- B. Kuipers.
**Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge**, Cambridge, MA: MIT Press, 1994, pp. 418.

The field of qualitative reasoning has matured considerably since the early 1980's and deserves the attention of researchers and practitioners in areas besides artificial intelligence (AI). A qualitative description is one that identifies and highlights relevant distinctions and disregards others. For example, the statement "It's raining too heavily to drive on the highway" is a qualitative description of current driving conditions.

Qualitative reasoning uses qualitative descriptions, which often include causal relationships, to solve a problem. It has been successfully applied to application areas such as design and diagnosis of engines, fault detection, and business planning. Qualitative reasoning is concerned with dynamic systems and their behavior and assumes that these systems can be decomposed into related entities, and a description of their behavior and interrelationships. Another implicit assumption is the idea of causality, that is, of cause-effect relationships among entities. Since qualitative reasoning is motivated by the need to model real world situations or physical systems in order to support, and in some instances mimic an engineer's reasoning process there are three primary approaches to qualitative reasoning (Werthner 1994). These are:

- Device-centered: Connected and interrelated components of a
device are governed by physical laws, i.e. behavioral constraints. The
behavior of the device is described in terms of the components and the
entities the device operates on (de Kleer and Brown 1984).
- Process-centered: A system is described in terms of a set of
variables, objects, and processes which affect the variables and the
state of the objects (Forbus 1984).
- Constraint-based: Dynamic systems are described in terms of
qualitative differential equations. This approach supports simulation
since the qualitative differential equations capture the functional
relationships of components of the system. The qualitative
differential equations are derived from an exact specification of the
system given by ordinary differential equations (Kuipers 1984).

The qualitative model must have a means of representing incomplete knowledge and partial knowledge about attributes such as quantity or change. Partial knowledge of quantity can be represented using interval arithmetic, ordinal values, landmark values like freezing and boiling, or fuzzy values such as hot and cold. Partial knowledge of change can be represented using discrete state graphs, or differential equations.

The QSIM qualitative model provides an explicit mechanism for the abstraction of differential equations resulting in a qualitative representation called qualitative differential equation (QDE). Chapter 2 introduces the QSIM representation for QDEs and the algorithm for qualitative simulation using the U-tube, a two-tank fluid flow system. The qualitative structure of the system is thus given by the qualitative constraints, their values, and the quantity spaces of their variables. The qualitative state of the system is dynamic and is described by the variables, their magnitude, and a direction of change. A qualitative simulation is performed by specifying an initial state, i.e. the magnitudes and direction of change of all independent variables, and then determining the effect of any qualitative change by using the qualitative constraints.

The QSIM representation and solution of qualitative constraints are discussed in Chapters 3 and 4. Chapter 4 also introduces two well-known problem solving methods in AI, namely constraint propogation and constraint satisfaction. It discusses the application of these methods in solving qualitative constraints.

Chapters 7 and 8 discuss reasoning with the steady-state assumption, i.e., a system tends to be in a state of equilibrium. The behavior of interest is the effect of a small perturbation to the system on an equilibrium state. The perturbation may result in a region transition. A transition is determined by the region of applicability of a QDE and a new state is entered if the limit of applicability is reached. Region transitions and their use in qualitative simulations are described in Chapter 8.

One of the benefits of qualitative reasoning is that it facilitates the refinement of incomplete quantitative knowledge. Reasoning with a combination of qualitative and incomplete quantitative knowledge, called semiquantitative reasoning, is the topic of Chapter 9. This is an extension to QSIM which makes it particularly useful for model-based reasoning tasks such as diagnosis, monitoring, and design. Chapter 10 onwards deals with advanced topics in qualitative reasoning such as time-scale abstraction, higher-order derivatives, and global dynamic constraints.

Overall the book is extremely well written. The book assumes, and requires, a fairly strong knowledge of AI; one beyond that provided by a typical introductory undergraduate course. For those with the relevant background, or strong motivation, the book will be an excellent resource. It has been written as a textbook with thought-provoking practice and research problems at the end of each chapter. The organization of chapters is excellent, starting with a gentle introduction and then increasing in detail and complexity, while building on the material of earlier chapters. Given the significant advances and successes in the field of qualitative reasoning this book is a very timely one and I would recommend it to anyone with an interest in AI, in general, and modeling and simulation, in particular.

Jayant Sharma

University of Maine

- DE KLEER. J., BROWN, J. S. (1984), "A Qualitative Physics based on Confluences," Artificial Intelligence, 24. 7-83.
- FORBUS, K D. (1984), "Qualitative Process Theory," Artificial Intelligence, 24, 85-168.
- KUIPERS, B. J. (1984), "Commonsense Reasoning about Causality: Deriving Behavior from Structure," Artificial Intelligence, 24, 169-203.
- WERTHNER, H. (1994), Qualitative Reasoning: Modeling and the Generation of Behavior, Berlin: Springer-Verlag.

Reviewer's address: Jayant Sharma, Oracle Corporation, 110 Spit Brook Road, Nashua, NH 03062, USA.

BJK