This paper presents a framework for reasoning using intervals. Two interpretations of intervals are examined, one treats intervals as bounds of a truth evaluation function, and the other treats end points of intervals as two truth evaluation functions. They lead to two different reasoning approaches, one is based on interval computations, and the other is based on interval structures. A number ...

Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of Affine Arithmetic called Revised Affine Arithmetic. We extend the range of functions presented in Revised Affi...