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Proof and Disproof in Formal Logic

An Introduction for programmers

Richard Bornat

Oxford Texts in Logic 2

264 pages | numerous line drawings and mathematical examples | 240x168mm

978-0-19-853027-5 | Paperback | 21 July 2005

Also available as: Hardback laminated boards

Price: £43.00

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There are many textbooks on logic aimed at philosophers but few cover the basics of formal logic for computer scientists and mathematicians, which is an important and growing area. This book will be an interesting and unrivalled addition to the field.
Lively and entertaining introduction to formal logic with comprehensive coverage of the basics
Suitable for students of logic, computer science, mathematics, and philosophy
Contains numerous exercises based on Jape - an interactive teaching and research tool designed and hosted by the author that is freely available on the web

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system--a collection of rules and axioms which define a universe of logical proofs--is what gives us programming languages and modern-day programming.

This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses--natural deduction--is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations.

The book is divided into four parts:
· Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words.
· Part II "Formal syntactic proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle.
· Part III "Formal semantic disproof" shows you how to construct mathematical counterexamples to show that proof is impossible. Jape can check the counterexamples you build.
· Part IV "Program specification and proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows.

Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.

Readership: Undergraduates and graduates in logic, computer science, mathematics, and philosophy seeking a comprehensive introduction to formal logic through proof and disproof.

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