Common/Classical Logic is often flawed, even when applied correctly.
Have you heard of Fuzzy logic?
The problem with classical True-False logic is that it doesn't represent uncertainty and inaccuracy very well. It is too rigid.
So, after only a few logical steps, a person's logic might not be accurate at all (the errors may compound and multiply).
Fuzzy logic is better at representing uncertainty so that it is known how inaccurate a conclusion may be.
Here is a link: http://en.wikipedia.org/wiki/Fuzzy_logic