(<=>
(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 ?GRAPH PseudoGraph)
(exists (?LOOP)
(and
(instance ?LOOP GraphLoop)
(graphPart ?LOOP ?GRAPH)))) 
Merge.kif 54695474 
A graph is an instance of pseudo graph if and only if there exists a graph element such that the graph element is an instance of graph loop and the graph element is a part of the graph 
(=>
(and
(instance ?TS TransitSystem)
(instance ?T Transitway)
(abstractCounterpart ?G ?TS)
(systemPart ?T ?TS))
(exists (?GA)
(and
(instance ?GA GraphArc)
(abstractCounterpart ?GA ?T)
(graphPart ?GA ?G)))) 
Transportation.kif 28242834 

(=>
(and
(instance ?TS TransitSystem)
(instance ?TJ TransitwayJunction)
(abstractCounterpart ?G ?TS)
(systemPart ?TJ ?TS))
(exists (?GN)
(and
(instance ?GN GraphNode)
(abstractCounterpart ?GN ?TJ)
(graphPart ?GN ?G)))) 
Transportation.kif 28362846 

(=>
(and
(subGraph ?GRAPH1 ?GRAPH2)
(graphPart ?ELEMENT ?GRAPH1))
(graphPart ?ELEMENT ?GRAPH2)) 
Merge.kif 55585562 

(=>
(graphMeasure ?G ?M)
(forall (?AC)
(and
(graphPart ?AC ?G)
(exists (?PC)
(abstractCounterpart ?AC ?PC))))) 
Merge.kif 58185824 

(=>
(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 ?GRAPH Tree)
(not
(exists (?ARC1 ?ARC2 ?NODE)
(and
(graphPart ?ARC1 ?GRAPH)
(graphPart ?ARC2 ?GRAPH)
(graphPart ?NODE ?GRAPH)
(equal
(TerminalNodeFn ?ARC1) ?NODE)
(equal
(TerminalNodeFn ?ARC2) ?NODE)
(not
(equal ?ARC1 ?ARC2)))))) 
Merge.kif 53895399 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphCircuit)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 53815387 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphLoop)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 53735379 

(=>
(instance ?PART GraphElement)
(exists (?GRAPH)
(and
(instance ?GRAPH Graph)
(graphPart ?PART ?GRAPH)))) 
Merge.kif 54825487 
