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Entity > Abstract > Class > Relation > BinaryRelation > SymmetricRelation |

SymmetricRelation | ||||

subject | fact |

SymmetricRelation | A BinaryRelation ?REL is symmetric just in case (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 documentationand ?INST2 | |

has axiom (=> | ||

has axiom (=> | ||

is a kind of BinaryRelation | ||

BinaryRelation | is first domain ofDomainFn | |

is first domain ofequivalenceRelationOn | ||

is first domain ofinverse | ||

is first domain ofirreflexiveOn | ||

is first domain ofpartialOrderingOn | ||

is first domain ofRangeFn | ||

is first domain ofreflexiveOn | ||

is first domain oftotalOrderingOn | ||

is first domain oftrichotomizingOn | ||

is second domain ofinverse | ||

Class | is third domain ofdomain | |

is third domain ofdomainSubclass | ||

Abstract | is Physicaldisjoint from |

**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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