(<=>
(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 ?GRAPH PseudoGraph)
(exists (?LOOP)
(and
(instance ?LOOP GraphLoop)
(graphPart ?LOOP ?GRAPH)))) 
Merge.kif 53735378 
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 28152825 

(=>
(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 28272837 

(=>
(and
(subGraph ?GRAPH1 ?GRAPH2)
(graphPart ?ELEMENT ?GRAPH1))
(graphPart ?ELEMENT ?GRAPH2)) 
Merge.kif 54625466 

(=>
(graphMeasure ?G ?M)
(forall (?AC)
(and
(graphPart ?AC ?G)
(exists (?PC)
(abstractCounterpart ?AC ?PC))))) 
Merge.kif 57225728 

(=>
(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 ?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 52935303 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphCircuit)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 52855291 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphLoop)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 52775283 

(=>
(instance ?PART GraphElement)
(exists (?GRAPH)
(and
(instance ?GRAPH Graph)
(graphPart ?PART ?GRAPH)))) 
Merge.kif 53865391 
