TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 3776-3776	Transitive relation is disjoint from intransitive relation
(documentation TransitiveRelation ChineseLanguage "一个 BinaryRelation ?REL 是传递关系如果所有的 ?INST1， ?INST2和 ?INST3 是(?REL ?INST1 ?INST2) 和 (?REL ?INST2 ?INST3) 意味着 (?REL ?INST1 ?INST3)。")	Merge.kif 3782-3784
(documentation TransitiveRelation EnglishLanguage "A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.")	Merge.kif 3778-3780
(documentation TransitiveRelation JapaneseLanguage "BinaryRelation ?REL は、すべての ?INST1, ?INST2, および ?INST3 に対して (?REL ?INST1 ?INST2) および (?REL ?INST2 ?INST3) が (?REL ?INST1 ?INST3) を意味する場合、推移的である。")	Merge.kif 3786-3788
(subclass TransitiveRelation BinaryRelation)	Merge.kif 3775-3775	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 20941-20941	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 21929-21929	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 11619-11619	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 21108-21108	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6182-6182	conjugate is an instance of transitive relation
(instance covers TransitiveRelation)	Mid-level-ontology.kif 27920-27920	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 6272-6272	crosses is an instance of transitive relation
(instance dependentGeopoliticalArea TransitiveRelation)	Government.kif 446-446	dependent geopolitical area is an instance of transitive relation
(instance developmentalForm TransitiveRelation)	Merge.kif 18724-18724	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 11782-11782	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 11840-11840	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 11589-11589	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5089-5089	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 18415-18415	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 18465-18465	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 2953-2953	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 13403-13403	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 11181-11181	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 2935-2935	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 6091-6091	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 7224-7224	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 6372-6372	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 1424-1424	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 21119-21119	sister is an instance of transitive relation
(instance smaller TransitiveRelation)	Merge.kif 11209-11209	smaller is an instance of transitive relation

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antecedent

(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
        (=>
            (and
                (?REL ?INST1 ?INST2)
                (?REL ?INST2 ?INST3))
            (?REL ?INST1 ?INST3))))

Merge.kif 3790-3797

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

consequent

(=> (equivalenceRelationOn ?RELATION ?CLASS) (and (instance ?RELATION TransitiveRelation) (instance ?RELATION SymmetricRelation) (reflexiveOn ?RELATION ?CLASS)))	Merge.kif 5618-5623	If a binary relation is an equivalence relation on a set or 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 set or class
(=> (partialOrderingOn ?RELATION ?CLASS) (and (reflexiveOn ?RELATION ?CLASS) (instance ?RELATION TransitiveRelation) (instance ?RELATION AntisymmetricRelation)))	Merge.kif 5535-5540	If a binary relation is partial ordering on a set or class, then the binary relation is reflexive on the set or class and the binary relation is an instance of transitive relation and the binary relation is an instance of antisymmetric relation

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