I answered their questions 'to the best of my knowledge'. [=I gave the best answers I could based on what I knew, but I might have answered differently if I had known something else]
No one arrived late 'to my knowledge'. [=I am not aware that anyone arrived late, but it is possible that someone arrived late and I don't know about it]
They went on vacation, 'safe in the knowledge' that the farm would be well cared for while they were away.
(..) It's the simplest thing... ...to cause more pain than a man can possibly endure. And of course... ...it's not only the immediate agony, but the knowledge... ...that if you do not yield soon enough... ...there will be little left to identify you as a man. The only question remains... (..)2006 Casino Royale