The purpose of this paper is to take some of the mystery out of what is known as nonmonotonic logic, by showing that it is not as unfamiliar as may at first sight appear. In fact, it is easily accessible to anybody with a background in classical propositional logic, provided that certain misunderstandings are avoided and a tenacious habit is put aside. In effect, there are logics that act as natural bridges between classical consequence and the principal kinds of nonmonotonic (...) logic to be found in the literature. Like classical logic, they are perfectly monotonic, but they already display some of the distinctive features of the nonmonotonic systems. As well as providing easy conceptual passage to the nonmonotonic case these logics, which we call paraclassical, have an interest of their own. (shrink)