1 - Introduction

Summary

A comparison may help to describe the intention of this book: natural sciences and engineering sciences have their differential and integral calculi. Whenever practical work is to be done, one will easily find a numerical algebra package at the computing center which one will be able to use. This applies to solving linear equations or determining eigenvalues, for example, in connection with finite element methods.

The situation is different for various forms of information sciences as in the study of vagueness, fuzziness, spatial or temporal reasoning, handling of uncertain/rough/ qualitative knowledge in mathematical psychology, sociology, and computational linguistics, to mention a few areas. These also model theoretically with certain calculi, the calculi of logic, of sets, the calculus of relations, etc. However, for applications practitioners will usually apply Prolog-like calculi. Hardly anybody confronted with practical problems knows how to apply relational calculi; there is almost no broadly available computer support. There is usually no package able to handle problems beyond toy size. One will have to approach theoreticians since there are not many practitioners in such fields. So it might seem that George Boole in 1854 [26, 28] was right in saying:

It would, perhaps, be premature to speculate here upon the question whether the methods of abstract science are likely at any future day to render service in the investigation of social problems at all commensurate with those which they have rendered in various departments of physical inquiry.