MinimalCutSetFn - Sigma Knowledge base Browser

appearance as argument number 1

(documentation MinimalCutSetFn ChineseLanguage "这是一个 UnaryFunction，它以最少条 GraphArc 把一个 Graph 划分的分割组合，给这个 Graph 分配 GraphPath Class。")	chinese_format.kif 2380-2381
(documentation MinimalCutSetFn EnglishLanguage "A UnaryFunction that assigns a Graph the Class of GraphPaths which comprise cutsets for the Graph and which have the least number of GraphArcs.")	Merge.kif 6084-6086
(documentation MinimalCutSetFn JapaneseLanguage "UnaryFunction は、Graph のカットセットを構成し、GraphArc の数が最も少ない GraphPath の Graph Class を割り当てる。")	japanese_format.kif 1059-1060
(domain MinimalCutSetFn 1 Graph)	Merge.kif 6080-6080	The number 1 argument of minimal cut set is an instance of graph
(instance MinimalCutSetFn UnaryFunction)	Merge.kif 6079-6079	Minimal cut set is an instance of unary function
(rangeSubclass MinimalCutSetFn GraphPath)	Merge.kif 6081-6081	The values returned by minimal cut set are subclasses of graph path
(relatedInternalConcept MinimalCutSetFn CutSetFn)	Merge.kif 6082-6082	Minimal cut set is internally related to cut set

appearance as argument number 2

(format ChineseLanguage MinimalCutSetFn "把 %1 分成另外两个图的最短路径 Set")	chinese_format.kif 779-779
(format EnglishLanguage MinimalCutSetFn "the set of minimal paths that partition %1 into two separate graphs")	english_format.kif 779-779
(format FrenchLanguage MinimalCutSetFn "l' ensemble minimal de chemins qui partitionnent %1 en deux graph s�par�")	french_format.kif 469-469
(format ItalianLanguage MinimalCutSetFn "l' insieme di cammini minimi che partiziona %1in due separati grafi")	relations-it.txt 189-189
(format JapaneseLanguage MinimalCutSetFn "%1 を2つの別々のグラフに分割する最小パスの set")	japanese_format.kif 2173-2173
(format PortugueseLanguage MinimalCutSetFn "o conjunto minimal de caminhos que dividem %1 em dois grafos distintos")	portuguese_format.kif 421-421
(format de MinimalCutSetFn "die menge von minimalen Pfaden die %1 in zwei verschiedene Graphen schnitten")	relations-de.txt 1009-1009
(format hi MinimalCutSetFn "vaha nimnatama pathasamuuha jo %1 ko do alaga-alaga graaphon men vibhaajita karataa hai")	relations-hindi.txt 227-227
(format ro MinimalCutSetFn "set%t{mulþimea} drumurilor minimale care partiþioneazã %1 în douã grafuri separate")	relations-ro.kif 491-491
(format sv MinimalCutSetFn "minimala mängden av vägar some partitionerar %1 i två separata grafer")	relations-sv.txt 539-539
(termFormat ChineseLanguage MinimalCutSetFn "分最短图路径函数")	chinese_format.kif 780-780
(termFormat ChineseLanguage MinimalCutSetFn "最小割集")	domainEnglishFormat.kif 37899-37899
(termFormat ChineseTraditionalLanguage MinimalCutSetFn "最小割集")	domainEnglishFormat.kif 37898-37898
(termFormat EnglishLanguage MinimalCutSetFn "minimal cut set")	domainEnglishFormat.kif 37897-37897

antecedent

(=>
    (equal
        (MinimalCutSetFn ?GRAPH) ?PATHCLASS)
    (exists (?NUMBER)
        (forall (?PATH)
            (=>
                (instance ?PATH ?PATHCLASS)
                (pathLength ?PATH ?NUMBER)))))

Merge.kif 6092-6098

If the set of minimal paths that partition a graph into two separate graphs is equal to a kind of graph path,
then there exists a positive integer such that for all another graph path
- if the other graph path is an instance of a kind of graph path,
- then the length of the other graph path is the positive integer

consequent

(=>
    (instance ?GRAPH Graph)
    (subclass
        (MinimalCutSetFn ?GRAPH)
        (CutSetFn ?GRAPH)))

Merge.kif 6088-6090

If a graph is an instance of graph,
then the set of minimal paths that partition the graph into two separate graphs is a subclass of the set of paths that partition the graph into two separate graphs

statement

(not
    (exists (?PATH1 ?PATH2)
        (and
            (instance ?PATH1
                (CutSetFn ?GRAPH))
            (instance ?PATH2
                (MinimalCutSetFn ?GRAPH))
            (pathLength ?PATH1 ?NUMBER1)
            (pathLength ?PATH2 ?NUMBER2)
            (lessThan ?NUMBER1 ?NUMBER2))))

Merge.kif 6100-6107

There don't exist a graph path and another graph path such that the graph path is an instance of the set of paths that partition a graph into two separate graphs and the other graph path is an instance of the set of minimal paths that partition the graph into two separate graphs and the length of the graph path is a positive integer and the length of the other graph path is another positive integer and the positive integer is less than the other positive integer

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