College Publications. Series: Texts in Computing, vol 5. ISBN 1-904987-00-1. Published February 2005. Paperback.

#### From the Preface

From the outside, nonmonotonic logic is often seen as a rather mysterious affair. Even from the inside, it can appear to lack unity, with multiple systems proposed by as many authors going in different directions. The few available textbooks tend to perpetuate this impression.

The purpose of this book is to take some of the mystery out of the subject and show that it is not as unfamiliar as may at first sight seem. In fact, it is easily accessible to anybody with a minimal background in classical propositional logic and a few basic mathematical tools - provided certain misunderstandings and a tenacious habit are put aside.

The text shows that there are logics that act as natural bridges between classical consequence and the principal kinds of nonmonotonic logic to be found in the literature. These bridge systems, which are called 'paraclassical' logics, are very simple to define and easy to study. They provide three main ways of getting more out of your premises than is allowed by strict deduction, that is, by good old classical consequence. In other words, they are principled ways of creeping, crawling or jumping to conclusions. Like classical logic, they are perfectly monotonic, but they already display some of the distinctive features of the nonmonotonic systems that they prefigure, as well as providing easy conceptual passage to them. They give us, in effect, three main paths from the classical homeland to nonmonotonic shores.

The book examines the three bridges one by one. It begins with the simplest among them, whose moving idea is to use additional background assumptions along with current premises. Then it considers ways of getting similar results by excluding certain classical valuations, and a third means to the same end, adding rules alongside the premises. Each of these three procedures permit us to pass from classical consequence to paraclassical consequence relations, which are supraclassical but still monotonic; then in turn, by a further twist of relativization, to the principal kinds of nonmonotonic consequence.

Two final chapters serve to locate nonmonotonic reasoning in a wider landscape. One dissects the subtle relations between classical logic, probabilistic inference, and nonmonotonic reasoning. The other discusses links and residual differences between nonmonotonic inference on the one hand and other kinds of belief management on the other hand: belief revision, update, counterfactual conditionals, and conditional directives.

The text is written for the student in a classroom and the instructor teaching a course, as well as for the solitary reader. It provides recapitulations at the end of each chapter, exercises and problems, selected solutions to them, suggested projects, and guides to further reading.

Sydney Harbour Bridge viewed from Balmain Point

Available from Amazon.co.uk.

Polish translation, by Tomasz Jarmuzek, published in 2008, in pdf here.

Reviews

In Zentralblatt f. Math 2006:1084.03001 by Neculai Curteanu

In Bull. Symb. Logic 2006 vol 12 2006 499-502 by Hykel Hosni.

In Theoria vol 72 2006 336-340 by Heinrich Wansing

In Mathematical Reviews  MR2170233 (2007b:03001) 03-02 by Giovanni Criscuolo

In Logic and Logical Philosophy vol 16 2007 by Tomasz Jarmuzek

In Studia Logica vol 89 2008 437-439 by Choh Man Teng