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.
(..) without destroying it. You are Mr. Incredible. I've got to warn you, it's a learning robot. Every moment you fight it increases its knowledge of how to beat you. Shut it down. Do it quickly. Don't destroy it. - And don't die. - Great. Thanks. Showtime. (..)2004 The Incredibles
(..) Why are you unhappy? Your customers make me unhappy. What, you've gotten complaints? Complaints I can handle. What I can't handle is your customers' inexplicable knowledge of Insuricare's inner workings! They're experts. Experts, Bob! Exploiting every loophole, dodging every obstacle! (..)2004 The Incredibles