Strange to see no mention of confirmation bias on the logical fallacies poster. That would have been the first on my list.
This is both logical (because it follows that in order to "think", one must "exist") and known.
There are things that are logical but not known, and others that are known but not logical. Gravity, for example, is pretty well known. Does it follow as a matter of logic? Not that I'm aware of. We believe it to be true because it works.
The basis for knowledge is a complicated subject. One framework is that to truly know something, you must have justified true belief. i.e. You must believe the statement, you must be justified in believing it (so a fortune that turns out to be right doesn't count as knowledge), and it must be true. Naturally, thousands of years of debate continue as to what the definition of "true" is.