Traditionally, Logic has been formalized with the following three basic rules:
1) Law of Non-Contradiction - (symbolized -(a•-a) - That is, something cannot be both a and not a at the same time
2) Law of the Excluded Middle - (symbolized (a v -a) - That something is either a or not a
3) Law of Identity - (symbolized as either a biconditional or a tautology, a=a and a•a respectively) - simply states that a "is" a.
The laws of logic have been used in a variety of ways by philosophers in the past. Under the guise of human Reason, logic itself has been used as the epistemology of among others popular philosophers Aristotle and Rene Descartes. Interestingly enough, the rules of logic themselves have recently come under attack by the philosophy of postmodernism, mainly because of Aristotle and Descartes' assumption of their truth or correctness. Exactly where we get the basis of logic is really the sticking point for postmodernists, and therefore they correctly choose to not subject themselves to its bounds. Exactly how consistently they can do this varies. For anyone interested in the basis of logic, you cannot go wrong reading the works of Francis Schaeffer - he does a fantastic job of explaining the basis for logic and a proper view of Epistemology, Metaphysics, and Ethics.