ON SEVERAL FUNDAMENTAL PRINCIPLES OF INTERVAL ARITHMETIC

This paper is concerned with some basic notions of intervall arithmetic, particularly with the definitions independent intervals, dependent intervals, interdependent intervals, and with ideas of the extended interval arithmetic, cf. Apostolatos and Kulisch, [1] and [2]. These notions will be investigated from a formal point of view and put into a logically satisfactory frame. We shall also demonstrate that the set of all intervals which are dependent on A and whose generating function is a point function does not form a field, contrary to a theorem in [1]. Furthermore we shall consider two formal ambiguities resulting from a certain identification as well as from a special form of representing rational interval functions. In this connection we shall also formulate several requirements that the derivative of an interval function should satisfy. In the appendix to the paper we shall propose a more precise and logically correct form of the simple and the extended interval arithmetic. © 1969 Springer-Verlag.