SymmetricRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint SymmetricRelation AntisymmetricRelation)	Merge.kif 2261-2261	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
(documentation SymmetricRelation EnglishLanguage "A BinaryRelation ?REL is symmetric just iff (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2.")	Merge.kif 2263-2265
(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
(subclass SymmetricRelation BinaryRelation)	Merge.kif 2260-2260	Symmetric relation is a subclass of binary relation

appearance as argument number 2

(instance cohabitant SymmetricRelation)	Mid-level-ontology.kif 22976-22976	cohabitant is an instance of symmetric relation
(instance conjugate SymmetricRelation)	Mid-level-ontology.kif 6491-6491	conjugate is an instance of symmetric relation
(instance connected SymmetricRelation)	Merge.kif 9524-9524	connected is an instance of symmetric relation
(instance connectedEngineeringComponents SymmetricRelation)	Merge.kif 16114-16114	connected engineering components is an instance of symmetric relation
(instance consistent SymmetricRelation)	Merge.kif 16925-16925	consistent is an instance of symmetric relation
(instance coworker SymmetricRelation)	Mid-level-ontology.kif 22953-22953	coworker is an instance of symmetric relation
(instance diplomaticRelations SymmetricRelation)	Government.kif 4543-4543	diplomatic relations is an instance of symmetric relation
(instance disjoint SymmetricRelation)	Merge.kif 394-394	disjoint is an instance of symmetric relation
(instance domesticPartner SymmetricRelation)	Mid-level-ontology.kif 23360-23360	domestic partner is an instance of symmetric relation
(instance enemy SymmetricRelation)	MilitaryProcesses.kif 2450-2450	enemy is an instance of symmetric relation
(instance friend SymmetricRelation)	Mid-level-ontology.kif 22941-22941	friend is an instance of symmetric relation
(instance independentProbability SymmetricRelation)	Merge.kif 2632-2632	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 16540-16540	legal relation is an instance of symmetric relation
(instance meetsSpatially SymmetricRelation)	Merge.kif 9594-9594	meets spatially is an instance of symmetric relation
(instance mutualAcquaintance SymmetricRelation)	Merge.kif 16567-16567	mutual acquaintance is an instance of symmetric relation
(instance mutualStranger SymmetricRelation)	Mid-level-ontology.kif 23345-23345	mutual stranger is an instance of symmetric relation
(instance neighbor SymmetricRelation)	Mid-level-ontology.kif 6662-6662	neighbor is an instance of symmetric relation
(instance oppositeDirection SymmetricRelation)	Mid-level-ontology.kif 18123-18123	opposite direction is an instance of symmetric relation
(instance orthogonalTests SymmetricRelation)	UXExperimentalTerms.kif 4444-4444	managed orthogonal is an instance of symmetric relation
(instance overlapsPartially SymmetricRelation)	Merge.kif 9632-9632	overlap partially is an instance of symmetric relation
(instance overlapsSpatially SymmetricRelation)	Merge.kif 4035-4035	overlap spatially is an instance of symmetric relation
(instance overlapsTemporally SymmetricRelation)	Merge.kif 8248-8248	overlap temporally is an instance of symmetric relation
(instance relatedEvent SymmetricRelation)	Merge.kif 3767-3767	related event is an instance of symmetric relation
(instance sibling SymmetricRelation)	Merge.kif 16485-16485	sibling 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 2267-2272

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 3713-3718

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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