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.
(..) ...your home as it was. This year we shall examine the various concepts of immortality... ...and their basis in actual fact. The total accumulation of all knowledge spanning the known galaxies... ...is embedded in the crystals which I have sent along with you. Study them well, my son. (..)1978 Superman
(..) your eighteenth year... ...as it is measured on Earth. By that reckoning... ...l will have been dead for many thousands of your years. The knowledge... ...that I have of matters, physicalandhistorical... ...I have given you fully on your voyage to your new home. (..)1978 Superman