- B. J. Kuipers.
**Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge**. MIT Press. $45/hardbound. ISBN 0-262-11190.

Geography deals with processes in space. Quantitative descriptions of these processes are quite often not possible, due to the lack of accurate data. Only qualitative information is available. Even without details, general level prediction about the effects of such processes can be made: Mountains are reduced through erosion processes, population growth, erosion of top soil and agricultural production are interrelated. The theories explained in Ben Kuipers' book are applicable to describe and quantitatively analyze geographical problems.

Qualitative reasoning describes processes not with quantitative expressions, i.e. values measured on the ratio or interval scale, but on an ordinal scale. The quantitative scale is divided by landmark values into intervals. The fundamental example is the division of the real number line by the value zero in two intervals (from negative infinity to zero and from zero to infinity: important is only the change of the sign. Describing the behavior of water when heated needs two landmark values: zero degree centigrade and 100 degrees. It is possible to translate the practically important part of differential equations from the real numbers to such qualitative spaces and to reason about processes in this framework. Without knowledge of the precise starting conditions or the precise flow values no precise description result, but important qualitative results can be deduced.

Behavior of physical systems like pendulum, flow of water through tanks, electric circuits, but also the well known predator-prey population problem can be described in qualitative differential equations. Without precise figures not a single outcome can be computed, but the qualitative description of all possible behaviors of the system can be produced.

Chapter 3 of the book introduces a specific notation for qualitative differential equation. The translation of ordinary differential equations is shown. The following chapter shows the method used for finding all possible solutions to a set of equations, and the chapter 5 details the dynamic aspects. The author provides the QSIM software for Qualitative Modeling and Simulation to allow experiments with these methods (available on the Internet). Chapter 6 shows some elementary models and chapter 7 deals with systems where equilibriums are encountered. The extensions to models, where substantive changes in the behavior are encountered, e.g. population systems, with irreversible changes in the population. The next 3 chapters extend the applicability with special methods to make the basic method applicable to more complex cases: semi-quantitative reasoning, higher order derivatives and global dynamical constraint.

The chapter 12 discusses systems where processes act on different time scales and shows formally how this is used to construct a hierarchical solution method. In chapter 13 and 14 the composition of models from simpler parts is extensively discussed. These last 3 chapters are -- independent of the specific methods used within the QSIM framework -- outstanding treatments of the problem of hierarchization of processes and their dynamic behavior.

The book is well written and does review the literature extensively. The prerequisites are some basic understanding of differential equation (at the level of Physics 101) and Calculus. All ideas are explained with extensive examples and diagrams depicting dynamic behavior. The formalism uses a LISP notation, which is easy to read and does for the most part not require detailed knowledge of LISP. The examples are mostly describing water flow in tanks, electrical circuits, springs, bouncing balls etc., but cover also biological population and economical models. Extensive lists of problems for class work are provided in each chapter.

Geographers may be surprised that Ben Kuipers does not include treatment of spatial reasoning and wayfinding -- a topic he is probably better known for among geographers than qualitative reasoning. The book concentrates on one topic and does an admirable job there. We can only hope, that the author writes a similar overview on spatial navigation and wayfinding later.

Reading the text it becomes, however, clear that the same methods apply to processes in space. It must be hoped that many geographers use the methods to model geographical processes and to explore the dynamic behavior of systems in physical and human geography. Many M.Sc. or Ph.D. thesis could benefit from the rigor of the method and the application of the software. Modeling of dynamic systems -- a la Forrester's Urban Dynamics -- become feasible, even in the absence of detailed quantitative knowledge.

The book is recommended to all geographers with interest in modeling of processes in physical or human geography. It provides a consistent conceptual framework for the qualitative discussion of processes and their behavior, even if one does not use the formalism or the programs provided.

Andrew Frank, Professor of Geoinformation, Technical University of Vienna, Austria.

[Book home] BJK