How do you think that people think? If there is nothing beyond the physical world, then the way people think is just physical interactions between microscopic particles. Those can be simulated by a powerful-enough computer. So it would be the same as the way that you think, except it would be in a simulation instead of the real physical world.

So, no, "know" and "think" are not labels for an algorithm, but labels for things that can happen inside brains, whether the brains be physical brains or virtual brains (using virtual particles instead of real particles). "person" is also not a label for an algorithm. I was a bit imprecise in my wording. It's debatable whether the virtual person could actually be referred to as a "person".