let me clear up my explaination (sorry i tend to be annoy when it comes to math ): the prisoner's deduction that he can't be killed by Friday is solely based on the assumption that he hasn't been killed by Thursday.

If indeed this is true, then the prisoner's logic seems to be agreeable. but keep in mind that he cannot be killed on monday to thursday (since he is alive on thursday afternoon according to the assumption, killing him early would be out of the question)