Discussion of Back Reasoning from partial Syllogism [3]
sl...@sh163.net
By Shilong Wu June 15, 2006
The back reasoning is to get the missing premises from the partial
premises and the wanted conclusion. The Syllogism is invented by
Aristotle 300 B.C. The traditional expression is as follows:
((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. According to the affirmative law theorem on logic algebra (Part
three of Concept Algebra <1>)
P <-> υ = P
<-> is “be the same as”. υ is a constant on logic algebra. (This
theorem was proved and you can find at web
http://blog.tom.com/blog/read.php?bloggerid=762122&blogid=45944 ). So
that we can get
((A -> B) & X) -> (A -> C) = υ
This is a logic equation <1>. One of the solutions of this equation is
(B -> C). We are going to discuss the other solutions one by one. When
the solution is X = ((NEW -> (B & A)) -> C), so that the new law is
((A -> B) & ((NEW -> (B & A)) -> C)) -> (A -> C)
The New is a new atom that does not appeared at the conditions. This
law can be read as (A -> C) could be reasoned from the conditions (A ->
B) and ((NEW -> (B & A)) -> C). This is a tautology formula, but how to
explain this formula into words correctly?
<1> Shilong Wu “Concept Algebra” book to publish