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Sigma KEE - partialOrderingOn
partialOrderingOn

appearance as argument number 1
-------------------------


(documentation partialOrderingOn ChineseLanguage "一个 BinaryRelation 在一个 SetOrClass 使部分顺序的,除非这个关系是在这个SetOrClassreflexiveOn,而且它既是 AntisymmetricRelation 又是 TransitiveRelation。") chinese_format.kif 2045-2047
(documentation partialOrderingOn EnglishLanguage "A BinaryRelation is a partial ordering on a SetOrClass only if the relation is reflexiveOn the SetOrClass, and it is both an AntisymmetricRelation, and a TransitiveRelation.") Merge.kif 3488-3491
(domain partialOrderingOn 1 BinaryRelation) Merge.kif 3485-3485 The number 1 argument of partial ordering on is an instance of binary relation
(domain partialOrderingOn 2 SetOrClass) Merge.kif 3486-3486 The number 2 argument of partial ordering on is an instance of set or class
(instance partialOrderingOn AsymmetricRelation) Merge.kif 3484-3484 partial ordering on is an instance of asymmetric relation
(instance partialOrderingOn BinaryPredicate) Merge.kif 3483-3483 partial ordering on is an instance of binary predicate

appearance as argument number 2
-------------------------


(format ChineseLanguage partialOrderingOn "%1 在 %2 %n 是 partialOrderingOn") chinese_format.kif 163-163
(format EnglishLanguage partialOrderingOn "%1 is %n partial ordering on %2") english_format.kif 167-167
(termFormat ChineseLanguage partialOrderingOn "含偏序关系") chinese_format.kif 164-164
(termFormat ChineseLanguage partialOrderingOn "部分订购在") domainEnglishFormat.kif 44437-44437
(termFormat ChineseTraditionalLanguage partialOrderingOn "部分訂購在") domainEnglishFormat.kif 44436-44436
(termFormat EnglishLanguage partialOrderingOn "partial ordering on") domainEnglishFormat.kif 44435-44435

antecedent
-------------------------


(=>
    (partialOrderingOn ?RELATION ?CLASS)
    (and
        (reflexiveOn ?RELATION ?CLASS)
        (instance ?RELATION TransitiveRelation)
        (instance ?RELATION AntisymmetricRelation)))
Merge.kif 3493-3498

consequent
-------------------------


(<=>
    (totalOrderingOn ?RELATION ?CLASS)
    (and
        (partialOrderingOn ?RELATION ?CLASS)
        (trichotomizingOn ?RELATION ?CLASS)))
Merge.kif 3510-3514 A binary relation is total ordering on a set or class if and only if the binary relation is partial ordering on the set or class and the binary relation is trichotomizing on the set or class


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