No, not really.
Let's see. I have this theory that I have a set of Bentley keys in my pantses pocketses. So whats does I has in my pocketses?
[turn out left pocket]
No evidence of Bentley keys here
[turn out right pocket]
No evidence of Bentley keys here, either.
I've run out of pocketses, and having turned them out have completed the task of gathering all available information about what is in them, so I definitely did not have Bentley keys in my pocketses. QED
so I definitely did not have Bentley keys in my pocketses.This statement is incorrect.
You may conclude from your example that you didn't have Bentley keys in your pocketses (

)
at the time you turned them out.The Bentley keys may have been removed before you checked your pocketses, so you can't say definitively that you did not have Bentley keys in your pocketses.
What tests have been performed to detect the presence or absence Bentley key in your pocketses prior to you turning them out? We are missing key information (do you see what I did there? "Key" information. Do you get it? "Key" as in...oh, forget it..."
Even in this most basic of all examples there is not complete information.
The simplest criminal case is manifestly more complex than this, so the idea of having "complete information" is a non-starter.