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連結 (links)

a TernaryPredicate that specifies the GraphArc connecting two GraphNodes.

Ontology

SUMO / GRAPH-THEORY

Class(es)

種類
is instance of
  可繼承關係  
is instance of
  三元述詞  
is instance of
  連結  

Coordinate term(s)

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Type restrictions

links(圖節點, 圖節點, 圖弧線)

Axioms (7)

If graph 是 圖 的 實例 and node1 是 圖節點 的 實例 and node2 是 圖節點 的 實例 and node1 是 graph 的 部分 and node2 是 graph 的 部分 and node1 等於 node2, then there exist arc,path so that 
(=>
      (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)))))))
If graph 是 圖 的 實例, then there exist node1,node2,node3,arc1,arc2 so that node1 是 graph 的 部分 and node2 是 graph 的 部分 and node3 是 graph 的 部分 and arc1 是 graph 的 部分 and arc2 是 graph 的 部分 and node2 (沒) 連結not(s) arc1 和 node1 and node3 (沒) 連結not(s) arc2 和 node2 and node1 等於 node2 and node2 等於 node3 and node1 等於 node3 and arc1 等於 arc2. 
(=>
      (instance ?GRAPH Graph)
      (exists
            (?NODE1 ?NODE2 ?NODE3 ?ARC1 ?ARC2)
            (and
                  (graphPart ?NODE1 ?GRAPH)
                  (graphPart ?NODE2 ?GRAPH)
                  (graphPart ?NODE3 ?GRAPH)
                  (graphPart ?ARC1 ?GRAPH)
                  (graphPart ?ARC2 ?GRAPH)
                  (links ?ARC1 ?NODE1 ?NODE2)
                  (links ?ARC2 ?NODE2 ?NODE3)
                  (not
                        (equal ?NODE1 ?NODE2))
                  (not
                        (equal ?NODE2 ?NODE3))
                  (not
                        (equal ?NODE1 ?NODE3))
                  (not
                        (equal ?ARC1 ?ARC2)))))
graph 是 多圖 的 實例 if and only if there exist arc1,arc2,node1,node2 so that arc1 是 graph 的 部分 and arc2 是 graph 的 部分 and node1 是 graph 的 部分 and node2 是 graph 的 部分 and arc1 (沒) 連結not(s) node1 和 node2 and arc2 (沒) 連結not(s) node1 和 node2 and arc1 等於 arc2. 
(<=>
      (instance ?GRAPH MultiGraph)
      (exists
            (?ARC1 ?ARC2 ?NODE1 ?NODE2)
            (and
                  (graphPart ?ARC1 ?GRAPH)
                  (graphPart ?ARC2 ?GRAPH)
                  (graphPart ?NODE1 ?GRAPH)
                  (graphPart ?NODE2 ?GRAPH)
                  (links ?NODE1 ?NODE2 ?ARC1)
                  (links ?NODE1 ?NODE2 ?ARC2)
                  (not
                        (equal ?ARC1 ?ARC2)))))
If node 是 圖節點 的 實例, then there exist other,arc so that arc (沒) 連結not(s) node 和 other. 
(=>
      (instance ?NODE GraphNode)
      (exists
            (?OTHER ?ARC)
            (links ?NODE ?OTHER ?ARC)))
If arc 是 圖弧線 的 實例, then there exist node1,node2 so that arc (沒) 連結not(s) node1 和 node2. 
(=>
      (instance ?ARC GraphArc)
      (exists
            (?NODE1 ?NODE2)
            (links ?NODE1 ?NODE2 ?ARC)))
loop 是 圖迴圈 的 實例 if and only if there exists node so that loop (沒) 連結not(s) node 和 node. 
(<=>
      (instance ?LOOP GraphLoop)
      (exists
            (?NODE)
            (links ?NODE ?NODE ?LOOP)))
If arc (沒) 連結not(s) node1 和 node2, then arc (沒) 連結not(s) node2 和 node1. 
(=>
      (links ?NODE1 ?NODE2 ?ARC)
      (links ?NODE2 ?NODE1 ?ARC))