- B. J. Kuipers. 9507-0463

**Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge**. Cambridge, MA: MIT Press, 1994, 414 pp. $45. ISBN 0-262-11190-X.

This volume is a textbook in qualitative methods. Its major themes are represented throughout in terms of QSIM. QSIM is a computer program intended to resolve qualitative simulation problems and is distributed for research purposes only. The main domains of investigation are physical and chemical processes, such as a system evolution in quasi-equilibrium states and dynamic state transitions.

Modeling exercises on fluid dynamics and mechanics exemplify the basic ideas of the qualitative simulation method. The basic principles introduced here are formally defined and analyzed in the section on the QSIM representation. "The key intuition" behind the use of qualitative differential equations "is that, although the world changes continuously, it changes qualitatively only at isolated points." To define the qualitative differential equations, the author considers four elements: qualitative variables, quantity spaces, qualitative constraints, and transitions. The transitions represent "rules defining the boundary of the domain of applicability" of the qualitative differential equations. The general scheme for qualitative modeling and simulation is as follows. The abstract elements in the system representation are created from a physical scenario by means of model selection. Through model building, one may find the qualitative differential equations. Qualitative simulation reveals the qualitative behavior of the system. Finally, applying quantitative refinement on the predicted behavior and taking into consideration the critical bounds on the system's evolution, one may obtain the quantitative behavior of the initial physical scenario.

An interesting part of the book describes the dynamic qualitative simulation in the QSIM representation. This section discusses the QSIM algorithm and its paradigmatic architecture by developing the reader's intuition and presenting QSIM implementation examples.

The major subjects of the book are semi-quantitative reasoning, higher-order derivatives, and compositional modeling. In the sphere of semi-quantitative reasoning, the author presents Q2, an extension to QSIM. Its role is to select allowed system behaviors using constraint propagation and interval arithmetic to obtain value-denoting terms. Q2 filters the scenarios predicted by QSIM to resolve the differential equations generated by each behavior.

To increase the granularity of the investigation, QSIM supports an analysis of the higher-order differential equations. The role of this method is to select valid behaviors from families of infinite solutions. The last chapter introduces the model building methodology and technology in the framework of qualitative process theory. A survey of compositional modeling techniques discusses research published in the last seven years.

Throughout the book, the material is presented on five levels. First, the author formulates an idea. Second, the basic paradigms are formalized and generalized. Third, Kuipers discusses examples. Fourth, the formalization is refined and its frame extension is presented. The last step is an invitation to resolve some related problems.

The book is a sparkling discourse that will engage the reader. The many recent references offer a solid basis for anyone beginning an adventure in modeling and simulation with incomplete knowledge.

C. Lucaciu, Vienna, Austria

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