A classic treatment of two-valued iterative systems of mathematical logic from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

The description for this book, The Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5, will be forthcoming.

This book constitutes the refereed proceedings of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR 2007, held in Tempe, AZ, USA, May 2007. This conference encompasses theoretical studies, design and implementation of logic based programming languages and database systems, and development of experimental systems.

In today’s world, people are using more and more digital systems in daily life. Such systems utilize the elementariness of Boolean values. A Boolean variable can carry only two different Boolean values: FALSE or TRUE (0 or 1), and has the best interference resistance in technical systems. However, a Boolean function exponentially depends on the number of its variables. This exponential complexity is the cause of major problems in the process of design and realization of circuits. According to Moore’s Law, the complexity of digital systems approximately doubles every 18 months. This requires comprehensive knowledge and techniques to solve very complex Boolean problems. This book summarizes the recent progress in the Boolean domain in solving such issues. Part 1 describes the most powerful approaches in solving exceptionally complex Boolean problems. It is shown how an extremely rare solution could be found in a gigantic search space of more than 10^195 (this is a number of 196 decimal digits) different color patterns. Part 2 describes new research into digital circuits that realize Boolean functions. This part contains the chapters “Design” and “Test”, which present solutions to problems of power dissipation, and the testing of digital circuits using a special data structure, as well as further topics. Part 3 contributes to the scientific basis of future circuit technologies, investigating the need for completely new design methods for the atomic level of quantum computers. This section also concerns itself with circuit structures in reversible logic as the basis for quantum logic.

The popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical!) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.