The last example is circular (the first three statements simplify to "if P then P"). The first three examples are not circular in the slightest!
"one assumes the fact that one is trying to prove". Take the first example, in that you have assumed:
1. If P then Q and
2. P
If one were trying to establish P the argument would be circular, but one isn't - the conclusion is "Q" which does not form one of the assumptions.--[[User:Toffeeman|Toffeeman]] 18:01, 26 March 2007 (EDT)