basic constructions: strong axioms further There are many systems of formal logic. By “classical logic” one broadly refers to those such systems which reflect the kind of logic as understood, quite literally, by the classics, say starting with Aristotle, Metaphysics 1011b24. If you have never heard of any alternative system of logic, then classical logic is just the kind of logic that you have heard about. There is some variance in what exactly counts as classical and as non-classical in logic,.