This book is about computer programs that can perform automated reasoning. I interpret ‘reasoning’ quite narrowly: the emphasis is on formal deductive inference rather than, for example, poker playing or medical diagnosis. On the other hand I interpret ‘automated’ broadly, to include interactive arrangements where a human being and machine reason together, and I'm always conscious of the applications of deductive reasoning to real world problems. Indeed, as well as being inherently fascinating, the subject is deriving increasing importance from its industrial applications.

This book is intended as a first introduction to the field, and also to logical reasoning itself. No previous knowledge of mathematical logic is assumed, although readers will inevitably find some prior experience of mathematics and of computer programming (especially in a functional language like OCaml, F#, Standard ML, Haskell or LISP) invaluable. In contrast to the many specialist texts on the subject, this book aims at a broad and balanced general introduction, and has two special characteristics.

• Pure logic and automated theorem proving are explained in a closely intertwined manner. Results in logic are developed with an eye to their role in automated theorem proving, and wherever possible are developed in an explicitly computational way.

• Automated theorem proving methods are explained with reference to actual concrete implementations, which readers can experiment with if they have convenient access to a computer. All code is written in the high-level functional language OCaml.

Although this organization is open to question, I adopted it after careful consideration, and extensive experimentation with alternatives. A more detailed self-justification follows, but most readers will want to skip straight to the main content, starting with ‘How to read this book’ on page xvi.