arc weight (arcWeight)

This predicate indicates the value of a GraphArc in a Graph. This could map to the length of a road in a road network or the flow rate of a pipe in a plumbing system.

Ontologie

SUMO / GRAPH-THEORY

Class(es)

třída

inheritable relation

binární predikát

arc weight

Související termín(y)

authors before or equal causes causes subclass citizen closed on connected contains information cooccur copy date decreases likelihood developmental form disjoint distributes documentation duration earlier editor element employs equal equivalence relation on exploits expressed in language faces family relation finishes frequency graph part greater than greater than or equal to has purpose has skill holds during holds obligation holds right hole identity element in list in scope of interest increases likelihood independent probability inhabits inhibits initial list instance inverse irreflexive on larger less than less than or equal to material measure meets temporally modal attribute overlaps temporally parent partial ordering on partly located path length possesses precondition prevents property publishes range range subclass refers reflexive on related internal concept sibling smaller starts sub attribute sub collection sub graph sub list sub process sub proposition subclass subrelation subsumes content class subsumes content instance successor attribute successor attribute closure temporal part time total ordering on trichotomizing on uses valence version

Typy argumentů

arcWeight(hrana grafu, reálné číslo)

Axiomy (2)

jestliže
- "path weight fn(path)" se rovná sum
- subpath je podgrafem path
- arc1 je částí path
- arc weight(arc1,number1) platí
- pro všechny arc2 platí: jestliže arc2 je částí path, potom arc2 je částí subpath nebo arc2 se rovná arc1
,
potom sum se rovná "("path weight fn(subpath)"+number1)"

(=>
      (and
            (equal
                  (PathWeightFn ?PATH)
                  ?SUM)
            (subGraph ?SUBPATH ?PATH)
            (graphPart ?ARC1 ?PATH)
            (arcWeight ?ARC1 ?NUMBER1)
            (forall
                  (?ARC2)
                  (=>
                        (graphPart ?ARC2 ?PATH)
                        (or
                              (graphPart ?ARC2 ?SUBPATH)
                              (equal ?ARC2 ?ARC1)))))
      (equal
            ?SUM
            (AdditionFn
                  (PathWeightFn ?SUBPATH)
                  ?NUMBER1)))

jestliže
- "path weight fn(path)" se rovná sum
- arc1 je částí path
- arc2 je částí path
- arc weight(arc1,number1) platí
- arc weight(arc2,number2) platí
- pro všechny arc3 platí: jestliže arc3 je částí path, potom arc3 se rovná arc1 nebo arc3 se rovná arc2
,
potom "path weight fn(path)" se rovná "(number1+number2)"

(=>
      (and
            (equal
                  (PathWeightFn ?PATH)
                  ?SUM)
            (graphPart ?ARC1 ?PATH)
            (graphPart ?ARC2 ?PATH)
            (arcWeight ?ARC1 ?NUMBER1)
            (arcWeight ?ARC2 ?NUMBER2)
            (forall
                  (?ARC3)
                  (=>
                        (graphPart ?ARC3 ?PATH)
                        (or
                              (equal ?ARC3 ?ARC1)
                              (equal ?ARC3 ?ARC2)))))
      (equal
            (PathWeightFn ?PATH)
            (AdditionFn ?NUMBER1 ?NUMBER2)))