I think logic is dependent on time.
My reasoning is that all of the basic logic concepts are based on axioms that are observations in time (so basic that they do not require proof). This then leads to the conclusion that logic only works in time, and that if time would not move in a one directional stream but instead would move at random, sometimes forward, sometimes backwards, one would not be able to use these axioms and the whole thing would fall over.
EDIT: For example, if we want to take a measurement of something, we take it while time is moving forward. The result comes out as x. Then suppose we take the same measurement while time is moving backwards. If we get a different result, it would imply that to do the calculation we would need to know in which direction time is moving. (The direction of time would become an input parameter into the function.) Now if we get the same result, no matter in which direction time is moving, it would imply that it is not dependent on time. I do understand that there is no way to move in time backwards to take the measurement, but that's what philosophy is for.
Can anyone come up with an example where logic would work independent of time?