Vicious Circles - Couverture souple

Barwise, Jon; Moss, Lawrence S.

Couverture souple

ISBN 10 : 1575860082 ISBN 13 : 9781575860084

Editeur : Center for the Study of Language and Inf, 2004

Synopsis

Circular analyses of philosophical, linguistic, or computational phenomena have been attacked on the assumption that they conflict with mathematical rigour. Barwise and Moss have undertaken to prove this assumption false. This volume is concerned with extending the modelling capabilities of set theory to provide a uniform treatment of circular phenomena. As a means of guiding the reader through the concrete examples of the theory, the authors have included many exercises and solutions: these exercises range in difficulty and ultimately stimulate the reader to come up with new results. Vicious Circles is intended for use by researchers who want to use hypersets; although some experience in mathematics is necessary, the book is accessible to people with widely differing backgrounds and interests.

A propos du livre

Présentation de l'éditeur :

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.

À propos de cette édition

• Éditeur: Center for the Study of Language and Inf
• Date d'édition: 2004
• ISBN 10: 1575860082
• ISBN 13: 9781575860084
• Reliure: Broché
• Nombre de pages: 400