The frame problem has been occupying generations of AI researchers since McCarthy and Hayes described it in 1969. It concerns the difficulty of formalizing in a treatable way the commonsense assumptions about the causes and effects of actions, and especially of formalizing the knowledge of what is not changed by an action.

The author provides an exemplary treatment of the subject. Mathematical logic is used as a solid foundation for the entire book, and provides a strong sense of continuity. The treatment is clearly mathematically inspired, and uses the standard mechanisms of lemmas, proofs, theorems, and such. However, the material is far from intimidating, and the presentation is lively. A clever mixture of examples, high-level overviews, and less formal proof sketches is freely intermingled with the more formal material. Shanahan uses the ploy of moving from proof-theoretic to model-theoretic proofs repeatedly, and to great advantage. This achieves an intuitive result that can be followed easily, even by readers with little background in logic and no background in nonmonotonic reasoning.

The frame problem is first described in some detail, and then the various (partial) solutions developed over the years are presented, in roughly chronological order. The final chapters describe the event calculus, which is Shanahan’s own contribution to the solution of the frame problem. This approach paints the picture of a living, evolving field of research, with insights, false starts, and more insights. In so doing, Shanahan presents the evolution of a typical subspecialty research field. Details aside, this story could apply to any number of scientific subdisciplines. Whether or not he fully intended to tell this story, it is fascinating to read.

I greatly enjoyed this book, and found it to be a satisfying treatment of a subject that is often either buried under unnecessary detail or discussed in a vague, hand-waving manner. By organizing the various solutions in a logical way and casting them all into the same formalism, he has done a service to this field of research. I highly recommend this book to readers interested in AI, nonmonotonic reasoning, and representational issues in general.