Vicious Circles

On the Mathematics of Non-Wellfounded Phenomena
Centre for the Study of Language & Information (Verlag)
  • erschienen am 30. Juni 1996
  • Buch
  • |
  • Hardcover
  • |
  • 400 Seiten
978-1-57586-009-1 (ISBN)
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.
  • Englisch
  • New York
  • |
  • USA
  • Für Beruf und Forschung
  • Höhe: 237 mm
  • |
  • Breite: 160 mm
  • |
  • Dicke: 35 mm
  • 726 gr
978-1-57586-009-1 (9781575860091)
1575860090 (1575860090)
Jon Barwise (1942 2000) was professor of philosophy, mathematics, and computer science at Indiana University and one of the founding members of the Center for the Study of Language and Information (CSLI).
Part I. Background: 1. Introduction; 2. Background on set theory; Part II. Vicious Circles: 3. Circularity in computer science; 4. Circularity in philosophy; 5. Circularity and paradox; Part III. Basic Theory: 6. The solution dilemma; 7. Bisimulation; Part IV. Elementary applications: 8. Graphs; 9. Modal logic; 10. Streams; 11. Games; 12. Modeling the semantic paradoxes; Part V. Further Theory: 13. Greatest fixed points; 14. Uniform operators; 15. Corecursion; Part VI. Further Applications: 16. Some applications; 17. Modeling partial information; 18. Circularity and the notion of set; 19. Conclusions and future directions.
' ... a book to learn from.' L'Enseignement Mathematique

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