Outstanding Contributions to Logic

Leo Esakia on Duality in Modal and Intuitionistic Logics

Editors: Bezhanishvili, Guram (Ed.)

  • Offers an overview and analysis of Leo Esakia’s contributions to the theory of modal and intuitionistic systems
  • Explores a wide range of Esakia’s work in the area with explanations and analyses by leading experts in the field
  • Traces Esakia’s lifelong work in the field from its beginnings in the 1960s to the 2000s
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eBook $139.00
price for USA (gross)
  • ISBN 978-94-017-8860-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-94-017-8859-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 11, 2016
  • ISBN 978-94-024-0338-1
  • Free shipping for individuals worldwide
About this book

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area.

Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.

Reviews

“All chapters of the collection pay tribute to L. Esakia’s outstanding technical work, which inspired greatly several researchers, not only in Georgia but also all over the world, to carry out extensive and deep investigations on modal and intuitionistic logics. For this reason, the volume under review is necessary reading for anyone interested in Esakia’s contributions, as well as the current state of the large area in which he conducted his research.” (Costas Dimitracopoulos, Metascience, Vol. 24, 2015)

“This is a good book on algebras and set theories of intuitionistic and modal logics. … This a very good book for logicians and mathematics scholars.” (Joseph J. Grenier, Amazon.com, June, 2014)

Table of contents (11 chapters)

  • Esakia’s Biography and Bibliography

    Bezhanishvili, Guram

    Pages 1-7

  • Canonical Extensions, Esakia Spaces, and Universal Models

    Gehrke, Mai

    Pages 9-41

  • Free Modal Algebras Revisited: The Step-by-Step Method

    Bezhanishvili, Nick (et al.)

    Pages 43-62

  • Easkia Duality and Its Extensions

    Celani, Sergio A. (et al.)

    Pages 63-98

  • On the Blok-Esakia Theorem

    Wolter, Frank (et al.)

    Pages 99-118

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-94-017-8860-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-94-017-8859-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 11, 2016
  • ISBN 978-94-024-0338-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Leo Esakia on Duality in Modal and Intuitionistic Logics
Editors
  • Guram Bezhanishvili
Series Title
Outstanding Contributions to Logic
Series Volume
4
Copyright
2014
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-8860-1
DOI
10.1007/978-94-017-8860-1
Hardcover ISBN
978-94-017-8859-5
Softcover ISBN
978-94-024-0338-1
Series ISSN
2211-2758
Edition Number
1
Number of Pages
XIII, 334
Number of Illustrations and Tables
44 b/w illustrations
Topics