You perfectly demonstrated that you do not understand what logic is. Check out this wikipedia article for a crashcourse:
http://en.wikibooks.org/wiki/Logic/Propositional_Logic. It is the most fundamental part of logic, although it extends into "higher order" logics which are built on top of it.
"I see an apple fall from the tree, therefore I infer a force is acting upon it." may be an inference, but it is
not a logically valid one.
Now, a logically valid argument is one in which the conclusion is absolutely true given the premises. That's what logic is ... deriving statements which are absolutely, unquestionably true,
if the premises are true. Hence my statement "deriving truths from other truths".
Logic is practically useless though, until you have a truth from which to derive others. I may not know that Fuzzy the cat is completely black, but I
do know for certain that
if Fuzzy is completely black
and if something being completely one color means that it is has no other color on it,
then he certainly, absolutely, unquestionably has no white on him. That is logic.
Logic is
not making intuitive guesses, such as that a force is acting on the apple to make it fall.
Also, logic does, in fact, not break down when addressing quantum level physics. The only thing that changes is that the Classical Physics model no longer applies. There is no context in which logic necessarily breaks down, but there are people who can't apply it in any context.