Logic is a basic tool not only in computer science but in all sciences and philosophy. Students and computer scientists need to grasp the basic ideas behind logic so that they can use all their power in developing new hardware and software. Anita Wasilewska has written an elementary book on nearly all types of logic that can be also addressed to mathematicians and logicians.

*Logics for Computer Science Classical and Non-Classical* is a self-contained book that builds logic from scratch. Readers need no special knowledge of either logic or mathematics though having followed some introductory logic course will make reading the book easier.

After a short introduction to logical paradoxes and computer puzzles, in an attempt to relate the two subjects: computer science and logic, Wasilewska goes on to construct propositional logic starting from defining a language, an atomic proposition, formulae, truth values, the classical connectives, classical and many valued semantic, she uses this structure to later build first-order predicate, many-valued, intuitionistic and modal logics.

The second topic discussed in this book is proof systems. including Gentzen style, Hilbert proof systems, consistency, relation between syntax and semantics, and the completeness theorems of Gödel and Hauptzatz.

This book is written in a very nice and easy to understand language. The definitions and theorems are usually well motivated and are later meticulously proved. Many of the examples and solved exercises illustrate the materiel under discussion and clear up any confusion that may arise. Each chapter ends with a set of nicely chosen homework problems that expand on the main text.

Wasilewska’s book is elementary in that it doesn’t go into model theory or very deep philosophical discussion of differences between classical and non-classical logics. The clarity and the step by step construction of the proofs is remarkable and this teaches students to be clear and meticulous in writing their answers to the homework problems.

Though the title indicates that the book is meant for computer science students, apart from the application of predicate logic to artificial intelligence in the second chapter, readers will not find any other applications and they will not see how these classical and non-classical logics are used in computer science. It is also rather unfortunate that fuzzy logic is not mentioned in the book. The book does not include a forward, references, or an index.

This book could be used as a textbook or reference book for a course on logic.

Salim Salem is a retired professor and Ex-head of the Department of Preparatory years at the Faculty of Engineering at Saint-Joseph University of Beirut.