Diagrammatic representation for interval arithmetic

The paper presents a diagrammatic representation of a standard interval spa ce (the so-called "MR-diagram"), and shows how to represent and perform int erval arithmetic and derive its various properties using the diagram. The r epresentation is an extension and refinement of the IS-diagram representati on devised earlier by the author to represent interval relations. First, th e MR-diagram is defined together with appropriate graphical notions and con structions for basic interval relations and operations. Second, diagrammati c constructions for all standard arithmetic operations are presented. Sever al examples of the use of these constructions to aid reasoning about variou s simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understand ing of the subject matter and reasoning about its properties. (C) 2001 Else vier Science Inc. All rights reserved, AMS classification: 65G40; 51M15; 00 A35.