For example.
John: "I am confident that Rebecca's birthday is on Thursday."
Mary: "I know you're wrong. She told me yesterday it was on Sunday."
John: "She told me she's been telling people it's on Sunday because that's when her party is, but it's technically Thursday."
That actually does not raise any problems at all. Her birthday is either one of those days, or possibly another. But it is on the same day every year. It just has to be ascertained and communicated what day that is.
We can and do "know" things, like when the Sun will "rise" and where in the sky it will be. We can predict it and be right with 100% accuracy. Predictability as well as falsifiability show that we do "know" many things, and I think can "know" everything eventually. But I think you're trying to "deconstruct" knowledge, and from a certain point of view you simply cannot do that. At least, to do it you have to set up parameters that are not reflective of reality.
