Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena (CSLI Lecture Notes)

Moss, Lawrence S.,Barwise, Jon

ISBN 10: 1575860082 / ISBN 13: 9781575860084

Published by Center for the Study of Language, 1996

About this Item

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Bibliographic Details

• Title: Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena (CSLI Lecture Notes)
• Publisher: Center for the Study of Language
• Publication Date: 1996
• Language: English
• ISBN 10: 1575860082
• ISBN 13: 9781575860084
• Binding: Paperback
• Condition: Good

About this title

Synopsis

The subject of non-wellfounded sets came to prominence with the 1988 publication of Peter Aczel's book on the subject. Since then, a number of researchers in widely differing fields have used non-wellfounded sets (also called "hypersets") in modeling many types of circular phenomena. The application areas range from knowledge representation and theoretical economics to the semantics of natural language and programming languages. Vicious Circles offers an introduction to this fascinating and timely topic. Written as a book to learn from, theoretical points are always illustrated by examples from the applications and by exercises whose solutions are also presented. The text is suitable for use in a classroom, seminar, or for individual study. In addition to presenting the basic material on hypersets and their applications, this volume thoroughly develops the mathematics behind solving systems of set equations, greatest fixed points, coinduction, and corecursion. Much of this material has not appeared before. The application chapters also contain new material on modal logic and new explorations of paradoxes from semantics and game theory.

About the Author

Lawrence S. Moss is professor of mathematics; director of the Program in Pure and Applied Logic; an adjunct professor of computer science, informatics, linguistics, and philosophy; and a member of the Programs in Cognitive Science and Computational Linguistics, all at Indiana University, Bloomington.