One of the two classical theories of uncertainty, which is the subject of this chapter, is based on the notion of possibility and the associated notion of necessity. The other classical theory, which is the subject of Chapter 3, is based on the notion of probability. Of the two classical theories, the one based on possibility is simpler, more fundamental, and older.To describe this rather simple theory, let X denote a finite set of mutually exclusive alternatives that are of concern to us (diagnoses, predictions, etc.). This means that in any given situation only one of the alternatives is true. To identify the true alternative, we need to obtain relevant information (e.g., by conducting relevant diagnostic tests).The most elementary and, at the same time, the most fundamental kind of information is a demonstration (based, for example, on outcomes of the conducted diagnostic tests) that some of the alternatives in X are not possible. After excluding these alternatives from X, we obtain a subset E of X.This subset contains only alternatives that, according to the obtained information, are possible.We can say that alternatives in E are supported by the evidence. Let the characteristic function of the set of all possible alternatives, E, be called in this context a basic possibility function and be denoted by rE. Then,