Logic is taking axioms, and following rules of inference to reach a conclusion. Science is setting up experiments, and testing whether conclusions are valid statements about the physical world. I may use logic to predict the outcome of experiments, but not all assumptions we use in our logic are valid. read more
The scientific method is founded on the practice of epistemology. Logic is the foundation of mathematics and philosophy. The scientific method is used to make sense of empirical questions but logic (generally) is used to make sense of rational questions. read more
I would say logic is a prerequisite for science. In other words science is specific application of logic, not something completely separate. Logic presents the next stage in the scientific process or thinking. So every logical thing can only be logical if its approved by a scientific method; (theory, hypothesis, e.t.c). One leads to another. read more