path length (pathLength)

A BinaryPredicate that specifies the length (in number of GraphNodes) of a GraphPath. (pathLength path number) means that there are number nodes in the GraphPath path.

Ontologie

SUMO / GRAPH-THEORY

Class(es)

třída

inheritable relation

binární predikát
is instance of

nesymetrická relace
is instance of

ireflexivní relace
is instance of

path length

Související termín(y)

back fn cardinality fn front fn principal host fn probability fn skin fn arc weight attribute authors before before or equal causes causes subclass citizen closed on completely fills connected connected engineering components contains information cooccur copy crosses date decreases likelihood developmental form disjoint distributes documentation duration during earlier editor element employs equal equivalence relation on exploits expressed in language faces family relation fills finishes frequency graph part greater than greater than or equal to has purpose has skill holds during holds obligation holds right hole identity element immediate instance immediate subclass in list in scope of interest increases likelihood independent probability inhabits inhibits initial list instance interior part inverse irreflexive on larger less than less than or equal to manner material measure meets spatially meets temporally member modal attribute overlaps partially overlaps temporally parent partial ordering on partially fills partly located penetrates possesses precondition prevents proper part properly fills property publishes range range subclass realization refers reflexive on related internal concept sibling smaller starts sub attribute sub collection sub graph sub list sub organizations sub plan sub process sub proposition subclass subrelation subsumes content class subsumes content instance successor attribute successor attribute closure superficial part surface temporal part time total ordering on trichotomizing on uses valence version

Typy argumentů

pathLength(cesta v grafu, kladné celé číslo)

Axiomy (2)

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))))