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Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena [Mīkstie vāki]

(Indiana University), (Indiana University)
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Vicious Circles: On the Mathematics of Non-Wellfounded PhenomenaPalielināt
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Permanent link: https://www.kriso.lv/db/9781575860084.html
Keywords:
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.

Vicious Circles is intended for researchers who use hypersets but is accessible to people of differing backgrounds.

Recenzijas

' ... a book to learn from.' L'Enseignement Mathématique

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.