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slwu@sh163.net
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Joined: 17 May 2006
Posts: 9

Posted: Thu Jun 22, 2006 11:42 pm    Post subject: Back Reasoning from partial Syllogism [10]

Back Reasoning from partial Syllogism [10]
By Shilong Wu June 22, 2006
This back reasoning is to get the missing premises according to partial
premises and the conclusion. The Syllogism is invented by Aristotle 300
B.C. The traditional expression is as follow:
((A -> B) & (B -> C)) -> (A -> C)
& is logic and, -> is implication. Now we are going to remove (B -> C)
and using X to replace it. The following formula is appeared
((A -> B) & X) -> (A -> C)
This is one form of the back reasoning. The unknown variable X could be
solved. When X = ((NEW -> (B & A)) -> C), the new law is
((A -> B) & ((NEW -> (B & A)) -> C)) -> (A -> C)
the New is new appeared atomic that does not appeared at conditions.
This law can be read as (A -> C) could be reasoned from the conditions
(A -> B) and ((NEW -> (B & A)) -> C)。

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The following backward reasoning
(X & (B -> C)) -> (A -> C)
will be appeared after tenth post.

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