Today’s scientific world has become strongly invested in the generic concept of computational science, that is, constructing computational models and numerical solution techniques that would allow computers to analyze and solve scientific, social scientific, and engineering problems. Almost every scientific discipline has now delved into modeling and simulation, and has employed powerful computational systems, such as parallel and distributed environments, in search for solutions. Some fundamental questions need to be answered: Can an accurate theoretical model be properly built for a certain phenomena? Is a problem associated with the phenomena solvable with reasonable computational complexity? To answer these questions, one needs a rigorous understanding of theoretical computer science. It is foreseeable that modeling will change the way computation is pursued in other disciplines, from simply a tool that leads to results faster, to an intrinsic component of problem description and solving. In other words, scientists need to interpret today’s problems by carefully crafting computational specifications, aligned with fundamental theoretical computing.

Turner’s book makes exactly this argument, and provides an articulate overview of the theory behind computational model design. As the author suggests in the brief preface, the goal of the book is twofold: to lay the basis for the design of specification languages, and to employ this foundation to build computational models. The book is the result of many years of research and teaching in the field and has all the attributes of a mature work, worthy of being included as a valuable reference for interested professionals. Turner is a well-established professional in the field, and his qualifications enhance the value of the material.

The author tackles the subject from the basics, and follows with modeling examples and advanced specifications. The book is organized in 23 chapters, each about ten pages long; they focus on particular concepts in model design, such as data types, functions, typed set theory, schemata, computable ontology, and language specifications. It is clear that the direction of the book follows more of a fundamentals of programming languages approach than a generic computational view of modeling. While not necessarily detrimental to the value of the work, this limits its appeal to non-computer-science professionals.

The book goes into significant detail and is written in a rigorous style that often includes standard mathematical and logic notations. Unfortunately, this approach is often hard to follow by a novice in the field, such as many non-computing professionals or beginning graduate students. It would have helped improve readability if the author had provided an appendix detailing the notation standards. In addition, the examples provided are insufficient. By its nature, the material is quite dry; expansive hands-on exercises would have fostered learning.

The publisher promotes the work as a textbook for “graduate students and researchers in theoretical computer science, artificial intelligence, and mathematical logic.” While there is no doubt that professionals in these areas will find the text valuable, it is difficult to envision it as a course textbook. No support for a teaching environment--such as exercises--is provided; this is surprising, given Turner’s experience in teaching these topics. Finally, the book fails to analyze any real-life software system specification, suggesting that, to do so, one would have to follow through with additional readings.