The author argues that deduction is a central aspect of cognition, by giving evidence that principles such as modus ponens underlie several deductive abilities. This idea, called the deduction-system hypothesis, is developed and tested in the book.

The book is subdivided into 11 chapters, organized in three parts. The first part (three chapters) gives the background and introduces the psychological theory of deductive reasoning. Knowledge of deduction is presented, taking into account different points of view. Chapter 1 introduces deduction from the point of view of psychology. The main ideas of the aspects of logic that play an important role in the debate on reasoning are analyzed in chapter 2. Chapter3 focuses on automated reasoning and its relations to human thinking.

The second part (four chapters) aims to build a theory of deductive reasoning in ordinary people. The author uses the expression “ordinary people” to refer to people without specific preparation in formal methods. The theory, based on natural deduction systems, introduces the concepts of mental proof and mental inference rule. The theory is built starting from a computational model, called PSYCOP, that can generate mental proofs for problems in sentential reasoning. PSYCOP is described in chapter 4, and experiments with the model are discussed in chapter 5. Chapters 6 and 7 discuss the generality of the model, by showing that it is also applicable to reasoning with quantified variables.

The third part discusses the advantages of a cognitive theory based on deduction, and shows the usefulness of PSYCOP to provide such a model for cognitive processes. Examples of PSYCOP’s performance in dealing with cognitive tasks are given in chapter 8. Other theories regarding psychology of reasoning are discussed in chapters 9 (on rule-based systems) and 10 (on a ruleless approach). Chapter 11 analyzes some of the most controversial aspects of deduction-based cognitive theories.

The theory presented in the book is interesting, is based on experiments on a wide range of cognitive tasks, and avails itself of results from different fields. The book is well written and documented. Connections among formal reasoning, human thinking, and automatic theorem proving are analyzed in depth, and their peculiarities are clearly pointed out.

The book is of interest for psychologists, mathematicians, and computer scientists. Moreover, it can be used for university courses oriented to psychology. In particular, the comparison of different approaches to deduction (computational, formal-logic-based, and psychological) is a valuable educational tool for introducing people to the field.

Finally, the subject considered is relevant not only from the research point of view but also for its educational implications. As the author points out in the preface, the problem of the development of deductive reasoning in children is not addressed. Some consideration of this theme would improve the reader’s understanding of the analysis of adults’ reasoning, on which the book focuses.