(<=>
(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))))) 
Merge.kif 54525462 
A graph is an instance of multi graph if and only if there exist a graph arc, another graph arc,, , a graph node and another graph node such that the graph arc is a part of the graph and the other graph arc is a part of the graph and the graph node is a part of the graph and the other graph node is a part of the graph and the graph arc links the graph node and the other graph node and the other graph arc links the graph node and the other graph node and the graph arc is not equal to the other graph arc 
(<=>
(instance ?LOOP GraphLoop)
(exists (?NODE)
(links ?NODE ?NODE ?LOOP))) 
Merge.kif 55145517 
A graph arc is an instance of graph loop if and only if there exists a graph node such that the graph arc links the graph node and the graph node 
(=>
(and
(connects ?A ?NODE1 ?NODE2)
(abstractCounterpart ?N1 ?NODE1)
(abstractCounterpart ?N2 ?NODE2)
(abstractCounterpart ?ARC ?A))
(links ?N1 ?N2 ?ARC)) 
Transportation.kif 28482854 

(=>
(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))))))) 
Merge.kif 53135333 

(=>
(instance ?ARC GraphArc)
(exists (?NODE1 ?NODE2)
(links ?NODE1 ?NODE2 ?ARC))) 
Merge.kif 55045507 

(=>
(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 ?NODE1 ?NODE2 ?ARC1)
(links ?NODE2 ?NODE3 ?ARC2)
(not
(equal ?NODE1 ?NODE2))
(not
(equal ?NODE2 ?NODE3))
(not
(equal ?NODE1 ?NODE3))
(not
(equal ?ARC1 ?ARC2))))) 
Merge.kif 53355349 

(=>
(instance ?NODE GraphNode)
(exists (?OTHER ?ARC)
(links ?NODE ?OTHER ?ARC))) 
Merge.kif 54945497 

(=>
(links ?NODE1 ?NODE2 ?ARC)
(links ?NODE2 ?NODE1 ?ARC)) 
Merge.kif 55335535 
