minimal cut set fn (MinimalCutSetFn)

A UnaryFunction that assigns a Graph the Class of GraphPaths which comprise cutsets for the Graph and which have the least number of GraphArcs.

Ontologie

SUMO / GRAPH-THEORY

Class(es)

třída

inheritable relation

unární funkce

minimal cut set fn

Související termín(y)

absolute value fn abstraction fn arc cosine fn arc sine fn arc tangent fn back fn begin fn begin node fn cardinality fn ceiling fn complement fn cosine fn cut set fn denominator fn end fn end node fn extension fn floor fn front fn future fn generalized intersection fn generalized union fn giga fn imaginary part fn immediate future fn immediate past fn initial node fn integer square root fn kilo fn list length fn magnitude fn mega fn micro fn milli fn nano fn numerator fn organization fn past fn path weight fn pico fn power set fn predecessor fn principal host fn probability fn property fn rational number fn real number fn reciprocal fn round fn signum fn sine fn skin fn square root fn successor fn tangent fn tera fn terminal node fn wealth fn when fn year fn

Typy argumentů

subclass cesta v grafu MinimalCutSetFn(graf)

Axiomy (4)

minimal cut set fn je internally related to cut set fn.

(relatedInternalConcept MinimalCutSetFn CutSetFn)

Jestliže graph je instancí třídy graf, potom "minimal cut set fn(graph)" je podtřídou "cut set fn(graph)".

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

jestliže "minimal cut set fn(graph)" se rovná pathclass,
potom existuje number tak, že pro všechny path platí: jestliže path je instancí třídy pathclass, potom délka path je number

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

Neexistují cut set fn(graph) path1,minimal cut set fn(graph) path2 tak, že délka path1 je number1 a délka path2 je number2 a number1 je menší než number2.

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