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.
(..) and still, to this day, no one has any idea how he did it. This is all entirely useless. You are both grown men and, to the best of my knowledge, scientists. Please tell me that despite your enthusiasm for magic, you have discovered something of value that can help move (..)2015 TvShow: Bones Title: The Promise in the Palace Season: 11 Episode 7
(..) having an affair, so I wanted to see for myself. That's why I lied about coming home early. You lied about your knowledge of the affair, you lied about when you came home. I'll tell you what, Anna, all this lying is adding up, and it's not looking (..)2015 TvShow: Bones Title: The Promise in the Palace Season: 11 Episode 7