sub graph (subGraph)

The relation between two Graphs when one Graph is a part of the other. (subGraph graph1 graph2) means that graph1 is a part of graph2.

Ontologie

SUMO / GRAPH-THEORY

Class(es)

třída

inheritable relation

binární predikát
is instance of

reflexivní relace
is instance of

tranzitivní relace
is instance of

sub graph

Související termín(y)

arc weight authors before before or equal causes causes subclass citizen closed on connected 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 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 interior part inverse irreflexive on larger less than less than or equal to material measure meets temporally modal attribute overlaps spatially overlaps temporally parent partial ordering on partly located path length possesses precondition prevents proper part property publishes range range subclass refers reflexive on related internal concept sibling smaller starts sub attribute sub collection 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 temporal part time total ordering on trichotomizing on uses valence version

Typy argumentů

subGraph(graf, graf)

Axiomy (3)

Jestliže graph je instancí třídy graf a node1 je instancí třídy uzel grafu a node2 je instancí třídy uzel grafu a node1 je částí graph a node2 je částí graph a node1 se nerovná node2, potom existují arc,path tak, že

arc spojuje node1 a node2
- path je podgrafem graph
- path je instancí třídy cesta v grafu
- - "the beginning of path" se rovná node1 a "the end of path" se rovná node2
  - "the beginning of path" se rovná node2 a "the end of path" se rovná node1

(=>
      (and
            (instance ?GRAPH Graph)
            (instance ?NODE1 GraphNode)
            (instance ?NODE2 GraphNode)
            (graphPart ?NODE1 ?GRAPH)
            (graphPart ?NODE2 ?GRAPH)
            (not
                  (equal ?NODE1 ?NODE2)))
      (exists
            (?ARC ?PATH)
            (or
                  (links ?NODE1 ?NODE2 ?ARC)
                  (and
                        (subGraph ?PATH ?GRAPH)
                        (instance ?PATH GraphPath)
                        (or
                              (and
                                    (equal
                                          (BeginNodeFn ?PATH)
                                          ?NODE1)
                                    (equal
                                          (EndNodeFn ?PATH)
                                          ?NODE2))
                              (and
                                    (equal
                                          (BeginNodeFn ?PATH)
                                          ?NODE2)
                                    (equal
                                          (EndNodeFn ?PATH)
                                          ?NODE1)))))))

Jestliže graph1 je podgrafem graph2 a element je částí graph1, potom element je částí graph2.

(=>
      (and
            (subGraph ?GRAPH1 ?GRAPH2)
            (graphPart ?ELEMENT ?GRAPH1))
      (graphPart ?ELEMENT ?GRAPH2))

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)))