TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2235-2235	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)。")	chinese_format.kif 1848-1850
(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 2237-2239
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2234-2234	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 15159-15159	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 21993-21993	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 7641-7641	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 15313-15313	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6187-6187	conjugate is an instance of transitive relation
(instance covers TransitiveRelation)	Mid-level-ontology.kif 27977-27977	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4016-4016	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 13268-13268	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 7767-7767	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 7812-7812	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 7619-7619	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5103-5103	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 13005-13005	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 13050-13050	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1752-1752	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9086-9086	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7326-7326	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1740-1740	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 3888-3888	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4662-4662	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4095-4095	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 883-883	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 15322-15322	sister is an instance of transitive relation
(instance smaller TransitiveRelation)	Merge.kif 7348-7348	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 2241-2248

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 3550-3555	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 3493-3498	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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