A) All Unicorns are Purple.

B) I am a Unicorn.

C) I am Purple.

C cannot be concluded, unless the validity of A and B has been addressed in order to justify C. So:

A) All Unicorns are Purple.

B) I am a Unicorn.

C) If A and B are valid, X is valid.

X) I am Purple.

X cannot be concluded without C being included in the relationship.

A) All Unicorns are Purple.

B) I am a Unicorn.

C) If A and B are valid, X is valid.

D) If A, B, and C are valid, X is valid.

X) I am Purple.

...regressus in infinitum.

Logic is a construct used to make sense of the world we live in, but it is chimerical to think this world is constrained by logic, or as we have made sense of it.

B) I am a Unicorn.

C) I am Purple.

C cannot be concluded, unless the validity of A and B has been addressed in order to justify C. So:

A) All Unicorns are Purple.

B) I am a Unicorn.

C) If A and B are valid, X is valid.

X) I am Purple.

X cannot be concluded without C being included in the relationship.

A) All Unicorns are Purple.

B) I am a Unicorn.

C) If A and B are valid, X is valid.

D) If A, B, and C are valid, X is valid.

X) I am Purple.

...regressus in infinitum.

Logic is a construct used to make sense of the world we live in, but it is chimerical to think this world is constrained by logic, or as we have made sense of it.

Here is one case.

1)All Cats Purrs

2)My pet purrs

3)Therefore my Pet is a Cat.

These are all valid statements even the conclusion could be valid. However, it is not logical because Just because all cats purr and my pet purr doesn't mean my pet is a cat because other animals besides cats may indeed purr and the statement doesn't exclude these other animals.

Therefore Validity doesn't imply Logic and the conclusion before proves that logic doesn't imply validity.

Both are needed to show rational thought however sometimes the validity of something isn't provable.

In these cases the best we can do is to make sure our conclusions actually fallow the evidence as best we can. If later we find out that one piece of evidence is invalid or valid we can then change and morph the conclusion to best fit our personal understanding of truth "Validity". This is logical and rational. Just because you disagree on truth doesn't mean the process someone is using is any less rational or logical. Unless of course you can prove that there evidence is invalid or false.

This is what I mean when I say personal logic.

Like you said what is a logical conclusion is related directly to what is valid. Therefore if I have a different understand of truth then you do. Which is natural (I.E. everyone has a different opinion of what is truth and false depending on there level of understanding on any given subjects are all of them as a whole) It would then fallow that are conclusions on subjects would be different. It doesn't mean that one of us is logical and the other is illogical. What it means is we have a different perspective on truth and therefore looking at our evidence (which will also be different with every different point of view). Therefore your opinion on a subject coming from a completely logical understanding of the world around you. Will be much different then my logical understand of the world around me.

This is one of the reason I find it useful to talk with as many people as possible. I understand that my point of view is limited myself. Therefore to gain greater wisdom and understand I must try and embrace different ideas then the one that I have understood form examining my experiences logically.