From Webster's New World Dictionary of American English, Third College Edition (1988):
logic: (1) the science of correct reasoning; science which describes relationships among propositions in terms of implication, contradiction, contartiety, conversion; (3) correct reasoning; valid induction or deduction; (4) way of reasoning, whether correct or incorrec; (5) the systerm of principles underlying any art or science; (6) necessary connection or outcome, as through the working of cause and effect.
common: (3) widely existing; general; prevalent [common knowledge].
common sense: ordinary good sense or sound practical judgement.
sense: (6a) the ability to think or reason soundly; normal intelligence and judgment, often as reflected in behavior; (6b) soundness of judgment or reasoning; (6c) something wise, sound, or reasonable; (8) the general opinion, sentiment, or attitude of a group.
I will take logic over common sense everytime. Thank you.