(<=>
(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 54425452 
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 54595464 
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 55485552 

(=>
(graphMeasure ?G ?M)
(forall (?AC)
(and
(graphPart ?AC ?G)
(exists (?PC)
(abstractCounterpart ?AC ?PC))))) 
Merge.kif 58085814 

(=>
(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 53255339 

(=>
(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 53795389 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphCircuit)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 53715377 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphLoop)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 53635369 

(=>
(instance ?PART GraphElement)
(exists (?GRAPH)
(and
(instance ?GRAPH Graph)
(graphPart ?PART ?GRAPH)))) 
Merge.kif 54725477 
