Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo's axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Loewenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory. There are exercises within the text, set out alongside the theoretical ideas that they involve.

Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo's axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Loewenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory. There are exercises within the text, set out alongside the theoretical ideas that they involve.

Imagine a robot trying to size up a difficult situation, to find a way of responding. Its sensors receive streams of information from which it tries to reach judgements. If it relies on deduction alone, it will not get far, no matter how fast its inference engines; for even the most massive information is still typically incomplete: there are relevant issues that it does not resolve one way or the other. The robot, or human agent for that matter, needs to go beyond these limits. It needs to go supraclassical', inferring more than is authorised by classical logic alone. But such inferences are inherently uncertain. They are also nonmonotonic, in the sense that the acquisition of further information, even when consistent with the existing stock, may lead us to abondon as well as add conclusions. Nonmonotonic logic is the study of such reasoning and has been the subject of intensive research for more than two decades. But for the newcomer it is still a disconcerting affair, lacking unity with many systems going in different directions. The purpose of this book is to take the mystery out of the subject, giving a clear overall picture of what is going on. It makes the essential ideas and main approaches to nonmonotonic logic accessible, and meaningful, to anyone with a few basic tools of discrete mathematics and a minimal background in classical propositional logic. It is written as a textbook, with detailed explanations, examples, comments, exercises and answers. Students and instructors alike will find it an invaluable guide.