Editors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Outstanding Contributions to Logic (OCTR, volume 4)
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Table of contents (11 chapters)
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Front Matter
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.
Keywords
- Blok-Esakia theorem
- Canonical extensions, Esakia spaces, universal models
- Constructive modalities with provability smack
- Easkia duality and its extensions
- Esakia and modal and intuitionistic systems
- Esakia duality for Heyting algebras
- Esakia duality for S4-algebras
- Free modal algebras
- Modal logic and Vietoris functor
- Topological interpretations of provability logic
- derivational semantics of modal logic
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)Editors and Affiliations
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New Mexico State University, Las Cruces, USA
Guram Bezhanishvili
Bibliographic Information
Book Title: Leo Esakia on Duality in Modal and Intuitionistic Logics
Editors: Guram Bezhanishvili
Series Title: Outstanding Contributions to Logic
DOI: https://doi.org/10.1007/978-94-017-8860-1
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2014
Hardcover ISBN: 978-94-017-8859-5Published: 20 June 2014
Softcover ISBN: 978-94-024-0338-1Published: 27 September 2016
eBook ISBN: 978-94-017-8860-1Published: 03 June 2014
Series ISSN: 2211-2758
Series E-ISSN: 2211-2766
Edition Number: 1
Number of Pages: XIII, 334
Number of Illustrations: 44 b/w illustrations
Topics: Logic, Mathematical Logic and Formal Languages, Theoretical Linguistics