(<=>
(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 53565366 
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 54185421 
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 28392845 

(=>
(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 52175237 

(=>
(instance ?ARC GraphArc)
(exists (?NODE1 ?NODE2)
(links ?NODE1 ?NODE2 ?ARC))) 
Merge.kif 54085411 

(=>
(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 52395253 

(=>
(instance ?NODE GraphNode)
(exists (?OTHER ?ARC)
(links ?NODE ?OTHER ?ARC))) 
Merge.kif 53985401 

(=>
(links ?NODE1 ?NODE2 ?ARC)
(links ?NODE2 ?NODE1 ?ARC)) 
Merge.kif 54375439 
