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.
(..) to inflict pain on you at any time, and in whatever degree I choose? Yes. You know perfectly well what is the matter with you, Winston. You've known it for years though you fought against the knowledge. You are mentally deranged. You suffer from a defective memory. (..)1984 1984
(..) In the face of the Thought Police, they cannot act collectively. Individually, they cheat, forge, blackmail, corrupt children, spread disease and prostitution, in the name of spreading knowledge from generation to generation until in a thousand years... You may find this of interest. Thank you. (..)1984 1984