SymmetricRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint SymmetricRelation AntisymmetricRelation)	Merge.kif 2272-2272	Symmetric relation is disjoint from antisymmetric relation
(documentation SymmetricRelation ChineseLanguage "一个 BinaryRelation ?REL 属于对称关系只是当且仅当所有的 ?INST1 和 ?INST2 是 (?REL ?INST1 ?INST2) 意味着 (?REL ?INST2 ?INST1)。")	chinese_format.kif 1837-1838	Symmetric relation is disjoint from antisymmetric relation
(documentation SymmetricRelation EnglishLanguage "A BinaryRelation ?REL is symmetric just iff (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2.")	Merge.kif 2274-2276	Symmetric relation is disjoint from antisymmetric relation
(documentation SymmetricRelation JapaneseLanguage "BinaryRelation ?REL は、すべての ?INST1 および ?INST2 に対して (?REL ?INST1 ?INST2) が (?REL ?INST2 ?INST1) の場合にのみ対称である。")	japanese_format.kif 457-458	Symmetric relation is disjoint from antisymmetric relation
(subclass SymmetricRelation BinaryRelation)	Merge.kif 2271-2271	Symmetric relation is a subclass of binary relation

appearance as argument number 2

(instance allied SymmetricRelation)	MilitaryProcesses.kif 2466-2466	allied is an instance of symmetric relation
(instance cohabitant SymmetricRelation)	Mid-level-ontology.kif 24606-24606	cohabitant is an instance of symmetric relation
(instance conjugate SymmetricRelation)	Mid-level-ontology.kif 7425-7425	conjugate is an instance of symmetric relation
(instance connected SymmetricRelation)	Merge.kif 9635-9635	connected is an instance of symmetric relation
(instance connectedEngineeringComponents SymmetricRelation)	Merge.kif 16265-16265	connected engineering components is an instance of symmetric relation
(instance connectedRegions SymmetricRelation)	Geography.kif 595-595	connected regions is an instance of symmetric relation
(instance consistent SymmetricRelation)	Merge.kif 17075-17075	consistent is an instance of symmetric relation
(instance coworker SymmetricRelation)	Mid-level-ontology.kif 24583-24583	coworker is an instance of symmetric relation
(instance diplomaticRelations SymmetricRelation)	Government.kif 4504-4504	diplomatic relations is an instance of symmetric relation
(instance disconnected SymmetricRelation)	Geography.kif 623-623	disconnected is an instance of symmetric relation
(instance disjoint SymmetricRelation)	Merge.kif 387-387	disjoint is an instance of symmetric relation
(instance domesticPartner SymmetricRelation)	Mid-level-ontology.kif 24990-24990	domestic partner is an instance of symmetric relation
(instance enemy SymmetricRelation)	MilitaryProcesses.kif 2451-2451	enemy is an instance of symmetric relation
(instance equalRegions SymmetricRelation)	Geography.kif 678-678	partially overlapping is an instance of symmetric relation
(instance externallyConnected SymmetricRelation)	Geography.kif 640-640	externally connected is an instance of symmetric relation
(instance friend SymmetricRelation)	Mid-level-ontology.kif 24571-24571	friend is an instance of symmetric relation
(instance independentProbability SymmetricRelation)	Merge.kif 2643-2643	independent probability is an instance of symmetric relation
(instance inverse SymmetricRelation)	Merge.kif 109-109	inverse is an instance of symmetric relation
(instance legalRelation SymmetricRelation)	Merge.kif 16690-16690	legal relation is an instance of symmetric relation
(instance meetsSpatially SymmetricRelation)	Merge.kif 9705-9705	meets spatially is an instance of symmetric relation
(instance mutualAcquaintance SymmetricRelation)	Merge.kif 16717-16717	mutual acquaintance is an instance of symmetric relation
(instance mutualStranger SymmetricRelation)	Mid-level-ontology.kif 24975-24975	mutual stranger is an instance of symmetric relation
(instance neighbor SymmetricRelation)	Mid-level-ontology.kif 7596-7596	neighbor is an instance of symmetric relation
(instance oppositeDirection SymmetricRelation)	Mid-level-ontology.kif 19681-19681	opposite direction is an instance of symmetric relation
(instance orthogonalTests SymmetricRelation)	UXExperimentalTerms.kif 4443-4443	managed orthogonal is an instance of symmetric relation

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antecedent

(=>
    (instance ?REL SymmetricRelation)
    (forall (?INST1 ?INST2)
        (=>
            (?REL ?INST1 ?INST2)
            (?REL ?INST2 ?INST1))))

Merge.kif 2278-2283

If an entity is an instance of symmetric relation,
then for all another entity and a third entity
- if the entity the other entity and the third entity,
- then the entity the third entity and the other entity

consequent

(=>
    (equivalenceRelationOn ?RELATION ?CLASS)
    (and
        (instance ?RELATION TransitiveRelation)
        (instance ?RELATION SymmetricRelation)
        (reflexiveOn ?RELATION ?CLASS)))

Merge.kif 3728-3733

If a binary relation is an equivalence relation on a class,
then the binary relation is an instance of transitive relation and the binary relation is an instance of symmetric relation and the binary relation is reflexive on the class

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