Vicious circles : on the mathematics of non-wellfounded phenomena
Author(s)
Bibliographic Information
Vicious circles : on the mathematics of non-wellfounded phenomena
（CSLI lecture notes, no. 60）
CSLI Publications, c1996
- : pbk
Available at / 46 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: pbk511.3/B2892070401951
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Note
Includes bibliography (p. 381-384) and index (p. 385-390)
Description and Table of Contents
Description
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.
Table of Contents
- 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.
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