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.

Ontology

SUMO / GRAPH-THEORY

Class(es)

Classe

inheritable relation

PredicatoBinario
is instance of

RelazioneRiflessiva
is instance of

RelazioneTransitiva
is instance of

sub graph

Coordinate term(s)

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

Type restrictions

subGraph(Grafo, Grafo)

Axioms (3)

Se graph é un' istanza di Grafo e node1 é un' istanza di NodoDelGrafo e node2 é un' istanza di NodoDelGrafo e node1 é una parte di graph e node2 é una parte di graph e node1 is not uguale a node2, allora esiste arc,path tale che

arc legas node1 e node2
- path é un sottografo di graph
- path é un' istanza di CamminoDelGrafo
- - "l' inizio di path" is uguale a node1 e "la fine di path" is uguale a node2
  - "l' inizio di path" is uguale a node2 e "la fine di path" is uguale a 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)))))))

Se graph1 é un sottografo di graph2 e element é una parte di graph1, allora element é una parte di graph2.

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

se
- "il valore di path" is uguale a sum
- subpath é un sottografo di path
- arc1 é una parte di path
- il valore diarc1 énumber1
- per ogni arc2 vale: se arc2 é una parte di path, allora arc2 é una parte di subpath o arc2 is uguale a arc1
,
allora sum is uguale a "("il valore di 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)))