(<=>
(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 83098319 
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 83328337 
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 27902800 

(=>
(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 28022812 

(=>
(and
(subGraph ?GRAPH1 ?GRAPH2)
(graphPart ?ELEMENT ?GRAPH1))
(graphPart ?ELEMENT ?GRAPH2)) 
Merge.kif 84658469 

(=>
(graphMeasure ?G ?M)
(forall (?AC)
(and
(graphPart ?AC ?G)
(exists (?PC)
(abstractCounterpart ?AC ?PC))))) 
Merge.kif 88448850 

(=>
(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 81588172 

(=>
(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 82248234 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphCircuit)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 82168222 

(=>
(instance ?GRAPH Tree)
(not
(exists (?LOOP)
(and
(instance ?LOOP GraphLoop)
(graphPart ?LOOP ?GRAPH))))) 
Merge.kif 82088214 

(=>
(instance ?PART GraphElement)
(exists (?GRAPH)
(and
(instance ?GRAPH Graph)
(graphPart ?PART ?GRAPH)))) 
Merge.kif 83518356 
