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.
(..) Please, put the gun down. Hurry! The wall is closing! Here is your mission now: Pass your knowledge to the next priest as it was passed on to you. l will. But please, hurry! You still have time! - Time not important. Only life important. l will fulfil my mission! You can count on me! l will pass the knowledge until your return. - Anything yet? - No, Sir. - Not even the temperature? - The analysers have jammed. (..)1997 The Fifth Element