The second chapter introduces the sequent calculus, a method of making sound deductions in second-order logic, and its incompleteness.
[3] Although the book is intended as a textbook for advanced undergraduates or beginning graduate students,[1] reviewer Mohamed Amer suggests that it does not have enough exercises to support a course in its subject, and that some of its proofs are lacking in detail.
[2] Reviewer Hans Jürgen Ohlbach suggests that it would be more usable as a reference than a textbook, and states that "it is certainly not suitable for undergraduates".
[4] Reviewer Yde Venema wonders how much of the logical power and useful properties of the various systems treated in this book have been lost in the translation to many-sorted logic, worries about the jump in computational complexity of automated theorem proving caused by the translation, complains about the book's clarity of exposition becoming lost in case analysis, and was disappointed at the lack of coverage of Montague grammar, fixed-point logic, and non-monotonic logic.
[1] And reviewer B. Boričić calls it "nice and clearly written", "an appropriate introduction and reference", recommending it to researchers in several disciplines (mathematics, computer science, linguistics, and philosophy) where advanced forms of logic are important.