Leo Esakia on Duality in Modal and Intuitionistic Logics

  • Guram Bezhanishvili

Part of the Outstanding Contributions to Logic book series (OCTR, volume 4)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Guram Bezhanishvili
    Pages 1-7
  3. Nick Bezhanishvili, Silvio Ghilardi, Mamuka Jibladze
    Pages 43-62
  4. Sergio A. Celani, Ramon Jansana
    Pages 63-98
  5. Frank Wolter, Michael Zakharyaschev
    Pages 99-118
  6. Yde Venema, Jacob Vosmaer
    Pages 119-153
  7. Alexei Muravitsky
    Pages 155-185
  8. Lev Beklemishev, David Gabelaia
    Pages 257-290
  9. Andrey Kudinov, Valentin Shehtman
    Pages 291-334

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.


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

Editors and affiliations

  • Guram Bezhanishvili
    • 1
  1. 1.New Mexico State UniversityLas CrucesUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media Dordrecht 2014
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-94-017-8859-5
  • Online ISBN 978-94-017-8860-1
  • Series Print ISSN 2211-2758
  • Series Online ISSN 2211-2766
  • Buy this book on publisher's site