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Entity > Abstract > Class > Relation > BinaryRelation > SymmetricRelation

SymmetricRelation
subject			fact

SymmetricRelation	documentation A BinaryRelation ?REL is symmetric just in case (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2
	has axiom (=> (equivalenceRelationOn ?RELATION ?CLASS) (and (instance ?RELATION TransitiveRelation) (instance ?RELATION SymmetricRelation) (reflexiveOn ?RELATION ?CLASS)))
	has axiom (=> (instance ?REL SymmetricRelation) (forall (?INST1 ?INST2) (=> (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST2))))
	is a kind of BinaryRelation
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
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of SymmetricRelation :

• connected (20 facts) - (connected ?OBJ1 ?OBJ2) means that ?OBJ1 meetsSpatially ?OBJ2 or that ?OBJ1 overlapsSpatially ?OBJ2
• connectedEngineeringComponents (8 facts) - 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
• contraryProperty (8 facts) - Means that the two arguments are properties that are opposed to one another, e.g. Pliable versus Rigid
• disjoint (10 facts) - Classes are disjoint only if they share no instances, i.e. just in case the result of applying IntersectionFn to them is empty
• EquivalenceRelation (10 kinds, 59 facts) - A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation
• inverse (6 facts) - 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

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