRelation BinaryRelation singleValued inverse The inverse of a BinaryRelation is a relation in which all the tuples of the original relation are reversed. In other words, one BinaryRelation is the inverse of another if they are equivalent when their arguments are swapped
(=>
(and
(inverse ?REL1 ?REL2)
(instance ?REL1 BinaryRelation)
(instance ?REL2 BinaryRelation))
(forall (?INST1 ?INST2)
(<=>
(holds ?REL1 ?INST1 ?INST2)
(holds ?REL2 ?INST2 ?INST1))))
SymmetricRelation

Subject	have domain2	have domain1	be first domain of	be second domain of	documentation	have axiom	is a kind of	is an instance of
connected	Object	Object	valence	subrelation	(connected ?OBJ1 ?OBJ2) means that ?OBJ1 meetsSpatially ?OBJ2 or that ?OBJ1 overlapsSpatially ?OBJ2	(=> (crosses ?OBJ1 ?OBJ2) (not (connected ?OBJ1 ?OBJ2)))		SymmetricRelation
connectedEngineeringComponents	EngineeringComponent	EngineeringComponent	trichotomizingOn	inverse	This is the most general connection relation between EngineeringComponents. If (connectedEngineeringComponents ?COMP1 ?COMP2), then neither ?COMP1 nor ?COMP2 can be an engineeringSubcomponent of the other. The relation connectedEngineeringComponents is a SymmetricRelation; there is no information in the direction of connection between two components. It is also an IrreflexiveRelation; no EngineeringComponent bears this relation to itself. Note that this relation does not associate a name or type with the connection	(=> (connectedEngineeringComponents ?COMP1 ?COMP2) (and (not (engineeringSubcomponent ?COMP1 ?COMP2)) (not (engineeringSubcomponent ?COMP2 ?COMP1))))		SymmetricRelation
contraryProperty	Attribute	Attribute	singleValued	inverse	Means that the two arguments are properties that are opposed to one another, e.g. Pliable versus Rigid	(=> (and (attribute ?OBJ ?ATTR1) (contraryProperty ?ATTR1 ?ATTR2)) (not (attribute ?OBJ ?ATTR2)))		TransitiveRelation
disjoint	Class	Class	singleValued	inverse	Classes are disjoint only if they share no instances, i.e. just in case the result of applying IntersectionFn to them is empty	(=> (instance ?SUPERCLASS PairwiseDisjointClass) (forall (?CLASS1 ?CLASS2) (=> (and (instance ?CLASS1 ?SUPERCLASS) (instance ?CLASS2 ?SUPERCLASS)) (or (equal ?CLASS1 ?CLASS2) (disjoint ?CLASS1 ?CLASS2)))))		SymmetricRelation
EquivalenceRelation			trichotomizingOn	inverse	A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation	(=> (instance ?REL TransitiveRelation) (forall (?INST1 ?INST2 ?INST3) (=> (and (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST3)) (holds ?REL ?INST1 ?INST3))))	TransitiveRelation
inverse	BinaryRelation	BinaryRelation	singleValued	inverse	The inverse of a BinaryRelation is a relation in which all the tuples of the original relation are reversed. In other words, one BinaryRelation is the inverse of another if they are equivalent when their arguments are swapped	(=> (and (inverse ?REL1 ?REL2) (instance ?REL1 BinaryRelation) (instance ?REL2 BinaryRelation)) (forall (?INST1 ?INST2) (<=> (holds ?REL1 ?INST1 ?INST2) (holds ?REL2 ?INST2 ?INST1))))		SymmetricRelation

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