equivalenceRelationOn - Sigma Knowledge base Browser

appearance as argument number 1

(documentation equivalenceRelationOn ChineseLanguage "一个 BinaryRelation 在一个 SetOrClass 是 equivalenceRelationOn，除非这个关系在这个 SetOrClass 是 reflexiveOn，而且也要既是 TransitiveRelation，又是 SymmetricRelation。")	chinese_format.kif 2055-2057
(documentation equivalenceRelationOn EnglishLanguage "A BinaryRelation is an equivalenceRelationOn a Class only if the relation is reflexiveOn the Class and it is both a TransitiveRelation and a SymmetricRelation.")	Merge.kif 3709-3712
(documentation equivalenceRelationOn JapaneseLanguage "BinaryRelation は、関係が SetOrClass の　reflexiveOn であり、TransitiveRelation と SymmetricRelation の両方である場合にのみ、SetOrClass の equivalenceRelationOn である。")	japanese_format.kif 700-702
(domain equivalenceRelationOn 1 BinaryRelation)	Merge.kif 3706-3706	The number 1 argument of equivalence relation on is an instance of binary relation
(domain equivalenceRelationOn 2 Class)	Merge.kif 3707-3707	The number 2 argument of equivalence relation on is an instance of class
(instance equivalenceRelationOn AsymmetricRelation)	Merge.kif 3705-3705	equivalence relation on is an instance of asymmetric relation
(instance equivalenceRelationOn BinaryPredicate)	Merge.kif 3704-3704	equivalence relation on is an instance of binary predicate

appearance as argument number 2

(format ChineseLanguage equivalenceRelationOn "%1 和 %2 %n 是 EquivalenceRelation")	chinese_format.kif 99-99
(format EnglishLanguage equivalenceRelationOn "%1 is %n an equivalence relation on %2")	english_format.kif 99-99
(format FrenchLanguage equivalenceRelationOn "%1 a une %n relation d'�quivalence avec %2")	french_format.kif 72-72
(format ItalianLanguage equivalenceRelationOn "%1 è %n relazione di equivalenza su %2")	relations-it.txt 97-97
(format JapaneseLanguage equivalenceRelationOn "%1 は %2 と equivalence 関係が %n")	japanese_format.kif 1898-1898
(format PortugueseLanguage equivalenceRelationOn "%1 tem uma %n relacao de equivalencia com %2")	portuguese_format.kif 24-24
(format cz equivalenceRelationOn "%1 %p{je} %n{nen�} equivalence relation on %2")	relations-cz.txt 112-112
(format de equivalenceRelationOn "%1 ist eine aequivalenzrelation mit %2 %n{nicht}")	relations-de.txt 112-112
(format hi equivalenceRelationOn "%1 %2 para tulyataasmbandha %n hai")	relations-hindi.txt 137-137
(format ro equivalenceRelationOn "%1 %n{nu} este o relaþie de equivalence%t{echivalenþã} peste %2")	relations-ro.kif 91-91
(format sv equivalenceRelationOn "%1 är %n{inte} en ekvivalensrelation till %2")	relations-sv.txt 71-71
(format tg equivalenceRelationOn "%1 %n ay ang ugnay ng tulad sa %2")	relations-tg.txt 207-207
(termFormat ChineseLanguage equivalenceRelationOn "属于等价关系")	chinese_format.kif 100-100
(termFormat ChineseLanguage equivalenceRelationOn "等价关系")	domainEnglishFormat.kif 22378-22378
(termFormat ChineseTraditionalLanguage equivalenceRelationOn "等價關係")	domainEnglishFormat.kif 22377-22377
(termFormat EnglishLanguage equivalenceRelationOn "equivalence relation on")	domainEnglishFormat.kif 22376-22376
(termFormat de equivalenceRelationOn "aequivalenzrelationMit")	terms-de.txt 32-32

antecedent

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

Merge.kif 3714-3719

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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